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href="#Reporting_large_ratios"> <div class="vector-toc-text"> 3.1 Reporting large ratios </div> </a> <ul id="toc-Reporting_large_ratios-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Representation_of_multiplication_operations" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Representation_of_multiplication_operations"> <div class="vector-toc-text"> 3.2 Representation of multiplication operations </div> </a> <ul id="toc-Representation_of_multiplication_operations-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Representation_of_addition_operations" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Representation_of_addition_operations"> <div class="vector-toc-text"> 3.3 Representation of addition operations </div> </a> <ul id="toc-Representation_of_addition_operations-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Fractions" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Fractions"> <div class="vector-toc-text"> 3.4 Fractions </div> </a> <ul id="toc-Fractions-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Uses" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Uses"> <div class="vector-toc-text"> 4 Uses </div> </a> <button aria-controls="toc-Uses-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle Uses subsection </button> <ul id="toc-Uses-sublist" class="vector-toc-list"> <li id="toc-Perception" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Perception"> <div class="vector-toc-text"> 4.1 Perception </div> </a> <ul id="toc-Perception-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Acoustics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Acoustics"> <div class="vector-toc-text"> 4.2 Acoustics </div> </a> <ul id="toc-Acoustics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Telephony" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Telephony"> <div class="vector-toc-text"> 4.3 Telephony </div> </a> <ul id="toc-Telephony-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Electronics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Electronics"> <div class="vector-toc-text"> 4.4 Electronics </div> </a> <ul id="toc-Electronics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Optics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Optics"> <div class="vector-toc-text"> 4.5 Optics </div> </a> <ul id="toc-Optics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Video_and_digital_imaging" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Video_and_digital_imaging"> <div class="vector-toc-text"> 4.6 Video and digital imaging </div> </a> <ul id="toc-Video_and_digital_imaging-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Suffixes_and_reference_values" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Suffixes_and_reference_values"> <div class="vector-toc-text"> 5 Suffixes and reference values </div> </a> <ul id="toc-Suffixes_and_reference_values-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-List_of_suffixes" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#List_of_suffixes"> <div class="vector-toc-text"> 6 List of suffixes </div> </a> <button aria-controls="toc-List_of_suffixes-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle List of suffixes subsection </button> <ul id="toc-List_of_suffixes-sublist" class="vector-toc-list"> <li id="toc-Voltage" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Voltage"> <div class="vector-toc-text"> 6.1 Voltage </div> </a> <ul id="toc-Voltage-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Acoustics_2" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Acoustics_2"> <div class="vector-toc-text"> 6.2 Acoustics </div> </a> <ul id="toc-Acoustics_2-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Audio_electronics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Audio_electronics"> <div class="vector-toc-text"> 6.3 Audio electronics </div> </a> <ul id="toc-Audio_electronics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Radar" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Radar"> <div class="vector-toc-text"> 6.4 Radar </div> </a> <ul id="toc-Radar-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Radio_power,_energy,_and_field_strength" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Radio_power,_energy,_and_field_strength"> <div class="vector-toc-text"> 6.5 Radio power, energy, and field strength </div> </a> <ul id="toc-Radio_power,_energy,_and_field_strength-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Antenna_measurements" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Antenna_measurements"> <div class="vector-toc-text"> 6.6 Antenna measurements </div> </a> <ul id="toc-Antenna_measurements-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Other_measurements" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Other_measurements"> <div class="vector-toc-text"> 6.7 Other measurements </div> </a> <ul id="toc-Other_measurements-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-List_of_suffixes_in_alphabetical_order" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#List_of_suffixes_in_alphabetical_order"> <div class="vector-toc-text"> 6.8 List of suffixes in alphabetical order </div> </a> <ul id="toc-List_of_suffixes_in_alphabetical_order-sublist" class="vector-toc-list"> <li id="toc-Unpunctuated_suffixes" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Unpunctuated_suffixes"> <div class="vector-toc-text"> 6.8.1 Unpunctuated suffixes </div> </a> <ul id="toc-Unpunctuated_suffixes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Suffixes_preceded_by_a_space" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Suffixes_preceded_by_a_space"> <div class="vector-toc-text"> 6.8.2 Suffixes preceded by a space </div> </a> <ul id="toc-Suffixes_preceded_by_a_space-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Suffixes_within_parentheses" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Suffixes_within_parentheses"> <div class="vector-toc-text"> 6.8.3 Suffixes within parentheses </div> </a> <ul id="toc-Suffixes_within_parentheses-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Other_suffixes" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Other_suffixes"> <div class="vector-toc-text"> 6.8.4 Other suffixes </div> </a> <ul id="toc-Other_suffixes-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> 7 See also </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> 8 Notes </div> </a> <ul id="toc-Notes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> 9 References </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> 10 Further reading </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> 11 External links </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Table of Contents" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" > Toggle the table of contents </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading">Decibel</h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 66 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-66" aria-hidden="true" > 66 languages </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AF%D9%8A%D8%B3%D9%8A%D8%A8%D9%84" title="ديسيبل – Arabic" lang="ar" hreflang="ar" data-title="ديسيبل" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target">العربية</a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Decibeliu" title="Decibeliu – Asturian" lang="ast" hreflang="ast" data-title="Decibeliu" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target">Asturianu</a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Desibel" title="Desibel – Azerbaijani" lang="az" hreflang="az" data-title="Desibel" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target">Azərbaycanca</a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%A1%E0%A7%87%E0%A6%B8%E0%A6%BF%E0%A6%AC%E0%A7%87%E0%A6%B2" title="ডেসিবেল – Bangla" lang="bn" hreflang="bn" data-title="ডেসিবেল" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target">বাংলা</a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%94%D0%B5%D1%86%D0%B8%D0%B1%D0%B5%D0%BB" title="Децибел – Bulgarian" lang="bg" hreflang="bg" data-title="Децибел" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target">Български</a></li><li class="interlanguage-link interwiki-bo mw-list-item"><a href="https://bo.wikipedia.org/wiki/%E0%BD%91%E0%BD%BA%E0%BC%8B%E0%BD%A6%E0%BE%A6%E0%BD%BA%E0%BD%A3%E0%BC%8D" title="དེ་སྦེལ། – Tibetan" lang="bo" hreflang="bo" data-title="དེ་སྦེལ།" data-language-autonym="བོད་ཡིག" data-language-local-name="Tibetan" class="interlanguage-link-target">བོད་ཡིག</a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Decibel" title="Decibel – Catalan" lang="ca" hreflang="ca" data-title="Decibel" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target">Català</a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%94%D0%B5%D1%86%D0%B8%D0%B1%D0%B5%D0%BB" title="Децибел – Chuvash" lang="cv" hreflang="cv" data-title="Децибел" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target">Чӑвашла</a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Decibel" title="Decibel – Czech" lang="cs" hreflang="cs" data-title="Decibel" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target">Čeština</a></li><li class="interlanguage-link interwiki-de badge-Q70894304 mw-list-item" title=""><a href="https://de.wikipedia.org/wiki/Dezibel" title="Dezibel – German" lang="de" hreflang="de" data-title="Dezibel" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target">Deutsch</a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Detsibell" title="Detsibell – Estonian" lang="et" hreflang="et" data-title="Detsibell" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target">Eesti</a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9D%CF%84%CE%B5%CF%83%CE%B9%CE%BC%CF%80%CE%AD%CE%BB" title="Ντεσιμπέλ – Greek" lang="el" hreflang="el" data-title="Ντεσιμπέλ" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target">Ελληνικά</a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Decibelio" title="Decibelio – Spanish" lang="es" hreflang="es" data-title="Decibelio" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target">Español</a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Decibelo" title="Decibelo – Esperanto" lang="eo" hreflang="eo" data-title="Decibelo" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target">Esperanto</a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Dezibel" title="Dezibel – Basque" lang="eu" hreflang="eu" data-title="Dezibel" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target">Euskara</a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AF%D8%B3%DB%8C%E2%80%8C%D8%A8%D9%84" title="دسی‌بل – Persian" lang="fa" hreflang="fa" data-title="دسی‌بل" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target">فارسی</a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/D%C3%A9cibel" title="Décibel – French" lang="fr" hreflang="fr" data-title="Décibel" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target">Français</a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Deicibeil" title="Deicibeil – Irish" lang="ga" hreflang="ga" data-title="Deicibeil" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target">Gaeilge</a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Decibel" title="Decibel – Galician" lang="gl" hreflang="gl" data-title="Decibel" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target">Galego</a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%8D%B0%EC%8B%9C%EB%B2%A8" title="데시벨 – Korean" lang="ko" hreflang="ko" data-title="데시벨" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target">한국어</a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B4%D5%A5%D6%81%D5%AB%D5%A2%D5%A5%D5%AC" title="Դեցիբել – Armenian" lang="hy" hreflang="hy" data-title="Դեցիբել" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target">Հայերեն</a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%A1%E0%A5%87%E0%A4%B8%E0%A5%80%E0%A4%AC%E0%A5%87%E0%A4%B2" title="डेसीबेल – Hindi" lang="hi" hreflang="hi" data-title="डेसीबेल" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target">हिन्दी</a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Decibel" title="Decibel – Croatian" lang="hr" hreflang="hr" data-title="Decibel" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target">Hrvatski</a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Desibel" title="Desibel – Indonesian" lang="id" hreflang="id" data-title="Desibel" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target">Bahasa Indonesia</a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Des%C3%ADbel" title="Desíbel – Icelandic" lang="is" hreflang="is" data-title="Desíbel" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target">Íslenska</a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Decibel" title="Decibel – Italian" lang="it" hreflang="it" data-title="Decibel" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target">Italiano</a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%93%D7%A6%D7%99%D7%91%D7%9C" title="דציבל – Hebrew" lang="he" hreflang="he" data-title="דציבל" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target">עברית</a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%93%E1%83%94%E1%83%AA%E1%83%98%E1%83%91%E1%83%94%E1%83%9A%E1%83%98" title="დეციბელი – Georgian" lang="ka" hreflang="ka" data-title="დეციბელი" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target">ქართული</a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%94%D0%B5%D1%86%D0%B8%D0%B1%D0%B5%D0%BB" title="Децибел – Kazakh" lang="kk" hreflang="kk" data-title="Децибел" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target">Қазақша</a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Desibeli" title="Desibeli – Swahili" lang="sw" hreflang="sw" data-title="Desibeli" data-language-autonym="Kiswahili" data-language-local-name="Swahili" class="interlanguage-link-target">Kiswahili</a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Desib%C3%A8l" title="Desibèl – Haitian Creole" lang="ht" hreflang="ht" data-title="Desibèl" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitian Creole" class="interlanguage-link-target">Kreyòl ayisyen</a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Decibel" title="Decibel – Latin" lang="la" hreflang="la" data-title="Decibel" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target">Latina</a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Decibels" title="Decibels – Latvian" lang="lv" hreflang="lv" data-title="Decibels" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target">Latviešu</a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Decibelas" title="Decibelas – Lithuanian" lang="lt" hreflang="lt" data-title="Decibelas" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target">Lietuvių</a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Decibel" title="Decibel – Lombard" lang="lmo" hreflang="lmo" data-title="Decibel" data-language-autonym="Lombard" data-language-local-name="Lombard" class="interlanguage-link-target">Lombard</a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Decibel" title="Decibel – Hungarian" lang="hu" hreflang="hu" data-title="Decibel" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target">Magyar</a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%94%D0%B5%D1%86%D0%B8%D0%B1%D0%B5%D0%BB" title="Децибел – Macedonian" lang="mk" hreflang="mk" data-title="Децибел" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target">Македонски</a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%A1%E0%B5%86%E0%B4%B8%E0%B4%BF%E0%B4%AC%E0%B5%86%E0%B5%BD" title="ഡെസിബെൽ – Malayalam" lang="ml" hreflang="ml" data-title="ഡെസിബെൽ" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target">മലയാളം</a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Desibel" title="Desibel – Malay" lang="ms" hreflang="ms" data-title="Desibel" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target">Bahasa Melayu</a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Decibel_(eenheid)" title="Decibel (eenheid) – Dutch" lang="nl" hreflang="nl" data-title="Decibel (eenheid)" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target">Nederlands</a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%87%E3%82%B7%E3%83%99%E3%83%AB" title="デシベル – Japanese" lang="ja" hreflang="ja" data-title="デシベル" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target">日本語</a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Desibel" title="Desibel – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Desibel" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target">Norsk bokmål</a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Desibel" title="Desibel – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Desibel" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target">Norsk nynorsk</a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Decib%C3%A8l" title="Decibèl – Occitan" lang="oc" hreflang="oc" data-title="Decibèl" data-language-autonym="Occitan" data-language-local-name="Occitan" class="interlanguage-link-target">Occitan</a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Detsibel" title="Detsibel – Uzbek" lang="uz" hreflang="uz" data-title="Detsibel" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target">Oʻzbekcha / ўзбекча</a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Decybel" title="Decybel – Polish" lang="pl" hreflang="pl" data-title="Decybel" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target">Polski</a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Decibel" title="Decibel – Portuguese" lang="pt" hreflang="pt" data-title="Decibel" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target">Português</a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Decibel" title="Decibel – Romanian" lang="ro" hreflang="ro" data-title="Decibel" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target">Română</a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%94%D0%B5%D1%86%D0%B8%D0%B1%D0%B5%D0%BB" title="Децибел – Russian" lang="ru" hreflang="ru" data-title="Децибел" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target">Русский</a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Decibeli" title="Decibeli – Albanian" lang="sq" hreflang="sq" data-title="Decibeli" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target">Shqip</a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Decibel" title="Decibel – Simple English" lang="en-simple" hreflang="en-simple" data-title="Decibel" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target">Simple English</a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Decibel" title="Decibel – Slovenian" lang="sl" hreflang="sl" data-title="Decibel" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target">Slovenščina</a></li><li class="interlanguage-link interwiki-so mw-list-item"><a href="https://so.wikipedia.org/wiki/Dhesibel" title="Dhesibel – Somali" lang="so" hreflang="so" data-title="Dhesibel" data-language-autonym="Soomaaliga" data-language-local-name="Somali" class="interlanguage-link-target">Soomaaliga</a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/Decibel" title="Decibel – Serbian" lang="sr" hreflang="sr" data-title="Decibel" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target">Српски / srpski</a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Decibel" title="Decibel – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Decibel" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target">Srpskohrvatski / српскохрватски</a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Desibeli" title="Desibeli – Finnish" lang="fi" hreflang="fi" data-title="Desibeli" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target">Suomi</a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Decibel" title="Decibel – Swedish" lang="sv" hreflang="sv" data-title="Decibel" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target">Svenska</a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%9F%E0%AF%86%E0%AE%9A%E0%AE%BF%E0%AE%AA%E0%AF%86%E0%AE%B2%E0%AF%8D" title="டெசிபெல் – Tamil" lang="ta" hreflang="ta" data-title="டெசிபெல்" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target">தமிழ்</a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%A1%E0%B1%86%E0%B0%B8%E0%B0%BF%E0%B0%AC%E0%B1%86%E0%B0%B2%E0%B1%8D" title="డెసిబెల్ – Telugu" lang="te" hreflang="te" data-title="డెసిబెల్" data-language-autonym="తెలుగు" data-language-local-name="Telugu" class="interlanguage-link-target">తెలుగు</a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B9%80%E0%B8%94%E0%B8%8B%E0%B8%B4%E0%B9%80%E0%B8%9A%E0%B8%A5" title="เดซิเบล – Thai" lang="th" hreflang="th" data-title="เดซิเบล" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target">ไทย</a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Desibel" title="Desibel – Turkish" lang="tr" hreflang="tr" data-title="Desibel" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target">Türkçe</a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%94%D0%B5%D1%86%D0%B8%D0%B1%D0%B5%D0%BB" title="Децибел – Ukrainian" lang="uk" hreflang="uk" data-title="Децибел" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target">Українська</a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Decibel" title="Decibel – Vietnamese" lang="vi" hreflang="vi" data-title="Decibel" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target">Tiếng Việt</a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%88%86%E8%B4%9D" title="分贝 – Wu" lang="wuu" hreflang="wuu" data-title="分贝" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target">吴语</a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%88%86%E8%B2%9D" title="分貝 – Cantonese" lang="yue" hreflang="yue" data-title="分貝" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target">粵語</a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%88%86%E8%B2%9D" title="分貝 – Chinese" lang="zh" hreflang="zh" data-title="分貝" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target">中文</a></li> </ul> <div class="after-portlet after-portlet-lang"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q5329#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namespaces"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul 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class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Logarithmic unit expressing the ratio of physical quantities</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">This article is about the logarithmic unit. For use of this unit in <a href="/wiki/Sound" title="Sound">sound</a> measurements, see <a href="/wiki/Sound_pressure_level" class="mw-redirect" title="Sound pressure level">Sound pressure level</a>. For other uses, see <a href="/wiki/Decibel_(disambiguation)" class="mw-disambig" title="Decibel (disambiguation)">Decibel (disambiguation)</a>.</div> <style data-mw-deduplicate="TemplateStyles:r1257001546">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox ib-unit"><tbody><tr><th colspan="2" class="infobox-above">decibel</th></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/System_of_units_of_measurement" title="System of units of measurement">Unit system</a></th><td class="infobox-data"><a href="/wiki/Non-SI_units_mentioned_in_the_SI" title="Non-SI units mentioned in the SI">Non-SI accepted unit</a></td></tr><tr><th scope="row" class="infobox-label">Symbol</th><td class="infobox-data">dB</td></tr><tr><th scope="row" class="infobox-label">Named after</th><td class="infobox-data"><a href="/wiki/Alexander_Graham_Bell" title="Alexander Graham Bell">Alexander Graham Bell</a></td></tr><tr><th colspan="2" class="infobox-header">Conversions </th></tr><tr class="nowrap"><td>1 dB in ...</td><td>... is equal to ...</td></tr><tr style="display:none"><th colspan="2"> </th></tr><tr><th scope="row" class="infobox-label">   bel</th><td class="infobox-data">   <style data-mw-deduplicate="TemplateStyles:r1214402035">.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num{display:block;line-height:1em;margin:0.0em 0.1em;border-bottom:1px solid}.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0.1em 0.1em}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style>⁠1/10⁠ bel</td></tr></tbody></table><style data-mw-deduplicate="TemplateStyles:r1236303919">@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-has-images-with-white-backgrounds img{background:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-has-images-with-white-backgrounds img{background:white}}</style> The decibel (symbol: dB) is a relative <a href="/wiki/Unit_of_measurement" title="Unit of measurement">unit of measurement</a> equal to one tenth of a bel (B). It expresses the ratio of two values of a <a href="/wiki/Power,_root-power,_and_field_quantities" title="Power, root-power, and field quantities">power or root-power quantity</a> on a <a href="/wiki/Logarithmic_scale" title="Logarithmic scale">logarithmic scale</a>. Two signals whose <a href="/wiki/Level_(logarithmic_quantity)" title="Level (logarithmic quantity)">levels</a> differ by one decibel have a power ratio of 101/10 (approximately 1.26) or root-power ratio of 101/20 (approximately 1.12).<a href="#cite_note-auto-1">[1]</a><a href="#cite_note-auto1-2">[2]</a> The unit fundamentally expresses a relative change but may also be used to express an absolute value as the ratio of a value to a fixed reference value; when used in this way, the unit symbol is often suffixed with letter codes that indicate the reference value. For example, for the reference value of 1 <a href="/wiki/Volt" title="Volt">volt</a>, a common suffix is "<a href="#Voltage">V</a>" (e.g., "20 dBV").<a href="#cite_note-clqgmk-3">[3]</a><a href="#cite_note-4">[4]</a> Two principal types of scaling of the decibel are in common use. When expressing a power ratio, it is defined as ten times the <a href="/wiki/Common_logarithm" title="Common logarithm">logarithm with base 10</a>.<a href="#cite_note-5">[5]</a> That is, a change in power by a factor of 10 corresponds to a 10 dB change in level. When expressing root-power quantities, a change in <a href="/wiki/Amplitude" title="Amplitude">amplitude</a> by a factor of 10 corresponds to a 20 dB change in level. The decibel scales differ by a factor of two, so that the related power and root-power levels change by the same value in linear systems, where power is proportional to the square of amplitude. The definition of the decibel originated in the measurement of transmission loss and power in <a href="/wiki/Telephony" title="Telephony">telephony</a> of the early 20th century in the <a href="/wiki/Bell_System" title="Bell System">Bell System</a> in the United States. The bel was named in honor of <a href="/wiki/Alexander_Graham_Bell" title="Alexander Graham Bell">Alexander Graham Bell</a>, but the bel is seldom used. Instead, the decibel is used for a wide variety of measurements in science and <a href="/wiki/Engineering" title="Engineering">engineering</a>, most prominently for <a href="/wiki/Sound_power" title="Sound power">sound power</a> in <a href="/wiki/Acoustics" title="Acoustics">acoustics</a>, in <a href="/wiki/Electronics" title="Electronics">electronics</a> and <a href="/wiki/Control_theory" title="Control theory">control theory</a>. In electronics, the <a href="/wiki/Gain_(electronics)" title="Gain (electronics)">gains</a> of amplifiers, <a href="/wiki/Attenuation" title="Attenuation">attenuation</a> of signals, and <a href="/wiki/Signal-to-noise_ratio" title="Signal-to-noise ratio">signal-to-noise ratios</a> are often expressed in decibels. <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="History">History</h2>[<a href="/w/index.php?title=Decibel&action=edit&section=1" title="Edit section: History">edit</a>]</div> The decibel originates from methods used to quantify signal loss in telegraph and telephone circuits. Until the mid-1920s, the unit for loss was miles of standard cable (MSC). 1 MSC corresponded to the loss of power over one <a href="/wiki/Mile" title="Mile">mile</a> (approximately 1.6 km) of standard telephone cable at a frequency of 5000 <a href="/wiki/Radian" title="Radian">radians</a> per second (795.8 Hz), and matched closely the smallest attenuation detectable to a listener. A standard telephone cable was "a cable having uniformly distributed resistance of 88 ohms per loop-mile and uniformly distributed <a href="/wiki/Shunt_(electrical)" title="Shunt (electrical)">shunt</a> <a href="/wiki/Capacitance" title="Capacitance">capacitance</a> of 0.054 <a href="/wiki/Microfarad" class="mw-redirect" title="Microfarad">microfarads</a> per mile" (approximately corresponding to 19 <a href="/wiki/Wire_gauge" title="Wire gauge">gauge</a> wire).<a href="#cite_note-6">[6]</a> In 1924, <a href="/wiki/Bell_Labs" title="Bell Labs">Bell Telephone Laboratories</a> received a favorable response to a new unit definition among members of the International Advisory Committee on Long Distance Telephony in Europe and replaced the MSC with the Transmission Unit (TU). 1 TU was defined such that the number of TUs was ten times the base-10 logarithm of the ratio of measured power to a reference power.<a href="#cite_note-7">[7]</a> The definition was conveniently chosen such that 1 TU approximated 1 MSC; specifically, 1 MSC was 1.056 TU. In 1928, the Bell system renamed the TU into the decibel,<a href="#cite_note-8">[8]</a> being one tenth of a newly defined unit for the base-10 logarithm of the power ratio. It was named the bel, in honor of the telecommunications pioneer <a href="/wiki/Alexander_Graham_Bell" title="Alexander Graham Bell">Alexander Graham Bell</a>.<a href="#cite_note-9">[9]</a> The bel is seldom used, as the decibel was the proposed working unit.<a href="#cite_note-10">[10]</a> The naming and early definition of the decibel is described in the <a href="/wiki/National_Institute_of_Standards_and_Technology" title="National Institute of Standards and Technology">NBS</a> Standard's Yearbook of 1931:<a href="#cite_note-11">[11]</a> <style data-mw-deduplicate="TemplateStyles:r1244412712">.mw-parser-output .templatequote{overflow:hidden;margin:1em 0;padding:0 32px}.mw-parser-output .templatequotecite{line-height:1.5em;text-align:left;margin-top:0}@media(min-width:500px){.mw-parser-output .templatequotecite{padding-left:1.6em}}</style><blockquote class="templatequote"> Since the earliest days of the telephone, the need for a unit in which to measure the transmission efficiency of telephone facilities has been recognized. The introduction of cable in 1896 afforded a stable basis for a convenient unit and the "mile of standard" cable came into general use shortly thereafter. This unit was employed up to 1923 when a new unit was adopted as being more suitable for modern telephone work. The new transmission unit is widely used among the foreign telephone organizations and recently it was termed the "decibel" at the suggestion of the International Advisory Committee on Long Distance Telephony. The decibel may be defined by the statement that two amounts of power differ by 1 decibel when they are in the ratio of 100.1 and any two amounts of power differ by N decibels when they are in the ratio of 10N(0.1). The number of transmission units expressing the ratio of any two powers is therefore ten times the common logarithm of that ratio. This method of designating the gain or loss of power in telephone circuits permits direct addition or subtraction of the units expressing the efficiency of different parts of the circuit ...</blockquote> In 1954, J. W. Horton argued that the use of the decibel as a unit for quantities other than transmission loss led to confusion, and suggested the name logit for "standard magnitudes which combine by multiplication", to contrast with the name unit for "standard magnitudes which combine by addition".<a href="#cite_note-12">[12]</a>[<a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify">clarification needed</a>] In April 2003, the <a href="/wiki/International_Committee_for_Weights_and_Measures" class="mw-redirect" title="International Committee for Weights and Measures">International Committee for Weights and Measures</a> (CIPM) considered a recommendation for the inclusion of the decibel in the <a href="/wiki/International_System_of_Units" title="International System of Units">International System of Units</a> (SI), but decided against the proposal.<a href="#cite_note-13">[13]</a> However, the decibel is recognized by other international bodies such as the <a href="/wiki/International_Electrotechnical_Commission" title="International Electrotechnical Commission">International Electrotechnical Commission</a> (IEC) and <a href="/wiki/International_Organization_for_Standardization" title="International Organization for Standardization">International Organization for Standardization</a> (ISO).<a href="#cite_note-IEC60027-3-14">[14]</a> The IEC permits the use of the decibel with root-power quantities as well as power and this recommendation is followed by many national standards bodies, such as <a href="/wiki/NIST" class="mw-redirect" title="NIST">NIST</a>, which justifies the use of the decibel for voltage ratios.<a href="#cite_note-NIST2008-15">[15]</a> In spite of their widespread use, <a href="#Suffixes_and_reference_values">suffixes</a> (such as in <a href="/wiki/A-weighting" title="A-weighting">dBA</a> or dBV) are not recognized by the IEC or ISO. <div class="mw-heading mw-heading2"><h2 id="Definition">Definition</h2>[<a href="/w/index.php?title=Decibel&action=edit&section=2" title="Edit section: Definition">edit</a>]</div> <table class="wikitable floatright" style="width:0; font-size:85%; margin-left:1em"> <tbody><tr> <th scope="col" style="text-align:right;">dB </th> <th scope="col" colspan="2">Power ratio </th> <th scope="col" colspan="2">Amplitude ratio </th></tr> <tr> <td style="text-align:right; border:none;">100 </td> <td style="text-align:right; border:none; padding-right:0">10000000000</td> <td style="border:none;"> </td> <td style="text-align:right; border:none; padding-right:0">100000</td> <td style="border:none;"> </td></tr> <tr> <td style="text-align:right; border:none;">90 </td> <td style="text-align:right; border:none; padding-right:0">1000000000</td> <td style="border:none;"> </td> <td style="text-align:right; border:none; padding-right:0">31623</td> <td style="border:none;"> </td></tr> <tr> <td style="text-align:right; border:none;">80 </td> <td style="text-align:right; border:none; padding-right:0">100000000</td> <td style="border:none;"> </td> <td style="text-align:right; border:none; padding-right:0">10000</td> <td style="border:none;"> </td></tr> <tr> <td style="text-align:right; border:none;">70 </td> <td style="text-align:right; border:none; padding-right:0">10000000</td> <td style="border:none;"> </td> <td style="text-align:right; border:none; padding-right:0">3162</td> <td style="border:none;"> </td></tr> <tr> <td style="text-align:right; border:none;">60 </td> <td style="text-align:right; border:none; padding-right:0">1000000</td> <td style="border:none;"> </td> <td style="text-align:right; border:none; padding-right:0">1000</td> <td style="border:none;"> </td></tr> <tr> <td style="text-align:right; border:none;">50 </td> <td style="text-align:right; border:none; padding-right:0">100000</td> <td style="border:none;"> </td> <td style="text-align:right; border:none; padding-right:0">316</td> <td style="border:none; padding-left:0;">.2 </td></tr> <tr> <td style="text-align:right; border:none;">40 </td> <td style="text-align:right; border:none; padding-right:0">10000</td> <td style="border:none;"> </td> <td style="text-align:right; border:none; padding-right:0">100</td> <td style="border:none;"> </td></tr> <tr> <td style="text-align:right; border:none;">30 </td> <td style="text-align:right; border:none; padding-right:0">1000</td> <td style="border:none;"> </td> <td style="text-align:right; border:none; padding-right:0">31</td> <td style="border:none; padding-left:0;">.62 </td></tr> <tr> <td style="text-align:right; border:none;">20 </td> <td style="text-align:right; border:none; padding-right:0">100</td> <td style="border:none;"> </td> <td style="text-align:right; border:none; padding-right:0">10</td> <td style="border:none;"> </td></tr> <tr> <td style="text-align:right; border:none;">10 </td> <td style="text-align:right; border:none; padding-right:0">10</td> <td style="border:none;"> </td> <td style="text-align:right; border:none; padding-right:0">3</td> <td style="border:none; padding-left:0;">.162 </td></tr> <tr> <td style="text-align:right; border:none;">6 </td> <td style="text-align:right; border:none; padding-right:0">3</td> <td style="border:none; padding-left:0;">.981 ≈ 4 </td> <td style="text-align:right; border:none; padding-right:0">1</td> <td style="border:none; padding-left:0;">.995 ≈ 2 </td></tr> <tr> <td style="text-align:right; border:none;">3 </td> <td style="text-align:right; border:none; padding-right:0">1</td> <td style="border:none; padding-left:0;">.995 ≈ 2 </td> <td style="text-align:right; border:none; padding-right:0">1</td> <td style="border:none; padding-left:0;">.413 ≈ √2 </td></tr> <tr> <td style="text-align:right; border:none;">1 </td> <td style="text-align:right; border:none; padding-right:0">1</td> <td style="border:none; padding-left:0;">.259 </td> <td style="text-align:right; border:none; padding-right:0">1</td> <td style="border:none; padding-left:0;">.122 </td></tr> <tr> <td style="text-align:right; border:none;">0 </td> <td style="text-align:right; border:none; padding-right:0">1</td> <td style="border:none;"> </td> <td style="text-align:right; border:none; padding-right:0">1</td> <td style="border:none;"> </td></tr> <tr> <td style="text-align:right; border:none;">−1 </td> <td style="text-align:right; border:none; padding-right:0">0</td> <td style="border:none; padding-left:0;">.794 </td> <td style="text-align:right; border:none; padding-right:0">0</td> <td style="border:none; padding-left:0;">.891 </td></tr> <tr> <td style="text-align:right; border:none;">−3 </td> <td style="text-align:right; border:none; padding-right:0">0</td> <td style="border:none; padding-left:0;">.501 ≈ <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035">⁠1/2⁠ </td> <td style="text-align:right; border:none; padding-right:0">0</td> <td style="border:none; padding-left:0;">.708 ≈ √<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035">⁠1/2⁠ </td></tr> <tr> <td style="text-align:right; border:none;">−6 </td> <td style="text-align:right; border:none; padding-right:0">0</td> <td style="border:none; padding-left:0;">.251 ≈ <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035">⁠1/4⁠ </td> <td style="text-align:right; border:none; padding-right:0">0</td> <td style="border:none; padding-left:0;">.501 ≈ <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035">⁠1/2⁠ </td></tr> <tr> <td style="text-align:right; border:none;">−10 </td> <td style="text-align:right; border:none; padding-right:0">0</td> <td style="border:none; padding-left:0;">.1 </td> <td style="text-align:right; border:none; padding-right:0">0</td> <td style="border:none; padding-left:0;">.3162 </td></tr> <tr> <td style="text-align:right; border:none;">−20 </td> <td style="text-align:right; border:none; padding-right:0">0</td> <td style="border:none; padding-left:0;">.01 </td> <td style="text-align:right; border:none; padding-right:0">0</td> <td style="border:none; padding-left:0;">.1 </td></tr> <tr> <td style="text-align:right; border:none;">−30 </td> <td style="text-align:right; border:none; padding-right:0">0</td> <td style="border:none; padding-left:0;">.001 </td> <td style="text-align:right; border:none; padding-right:0">0</td> <td style="border:none; padding-left:0;">.03162 </td></tr> <tr> <td style="text-align:right; border:none;">−40 </td> <td style="text-align:right; border:none; padding-right:0">0</td> <td style="border:none; padding-left:0;">.0001 </td> <td style="text-align:right; border:none; padding-right:0">0</td> <td style="border:none; padding-left:0;">.01 </td></tr> <tr> <td style="text-align:right; border:none;">−50 </td> <td style="text-align:right; border:none; padding-right:0">0</td> <td style="border:none; padding-left:0;">.00001 </td> <td style="text-align:right; border:none; padding-right:0">0</td> <td style="border:none; padding-left:0;">.003162 </td></tr> <tr> <td style="text-align:right; border:none;">−60 </td> <td style="text-align:right; border:none; padding-right:0">0</td> <td style="border:none; padding-left:0;">.000001 </td> <td style="text-align:right; border:none; padding-right:0">0</td> <td style="border:none; padding-left:0;">.001 </td></tr> <tr> <td style="text-align:right; border:none;">−70 </td> <td style="text-align:right; border:none; padding-right:0">0</td> <td style="border:none; padding-left:0;">.0000001 </td> <td style="text-align:right; border:none; padding-right:0">0</td> <td style="border:none; padding-left:0;">.0003162 </td></tr> <tr> <td style="text-align:right; border:none;">−80 </td> <td style="text-align:right; border:none; padding-right:0">0</td> <td style="border:none; padding-left:0;">.00000001 </td> <td style="text-align:right; border:none; padding-right:0">0</td> <td style="border:none; padding-left:0;">.0001 </td></tr> <tr> <td style="text-align:right; border:none;">−90 </td> <td style="text-align:right; border:none; padding-right:0">0</td> <td style="border:none; padding-left:0;">.000000001 </td> <td style="text-align:right; border:none; padding-right:0">0</td> <td style="border:none; padding-left:0;">.00003162 </td></tr> <tr> <td style="text-align:right; border:none;">−100 </td> <td style="text-align:right; border:none; padding-right:0">0</td> <td style="border:none; padding-left:0;">.0000000001 </td> <td style="text-align:right; border:none; padding-right:0">0</td> <td style="border:none; padding-left:0;">.00001 </td></tr> <tr> <td colspan="5" style="text-align:left; background:#f8f8ff;">An example scale showing power ratios x, amplitude ratios √x, and dB equivalents 10 log10 x </td></tr></tbody></table> The IEC Standard <a href="/wiki/IEC_60027" title="IEC 60027">60027-3:2002</a> defines the following quantities. The decibel (dB) is one-tenth of a bel: 1 dB = 0.1 B. The bel (B) is <style data-mw-deduplicate="TemplateStyles:r1154941027">.mw-parser-output .frac{white-space:nowrap}.mw-parser-output .frac .num,.mw-parser-output .frac .den{font-size:80%;line-height:0;vertical-align:super}.mw-parser-output .frac .den{vertical-align:sub}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style>1⁄2 ln(10) <a href="/wiki/Neper" title="Neper">nepers</a>: 1 B = <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027">1⁄2 ln(10) Np. The neper is the change in the <a href="/wiki/Level_(logarithmic_quantity)" title="Level (logarithmic quantity)">level</a> of a <a href="/wiki/Root-power_quantity" class="mw-redirect" title="Root-power quantity">root-power quantity</a> when the root-power quantity changes by a factor of <a href="/wiki/E_(mathematical_constant)" title="E (mathematical constant)">e</a>, that is 1 Np = ln(e) = 1, thereby relating all of the units as nondimensional <a href="/wiki/Natural_logarithm" title="Natural logarithm">natural log</a> of root-power-quantity ratios, 1 dB = 0.11513... Np = 0.11513.... Finally, the level of a quantity is the logarithm of the ratio of the value of that quantity to a reference value of the same kind of quantity. Therefore, the bel represents the logarithm of a ratio between two power quantities of 10:1, or the logarithm of a ratio between two root-power quantities of √10:1.<a href="#cite_note-16">[16]</a> Two signals whose levels differ by one decibel have a power ratio of 101/10, which is approximately 1.25893, and an amplitude (root-power quantity) ratio of 101/20 (1.12202).<a href="#cite_note-auto-1">[1]</a><a href="#cite_note-auto1-2">[2]</a> The bel is rarely used either without a prefix or with <a href="/wiki/Metric_prefix" title="Metric prefix">SI unit prefixes</a> other than <a href="/wiki/Deci-" title="Deci-">deci</a>; it is customary, for example, to use hundredths of a decibel rather than millibels. Thus, five one-thousandths of a bel would normally be written 0.05 dB, and not 5 mB.<a href="#cite_note-17">[17]</a> The method of expressing a ratio as a level in decibels depends on whether the measured property is a power quantity or a root-power quantity; see <a href="/wiki/Power,_root-power,_and_field_quantities" title="Power, root-power, and field quantities">Power, root-power, and field quantities</a> for details. <div class="mw-heading mw-heading3"><h3 id="Power_quantities">Power quantities</h3>[<a href="/w/index.php?title=Decibel&action=edit&section=3" title="Edit section: Power quantities">edit</a>]</div> When referring to measurements of <a href="/wiki/Power_(physics)" title="Power (physics)">power</a> quantities, a ratio can be expressed as a <a href="/wiki/Level_(logarithmic_quantity)" title="Level (logarithmic quantity)">level</a> in decibels by evaluating ten times the <a href="/wiki/Base-10_logarithm" class="mw-redirect" title="Base-10 logarithm">base-10 logarithm</a> of the ratio of the measured quantity to reference value. Thus, the ratio of P (measured power) to P0 (reference power) is represented by LP, that ratio expressed in decibels,<a href="#cite_note-18">[18]</a> which is calculated using the formula:<a href="#cite_note-19">[19]</a> <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L_{P}={\frac {1}{2}}\ln \!\left({\frac {P}{P_{0}}}\right)\,{\text{Np}}=10\log _{10}\!\left({\frac {P}{P_{0}}}\right)\,{\text{dB}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>ln</mi> <mspace width="negativethinmathspace" /> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>P</mi> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>Np</mtext> </mrow> <mo>=</mo> <mn>10</mn> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mspace width="negativethinmathspace" /> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>P</mi> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>dB</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L_{P}={\frac {1}{2}}\ln \!\left({\frac {P}{P_{0}}}\right)\,{\text{Np}}=10\log _{10}\!\left({\frac {P}{P_{0}}}\right)\,{\text{dB}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/050db35bdefc333f11eb597865ba1c837f2a76ae" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:42.261ex; height:6.176ex;" alt="{\displaystyle L_{P}={\frac {1}{2}}\ln \!\left({\frac {P}{P_{0}}}\right)\,{\text{Np}}=10\log _{10}\!\left({\frac {P}{P_{0}}}\right)\,{\text{dB}}}"></dd></dl> The base-10 logarithm of the ratio of the two power quantities is the number of bels. The number of decibels is ten times the number of bels (equivalently, a decibel is one-tenth of a bel). P and P0 must measure the same type of quantity, and have the same units before calculating the ratio. If P = P0 in the above equation, then LP = 0. If P is greater than P0 then LP is positive; if P is less than P0 then LP is negative. Rearranging the above equation gives the following formula for P in terms of P0 and LP : <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P=10^{\frac {L_{P}}{10\,{\text{dB}}}}P_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo>=</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> </mrow> </msub> <mrow> <mn>10</mn> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>dB</mtext> </mrow> </mrow> </mfrac> </mrow> </msup> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P=10^{\frac {L_{P}}{10\,{\text{dB}}}}P_{0}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/72da90418b7c660960318e52d9c5c3fd144e8003" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.192ex; height:4.343ex;" alt="{\displaystyle P=10^{\frac {L_{P}}{10\,{\text{dB}}}}P_{0}}"></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Root-power_(field)_quantities">Root-power (field) quantities</h3>[<a href="/w/index.php?title=Decibel&action=edit&section=4" title="Edit section: Root-power (field) quantities">edit</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Power,_root-power,_and_field_quantities" title="Power, root-power, and field quantities">Power, root-power, and field quantities</a></div> When referring to measurements of root-power quantities, it is usual to consider the ratio of the squares of F (measured) and F0 (reference). This is because the definitions were originally formulated to give the same value for relative ratios for both power and root-power quantities. Thus, the following definition is used: <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L_{F}=\ln \!\left({\frac {F}{F_{0}}}\right)\,{\text{Np}}=10\log _{10}\!\left({\frac {F^{2}}{F_{0}^{2}}}\right)\,{\text{dB}}=20\log _{10}\left({\frac {F}{F_{0}}}\right)\,{\text{dB}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>F</mi> </mrow> </msub> <mo>=</mo> <mi>ln</mi> <mspace width="negativethinmathspace" /> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>F</mi> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>Np</mtext> </mrow> <mo>=</mo> <mn>10</mn> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mspace width="negativethinmathspace" /> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msubsup> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mfrac> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>dB</mtext> </mrow> <mo>=</mo> <mn>20</mn> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>F</mi> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>dB</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L_{F}=\ln \!\left({\frac {F}{F_{0}}}\right)\,{\text{Np}}=10\log _{10}\!\left({\frac {F^{2}}{F_{0}^{2}}}\right)\,{\text{dB}}=20\log _{10}\left({\frac {F}{F_{0}}}\right)\,{\text{dB}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c84f87ca54dbf8cdd841a1dd0e6fbb01038864ba" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:61.247ex; height:7.509ex;" alt="{\displaystyle L_{F}=\ln \!\left({\frac {F}{F_{0}}}\right)\,{\text{Np}}=10\log _{10}\!\left({\frac {F^{2}}{F_{0}^{2}}}\right)\,{\text{dB}}=20\log _{10}\left({\frac {F}{F_{0}}}\right)\,{\text{dB}}}"></dd></dl> The formula may be rearranged to give <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F=10^{\frac {L_{F}}{20\,{\text{dB}}}}F_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo>=</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>F</mi> </mrow> </msub> <mrow> <mn>20</mn> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>dB</mtext> </mrow> </mrow> </mfrac> </mrow> </msup> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F=10^{\frac {L_{F}}{20\,{\text{dB}}}}F_{0}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f9cf591ca6f14bb1824475626103e9474e428f57" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.19ex; height:4.343ex;" alt="{\displaystyle F=10^{\frac {L_{F}}{20\,{\text{dB}}}}F_{0}}"></dd></dl> Similarly, in <a href="/wiki/Electronic_circuit" title="Electronic circuit">electrical circuits</a>, dissipated power is typically proportional to the square of <a href="/wiki/Voltage" title="Voltage">voltage</a> or <a href="/wiki/Electric_current" title="Electric current">current</a> when the <a href="/wiki/Electrical_impedance" title="Electrical impedance">impedance</a> is constant. Taking voltage as an example, this leads to the equation for power gain level LG: <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L_{G}=20\log _{10}\!\left({\frac {V_{\text{out}}}{V_{\text{in}}}}\right)\,{\text{dB}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>G</mi> </mrow> </msub> <mo>=</mo> <mn>20</mn> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mspace width="negativethinmathspace" /> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>out</mtext> </mrow> </msub> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>in</mtext> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>dB</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L_{G}=20\log _{10}\!\left({\frac {V_{\text{out}}}{V_{\text{in}}}}\right)\,{\text{dB}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/908ee2b15f4fea17e4a3c09f2ddceaa2df3b5caf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:25.698ex; height:6.176ex;" alt="{\displaystyle L_{G}=20\log _{10}\!\left({\frac {V_{\text{out}}}{V_{\text{in}}}}\right)\,{\text{dB}}}"></dd></dl> where Vout is the <a href="/wiki/Root-mean-square" class="mw-redirect" title="Root-mean-square">root-mean-square</a> (rms) output voltage, Vin is the rms input voltage. A similar formula holds for current. The term root-power quantity is introduced by ISO Standard <a href="/wiki/ISO/IEC_80000" title="ISO/IEC 80000">80000-1:2009</a> as a substitute of field quantity. The term field quantity is deprecated by that standard and root-power is used throughout this article. <div class="mw-heading mw-heading3"><h3 id="Relationship_between_power_and_root-power_levels">Relationship between power and root-power levels</h3>[<a href="/w/index.php?title=Decibel&action=edit&section=5" title="Edit section: Relationship between power and root-power levels">edit</a>]</div> Although power and root-power quantities are different quantities, their respective levels are historically measured in the same units, typically decibels. A factor of 2 is introduced to make changes in the respective levels match under restricted conditions such as when the medium is linear and the same waveform is under consideration with changes in amplitude, or the medium impedance is linear and independent of both frequency and time. This relies on the relationship <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {P(t)}{P_{0}}}=\left({\frac {F(t)}{F_{0}}}\right)^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>P</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>F</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {P(t)}{P_{0}}}=\left({\frac {F(t)}{F_{0}}}\right)^{2}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9dc74ae09562c46e9d5800373964100df2e87219" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:18.03ex; height:6.676ex;" alt="{\displaystyle {\frac {P(t)}{P_{0}}}=\left({\frac {F(t)}{F_{0}}}\right)^{2}}"></dd></dl> holding.<a href="#cite_note-20">[20]</a> In a nonlinear system, this relationship does not hold by the definition of linearity. However, even in a <a href="/wiki/Linear_system" title="Linear system">linear system</a> in which the power quantity is the product of two linearly related quantities (e.g. <a href="/wiki/Voltage" title="Voltage">voltage</a> and <a href="/wiki/Electric_current" title="Electric current">current</a>), if the <a href="/wiki/Electrical_impedance" title="Electrical impedance">impedance</a> is frequency- or time-dependent, this relationship does not hold in general, for example if the energy spectrum of the waveform changes. For differences in level, the required relationship is relaxed from that above to one of proportionality (i.e., the reference quantities P0 and F0 need not be related), or equivalently, <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {P_{2}}{P_{1}}}=\left({\frac {F_{2}}{F_{1}}}\right)^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {P_{2}}{P_{1}}}=\left({\frac {F_{2}}{F_{1}}}\right)^{2}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/223d75c46ba027e147296cdff096082240457da9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:14.341ex; height:6.509ex;" alt="{\displaystyle {\frac {P_{2}}{P_{1}}}=\left({\frac {F_{2}}{F_{1}}}\right)^{2}}"></dd></dl> must hold to allow the power level difference to be equal to the root-power level difference from power P1 and F1 to P2 and F2. An example might be an amplifier with unity voltage gain independent of load and frequency driving a load with a frequency-dependent impedance: the relative voltage gain of the amplifier is always 0 dB, but the power gain depends on the changing spectral composition of the waveform being amplified. Frequency-dependent impedances may be analyzed by considering the quantities <a href="/wiki/Power_spectral_density" class="mw-redirect" title="Power spectral density">power spectral density</a> and the associated root-power quantities via the <a href="/wiki/Fourier_transform" title="Fourier transform">Fourier transform</a>, which allows elimination of the frequency dependence in the analysis by analyzing the system at each frequency independently. <div class="mw-heading mw-heading3"><h3 id="Conversions">Conversions</h3>[<a href="/w/index.php?title=Decibel&action=edit&section=6" title="Edit section: Conversions">edit</a>]</div> Since logarithm differences measured in these units often represent power ratios and root-power ratios, values for both are shown below. The bel is traditionally used as a unit of logarithmic power ratio, while the neper is used for logarithmic root-power (amplitude) ratio. <table class="wikitable"> <caption>Conversion between units of level and a list of corresponding ratios </caption> <tbody><tr> <th>Unit</th> <th>In decibels</th> <th>In bels</th> <th>In <a href="/wiki/Neper" title="Neper">nepers</a></th> <th>Power ratio</th> <th>Root-power ratio </th></tr> <tr> <td>1 dB</td> <td>1 dB</td> <td>0.1 B</td> <td>0.11513 Np</td> <td>101/10 ≈ 1.25893</td> <td>101/20 ≈ 1.12202 </td></tr> <tr> <td>1 Np</td> <td>8.68589 dB</td> <td>0.868589 B</td> <td>1 Np</td> <td>e2 ≈ 7.38906</td> <td><a href="/wiki/E_(mathematical_constant)" title="E (mathematical constant)">e</a> ≈ 2.71828 </td></tr> <tr> <td>1 B</td> <td>10 dB</td> <td>1 B</td> <td>1.151 3 Np</td> <td>10</td> <td>101/2 ≈ 3.162 28 </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Examples">Examples</h3>[<a href="/w/index.php?title=Decibel&action=edit&section=7" title="Edit section: Examples">edit</a>]</div> The unit dBW is often used to denote a ratio for which the reference is 1 W, and similarly dBm for a 1 mW reference point. <ul><li>Calculating the ratio in decibels of 1 kW (one kilowatt, or 1000 watts) to 1 W yields: <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L_{G}=10\log _{10}\left({\frac {1\,000\,{\text{W}}}{1\,{\text{W}}}}\right)\,{\text{dB}}=30\,{\text{dB}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>G</mi> </mrow> </msub> <mo>=</mo> <mn>10</mn> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>1</mn> <mspace width="thinmathspace" /> <mn>000</mn> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>W</mtext> </mrow> </mrow> <mrow> <mn>1</mn> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>W</mtext> </mrow> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>dB</mtext> </mrow> <mo>=</mo> <mn>30</mn> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>dB</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L_{G}=10\log _{10}\left({\frac {1\,000\,{\text{W}}}{1\,{\text{W}}}}\right)\,{\text{dB}}=30\,{\text{dB}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/92c7b1c4f01f317581ed61607fc02666c0a0e38c" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:37.909ex; height:6.176ex;" alt="{\displaystyle L_{G}=10\log _{10}\left({\frac {1\,000\,{\text{W}}}{1\,{\text{W}}}}\right)\,{\text{dB}}=30\,{\text{dB}}}"></li> <li>The ratio in decibels of √1000 V ≈ 31.62 V to 1 V is: <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L_{G}=20\log _{10}\left({\frac {31.62\,{\text{V}}}{1\,{\text{V}}}}\right)\,{\text{dB}}=30\,{\text{dB}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>G</mi> </mrow> </msub> <mo>=</mo> <mn>20</mn> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>31.62</mn> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>V</mtext> </mrow> </mrow> <mrow> <mn>1</mn> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>V</mtext> </mrow> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>dB</mtext> </mrow> <mo>=</mo> <mn>30</mn> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>dB</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L_{G}=20\log _{10}\left({\frac {31.62\,{\text{V}}}{1\,{\text{V}}}}\right)\,{\text{dB}}=30\,{\text{dB}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9801b2512ddfc5e2380f18eeb4cceeec5f91a8c9" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:37.523ex; height:6.176ex;" alt="{\displaystyle L_{G}=20\log _{10}\left({\frac {31.62\,{\text{V}}}{1\,{\text{V}}}}\right)\,{\text{dB}}=30\,{\text{dB}}}"></li></ul> (31.62 V / 1 V)2 ≈ 1 kW / 1 W, illustrating the consequence from the definitions above that LG has the same value, 30 dB, regardless of whether it is obtained from powers or from amplitudes, provided that in the specific system being considered power ratios are equal to amplitude ratios squared. <ul><li>The ratio in decibels of 10 W to 1 mW (one milliwatt) is obtained with the formula: <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L_{G}=10\log _{10}\left({\frac {10{\text{W}}}{0.001{\text{W}}}}\right)\,{\text{dB}}=40\,{\text{dB}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>G</mi> </mrow> </msub> <mo>=</mo> <mn>10</mn> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mtext>W</mtext> </mrow> </mrow> <mrow> <mn>0.001</mn> <mrow class="MJX-TeXAtom-ORD"> <mtext>W</mtext> </mrow> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>dB</mtext> </mrow> <mo>=</mo> <mn>40</mn> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>dB</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L_{G}=10\log _{10}\left({\frac {10{\text{W}}}{0.001{\text{W}}}}\right)\,{\text{dB}}=40\,{\text{dB}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2c6d1d5cd1ec08b890fc74d2be4ca180dd7e7b7b" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:37.782ex; height:6.176ex;" alt="{\displaystyle L_{G}=10\log _{10}\left({\frac {10{\text{W}}}{0.001{\text{W}}}}\right)\,{\text{dB}}=40\,{\text{dB}}}"></li> <li>The power ratio corresponding to a 3 dB change in level is given by: <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G=10^{\frac {3}{10}}\times 1=1.995\,26\ldots \approx 2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> <mo>=</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>3</mn> <mn>10</mn> </mfrac> </mrow> </msup> <mo>×</mo> <mn>1</mn> <mo>=</mo> <mn>1.995</mn> <mspace width="thinmathspace" /> <mn>26</mn> <mo>…</mo> <mo>≈</mo> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G=10^{\frac {3}{10}}\times 1=1.995\,26\ldots \approx 2}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a55abe0f8b2509ce8de51beef84531c507d20090" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:32.134ex; height:3.509ex;" alt="{\displaystyle G=10^{\frac {3}{10}}\times 1=1.995\,26\ldots \approx 2}"></li></ul> A change in power ratio by a factor of 10 corresponds to a change in level of 10 dB. A change in power ratio by a factor of 2 or <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035">⁠1/2⁠ is approximately a <a href="/wiki/Half-power_point" title="Half-power point">change of 3 dB</a>. More precisely, the change is ±3.0103 dB, but this is almost universally rounded to 3 dB in technical writing.[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] This implies an increase in voltage by a factor of √2 ≈ 1.4142. Likewise, a doubling or halving of the voltage, corresponding to a quadrupling or quartering of the power, is commonly described as 6 dB rather than ±6.0206 dB. Should it be necessary to make the distinction, the number of decibels is written with additional <a href="/wiki/Significant_figures" title="Significant figures">significant figures</a>. 3.000 dB corresponds to a power ratio of 103/10, or 1.9953, about 0.24% different from exactly 2, and a voltage ratio of 1.4125, about 0.12% different from exactly √2. Similarly, an increase of 6.000 dB corresponds to a power ratio of 106/10 ≈ 3.9811, about 0.5% different from 4. <div class="mw-heading mw-heading2"><h2 id="Properties">Properties</h2>[<a href="/w/index.php?title=Decibel&action=edit&section=8" title="Edit section: Properties">edit</a>]</div> The decibel is useful for representing large ratios and for simplifying representation of multiplicative effects, such as attenuation from multiple sources along a signal chain. Its application in systems with additive effects is less intuitive, such as in the combined sound pressure level of two machines operating together. Care is also necessary with decibels directly in fractions and with the units of multiplicative operations. <div class="mw-heading mw-heading3"><h3 id="Reporting_large_ratios">Reporting large ratios</h3>[<a href="/w/index.php?title=Decibel&action=edit&section=9" title="Edit section: Reporting large ratios">edit</a>]</div> The <a href="/wiki/Logarithmic_scale" title="Logarithmic scale">logarithmic scale</a> nature of the decibel means that a very large range of ratios can be represented by a convenient number, in a manner similar to <a href="/wiki/Scientific_notation" title="Scientific notation">scientific notation</a>. This allows one to clearly visualize huge changes of some quantity. See <a href="/wiki/Bode_plot" title="Bode plot">Bode plot</a> and <a href="/wiki/Semi-log_plot" title="Semi-log plot">Semi-log plot</a>. For example, 120 dB SPL may be clearer than "a trillion times more intense than the threshold of hearing".[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] <div class="mw-heading mw-heading3"><h3 id="Representation_of_multiplication_operations">Representation of multiplication operations</h3>[<a href="/w/index.php?title=Decibel&action=edit&section=10" title="Edit section: Representation of multiplication operations">edit</a>]</div> Level values in decibels can be added instead of multiplying the underlying power values, which means that the overall gain of a multi-component system, such as a series of <a href="/wiki/Amplifier" title="Amplifier">amplifier</a> stages, can be calculated by summing the gains in decibels of the individual components, rather than multiply the amplification factors; that is, log(A × B × C) = log(A) + log(B) + log(C). Practically, this means that, armed only with the knowledge that 1 dB is a power gain of approximately 26%, 3 dB is approximately 2× power gain, and 10 dB is 10× power gain, it is possible to determine the power ratio of a system from the gain in dB with only simple addition and multiplication. For example: <ul><li>A system consists of 3 amplifiers in series, with gains (ratio of power out to in) of 10 dB, 8 dB, and 7 dB respectively, for a total gain of 25 dB. Broken into combinations of 10, 3, and 1 dB, this is: <style data-mw-deduplicate="TemplateStyles:r996643573">.mw-parser-output .block-indent{padding-left:3em;padding-right:0;overflow:hidden}</style><div class="block-indent" style="padding-left: 1.5em;">25 dB = 10 dB + 10 dB + 3 dB + 1 dB + 1 dB</div> With an input of 1 watt, the output is approximately <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r996643573"><div class="block-indent" style="padding-left: 1.5em;">1 W × 10 × 10 × 2 × 1.26 × 1.26 ≈ 317.5 W</div> Calculated precisely, the output is 1 W × 1025/10 ≈ 316.2 W. The approximate value has an error of only +0.4% with respect to the actual value, which is negligible given the precision of the values supplied and the accuracy of most measurement instrumentation.</li></ul> However, according to its critics, the decibel creates confusion, obscures reasoning, is more related to the era of <a href="/wiki/Slide_rule" title="Slide rule">slide rules</a> than to modern digital processing, and is cumbersome and difficult to interpret.<a href="#cite_note-Hickling-21">[21]</a><a href="#cite_note-22">[22]</a> Quantities in decibels are not necessarily <a href="/wiki/Dimensional_homogeneity" class="mw-redirect" title="Dimensional homogeneity">additive</a>,<a href="#cite_note-23">[23]</a><a href="#cite_note-24">[24]</a> thus being "of unacceptable form for use in <a href="/wiki/Dimensional_analysis" title="Dimensional analysis">dimensional analysis</a>".<a href="#cite_note-25">[25]</a> Thus, units require special care in decibel operations. Take, for example, <a href="/wiki/Carrier-to-noise-density_ratio" class="mw-redirect" title="Carrier-to-noise-density ratio">carrier-to-noise-density ratio</a> C/N0 (in hertz), involving carrier power C (in watts) and noise <a href="/wiki/Power_spectral_density" class="mw-redirect" title="Power spectral density">power spectral density</a> N0 (in W/Hz). Expressed in decibels, this ratio would be a subtraction (C/N0)dB = CdB − N0 dB. However, the linear-scale units still simplify in the implied fraction, so that the results would be expressed in dB-Hz. <div class="mw-heading mw-heading3"><h3 id="Representation_of_addition_operations">Representation of addition operations </h3>[<a href="/w/index.php?title=Decibel&action=edit&section=11" title="Edit section: Representation of addition operations">edit</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/Logarithmic_addition" class="mw-redirect" title="Logarithmic addition">Logarithmic addition</a></div> According to Mitschke,<a href="#cite_note-26">[26]</a> "The advantage of using a logarithmic measure is that in a transmission chain, there are many elements concatenated, and each has its own gain or attenuation. To obtain the total, addition of decibel values is much more convenient than multiplication of the individual factors." However, for the same reason that humans excel at additive operation over multiplication, decibels are awkward in inherently additive operations:<a href="#cite_note-27">[27]</a><blockquote>if two machines each individually produce a <a href="/wiki/Sound_pressure" title="Sound pressure">sound pressure</a> level of, say, 90 dB at a certain point, then when both are operating together we should expect the combined sound pressure level to increase to 93 dB, but certainly not to 180 dB!; suppose that the noise from a machine is measured (including the contribution of background noise) and found to be 87 dBA but when the machine is switched off the background noise alone is measured as 83 dBA. [...] the machine noise [level (alone)] may be obtained by 'subtracting' the 83 dBA background noise from the combined level of 87 dBA; i.e., 84.8 dBA.; in order to find a representative value of the sound level in a room a number of measurements are taken at different positions within the room, and an average value is calculated. [...] Compare the logarithmic and arithmetic averages of [...] 70 dB and 90 dB: <a href="/wiki/Logarithmic_average" class="mw-redirect" title="Logarithmic average">logarithmic average</a> = 87 dB; <a href="/wiki/Arithmetic_average" class="mw-redirect" title="Arithmetic average">arithmetic average</a> = 80 dB.</blockquote> Addition on a logarithmic scale is called <a href="/wiki/Logarithmic_addition" class="mw-redirect" title="Logarithmic addition">logarithmic addition</a>, and can be defined by taking exponentials to convert to a linear scale, adding there, and then taking logarithms to return. For example, where operations on decibels are logarithmic addition/subtraction and logarithmic multiplication/division, while operations on the linear scale are the usual operations: <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 87\,{\text{dBA}}\ominus 83\,{\text{dBA}}=10\cdot \log _{10}{\bigl (}10^{87/10}-10^{83/10}{\bigr )}\,{\text{dBA}}\approx 84.8\,{\text{dBA}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>87</mn> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>dBA</mtext> </mrow> <mo>⊖</mo> <mn>83</mn> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>dBA</mtext> </mrow> <mo>=</mo> <mn>10</mn> <mo>⋅</mo> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.2em" minsize="1.2em">(</mo> </mrow> </mrow> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>87</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>10</mn> </mrow> </msup> <mo>−</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>83</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>10</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.2em" minsize="1.2em">)</mo> </mrow> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>dBA</mtext> </mrow> <mo>≈</mo> <mn>84.8</mn> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>dBA</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 87\,{\text{dBA}}\ominus 83\,{\text{dBA}}=10\cdot \log _{10}{\bigl (}10^{87/10}-10^{83/10}{\bigr )}\,{\text{dBA}}\approx 84.8\,{\text{dBA}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cc12687d73e59fc6bbfd02aff524107b14f4ff1e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:65.638ex; height:3.509ex;" alt="{\displaystyle 87\,{\text{dBA}}\ominus 83\,{\text{dBA}}=10\cdot \log _{10}{\bigl (}10^{87/10}-10^{83/10}{\bigr )}\,{\text{dBA}}\approx 84.8\,{\text{dBA}}}"></dd> <dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}M_{\text{lm}}(70,90)&=\left(70\,{\text{dBA}}+90\,{\text{dBA}}\right)/2\\&=10\cdot \log _{10}\left({\bigl (}10^{70/10}+10^{90/10}{\bigr )}/2\right)\,{\text{dBA}}\\&=10\cdot \left(\log _{10}{\bigl (}10^{70/10}+10^{90/10}{\bigr )}-\log _{10}2\right)\,{\text{dBA}}\approx 87\,{\text{dBA}}\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>lm</mtext> </mrow> </msub> <mo stretchy="false">(</mo> <mn>70</mn> <mo>,</mo> <mn>90</mn> <mo stretchy="false">)</mo> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mn>70</mn> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>dBA</mtext> </mrow> <mo>+</mo> <mn>90</mn> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>dBA</mtext> </mrow> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mn>10</mn> <mo>⋅</mo> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.2em" minsize="1.2em">(</mo> </mrow> </mrow> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>70</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>10</mn> </mrow> </msup> <mo>+</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>90</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>10</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.2em" minsize="1.2em">)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>dBA</mtext> </mrow> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mn>10</mn> <mo>⋅</mo> <mrow> <mo>(</mo> <mrow> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.2em" minsize="1.2em">(</mo> </mrow> </mrow> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>70</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>10</mn> </mrow> </msup> <mo>+</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>90</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>10</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.2em" minsize="1.2em">)</mo> </mrow> </mrow> <mo>−</mo> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mo>⁡</mo> <mn>2</mn> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>dBA</mtext> </mrow> <mo>≈</mo> <mn>87</mn> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>dBA</mtext> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}M_{\text{lm}}(70,90)&=\left(70\,{\text{dBA}}+90\,{\text{dBA}}\right)/2\\&=10\cdot \log _{10}\left({\bigl (}10^{70/10}+10^{90/10}{\bigr )}/2\right)\,{\text{dBA}}\\&=10\cdot \left(\log _{10}{\bigl (}10^{70/10}+10^{90/10}{\bigr )}-\log _{10}2\right)\,{\text{dBA}}\approx 87\,{\text{dBA}}\end{aligned}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/900b222374e1fe1b8740d1ff583a4143be4feabd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -5.838ex; width:71.159ex; height:12.843ex;" alt="{\displaystyle {\begin{aligned}M_{\text{lm}}(70,90)&=\left(70\,{\text{dBA}}+90\,{\text{dBA}}\right)/2\\&=10\cdot \log _{10}\left({\bigl (}10^{70/10}+10^{90/10}{\bigr )}/2\right)\,{\text{dBA}}\\&=10\cdot \left(\log _{10}{\bigl (}10^{70/10}+10^{90/10}{\bigr )}-\log _{10}2\right)\,{\text{dBA}}\approx 87\,{\text{dBA}}\end{aligned}}}"></dd></dl> The <a href="/wiki/Logarithmic_mean" title="Logarithmic mean">logarithmic mean</a> is obtained from the logarithmic sum by subtracting <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 10\log _{10}2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>10</mn> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mo>⁡</mo> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 10\log _{10}2}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2a48d44c09693560fdc611e3993ddb5b77b1ba02" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.11ex; height:2.676ex;" alt="{\displaystyle 10\log _{10}2}">, since logarithmic division is linear subtraction. <div class="mw-heading mw-heading3"><h3 id="Fractions">Fractions</h3>[<a href="/w/index.php?title=Decibel&action=edit&section=12" title="Edit section: Fractions">edit</a>]</div> <a href="/wiki/Attenuation" title="Attenuation">Attenuation</a> constants, in topics such as <a href="/wiki/Optical_fiber" title="Optical fiber">optical fiber</a> communication and <a href="/wiki/Radio_propagation" title="Radio propagation">radio propagation</a> <a href="/wiki/Path_loss" title="Path loss">path loss</a>, are often expressed as a <a href="/wiki/Fraction_(mathematics)" class="mw-redirect" title="Fraction (mathematics)">fraction</a> or ratio to distance of transmission. In this case, dB/m represents decibel per meter, dB/mi represents decibel per mile, for example. These quantities are to be manipulated obeying the rules of <a href="/wiki/Dimensional_analysis" title="Dimensional analysis">dimensional analysis</a>, e.g., a 100-meter run with a 3.5 dB/km fiber yields a loss of 0.35 dB = 3.5 dB/km × 0.1 km. <div class="mw-heading mw-heading2"><h2 id="Uses">Uses</h2>[<a href="/w/index.php?title=Decibel&action=edit&section=13" title="Edit section: Uses">edit</a>]</div> <div class="mw-heading mw-heading3"><h3 id="Perception">Perception</h3>[<a href="/w/index.php?title=Decibel&action=edit&section=14" title="Edit section: Perception">edit</a>]</div> The human perception of the intensity of sound and light more nearly approximates the logarithm of intensity rather than a linear relationship (see <a href="/wiki/Weber%E2%80%93Fechner_law" title="Weber–Fechner law">Weber–Fechner law</a>), making the dB scale a useful measure.<a href="#cite_note-28">[28]</a><a href="#cite_note-29">[29]</a><a href="#cite_note-30">[30]</a><a href="#cite_note-31">[31]</a><a href="#cite_note-32">[32]</a><a href="#cite_note-33">[33]</a> <div class="mw-heading mw-heading3"><h3 id="Acoustics">Acoustics</h3>[<a href="/w/index.php?title=Decibel&action=edit&section=15" title="Edit section: Acoustics">edit</a>]</div> The decibel is commonly used in <a href="/wiki/Acoustics" title="Acoustics">acoustics</a> as a unit of <a href="/wiki/Sound_power_level" class="mw-redirect" title="Sound power level">sound power level</a> or <a href="/wiki/Sound_pressure_level" class="mw-redirect" title="Sound pressure level">sound pressure level</a>. The reference pressure for sound in air is set at the typical threshold of perception of an average human and there are <a href="/wiki/Sound_pressure#Examples_of_sound_pressure" title="Sound pressure">common comparisons used to illustrate different levels of sound pressure</a>. As sound pressure is a root-power quantity, the appropriate version of the unit definition is used: <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L_{p}=20\log _{10}\!\left({\frac {p_{\text{rms}}}{p_{\text{ref}}}}\right)\,{\text{dB}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>=</mo> <mn>20</mn> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mspace width="negativethinmathspace" /> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>rms</mtext> </mrow> </msub> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ref</mtext> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>dB</mtext> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L_{p}=20\log _{10}\!\left({\frac {p_{\text{rms}}}{p_{\text{ref}}}}\right)\,{\text{dB}},}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7db7b7d90eb3fe1f6ae82f564c3bac625e4ad57c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:25.98ex; height:6.176ex;" alt="{\displaystyle L_{p}=20\log _{10}\!\left({\frac {p_{\text{rms}}}{p_{\text{ref}}}}\right)\,{\text{dB}},}"></dd></dl> where prms is the <a href="/wiki/Root_mean_square" title="Root mean square">root mean square</a> of the measured sound pressure and pref is the standard reference sound pressure of 20 <a href="/wiki/Micropascal" class="mw-redirect" title="Micropascal">micropascals</a> in air or 1 micropascal in water.<a href="#cite_note-34">[34]</a> Use of the decibel in underwater acoustics leads to confusion, in part because of this difference in reference value.<a href="#cite_note-35">[35]</a><a href="#cite_note-36">[36]</a> <a href="/wiki/Sound_intensity#Sound_intensity_level" title="Sound intensity">Sound intensity</a> is proportional to the square of sound pressure. Therefore, the sound intensity level can also be defined as: <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L_{p}=10\log _{10}\!\left({\frac {I}{I_{\text{ref}}}}\right)\,{\text{dB}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>=</mo> <mn>10</mn> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mspace width="negativethinmathspace" /> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>I</mi> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ref</mtext> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>dB</mtext> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L_{p}=10\log _{10}\!\left({\frac {I}{I_{\text{ref}}}}\right)\,{\text{dB}},}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4933b0543d544464bb11b3b053d1079266c3da40" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:25.05ex; height:6.176ex;" alt="{\displaystyle L_{p}=10\log _{10}\!\left({\frac {I}{I_{\text{ref}}}}\right)\,{\text{dB}},}"></dd></dl> The human ear has a large <a href="/wiki/Dynamic_range" title="Dynamic range">dynamic range</a> in sound reception. The ratio of the sound intensity that causes permanent damage during short exposure to that of the quietest sound that the ear can hear is equal to or greater than 1 trillion (1012).<a href="#cite_note-37">[37]</a> Such large measurement ranges are conveniently expressed in <a href="/wiki/Logarithmic_scale" title="Logarithmic scale">logarithmic scale</a>: the base-10 logarithm of 1012 is 12, which is expressed as a sound intensity level of 120 dB re 1 pW/m2. The reference values of I and p in air have been chosen such that this corresponds approximately to a sound pressure level of 120 dB re 20 <a href="/wiki/Pascal_(unit)" title="Pascal (unit)">μPa</a>. Since the human ear is not equally sensitive to all sound frequencies, the acoustic power spectrum is modified by <a href="/wiki/Frequency_weighting" class="mw-redirect" title="Frequency weighting">frequency weighting</a> (<a href="/wiki/A-weighting" title="A-weighting">A-weighting</a> being the most common standard) to get the weighted acoustic power before converting to a sound level or noise level in decibels.<a href="#cite_note-Pierre-38">[38]</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/Sound_pressure#Examples_of_sound_pressure" title="Sound pressure">Sound pressure § Examples of sound pressure</a></div> <div class="mw-heading mw-heading3"><h3 id="Telephony">Telephony</h3>[<a href="/w/index.php?title=Decibel&action=edit&section=16" title="Edit section: Telephony">edit</a>]</div> The decibel is used in <a href="/wiki/Telephony" title="Telephony">telephony</a> and <a href="/wiki/Audio_signal" title="Audio signal">audio</a>. Similarly to the use in acoustics, a frequency weighted power is often used. For audio noise measurements in electrical circuits, the weightings are called <a href="/wiki/Psophometric_weighting" title="Psophometric weighting">psophometric weightings</a>.<a href="#cite_note-Reeve-39">[39]</a> <div class="mw-heading mw-heading3"><h3 id="Electronics">Electronics</h3>[<a href="/w/index.php?title=Decibel&action=edit&section=17" title="Edit section: Electronics">edit</a>]</div> In electronics, the decibel is often used to express power or amplitude ratios (as for <a href="/wiki/Gain_(electronics)" title="Gain (electronics)">gains</a>) in preference to <a href="/wiki/Arithmetic" title="Arithmetic">arithmetic</a> ratios or <a href="/wiki/Percent" class="mw-redirect" title="Percent">percentages</a>. One advantage is that the total decibel gain of a series of components (such as <a href="/wiki/Amplifier" title="Amplifier">amplifiers</a> and <a href="/wiki/Attenuator_(electronics)" title="Attenuator (electronics)">attenuators</a>) can be calculated simply by summing the decibel gains of the individual components. Similarly, in telecommunications, decibels denote signal gain or loss from a transmitter to a receiver through some medium (<a href="/wiki/Free_space_optical_communication" class="mw-redirect" title="Free space optical communication">free space</a>, <a href="/wiki/Waveguide" title="Waveguide">waveguide</a>, <a href="/wiki/Coaxial_cable" title="Coaxial cable">coaxial cable</a>, <a href="/wiki/Fiber_optics" class="mw-redirect" title="Fiber optics">fiber optics</a>, etc.) using a <a href="/wiki/Link_budget" title="Link budget">link budget</a>. The decibel unit can also be combined with a reference level, often indicated via a suffix, to create an absolute unit of electric power. For example, it can be combined with "m" for "milliwatt" to produce the "<a href="/wiki/DBm" title="DBm">dBm</a>". A power level of 0 dBm corresponds to one milliwatt, and 1 dBm is one decibel greater (about 1.259 mW). In professional audio specifications, a popular unit is the <a href="/wiki/DBu" class="mw-redirect" title="DBu">dBu</a>. This is relative to the <a href="/wiki/Root_mean_square" title="Root mean square">root mean square</a> voltage which delivers 1 mW (0 dBm) into a 600-ohm resistor, or √1 mW × 600 Ω ≈ 0.775 VRMS. When used in a 600-ohm circuit (historically, the standard reference impedance in telephone circuits), dBu and dBm are <a href="#dBu_or_dBv">identical</a>. <div class="mw-heading mw-heading3"><h3 id="Optics">Optics</h3>[<a href="/w/index.php?title=Decibel&action=edit&section=18" title="Edit section: Optics">edit</a>]</div> In an <a href="/wiki/Optical_link" title="Optical link">optical link</a>, if a known amount of <a href="/wiki/Optics" title="Optics">optical</a> power, in <a href="/wiki/DBm" title="DBm">dBm</a> (referenced to 1 mW), is launched into a <a href="/wiki/Optical_fiber" title="Optical fiber">fiber</a>, and the losses, in dB (decibels), of each component (e.g., connectors, splices, and lengths of fiber) are known, the overall link loss may be quickly calculated by addition and subtraction of decibel quantities.<a href="#cite_note-40">[40]</a> In spectrometry and optics, the <a href="/wiki/Absorbance" title="Absorbance">blocking unit</a> used to measure <a href="/wiki/Optical_density" class="mw-redirect" title="Optical density">optical density</a> is equivalent to −1 B. <div class="mw-heading mw-heading3"><h3 id="Video_and_digital_imaging">Video and digital imaging</h3>[<a href="/w/index.php?title=Decibel&action=edit&section=19" title="Edit section: Video and digital imaging">edit</a>]</div> In connection with video and digital <a href="/wiki/Image_sensor" title="Image sensor">image sensors</a>, decibels generally represent ratios of video voltages or digitized light intensities, using 20 log of the ratio, even when the represented intensity (optical power) is directly proportional to the voltage generated by the sensor, not to its square, as in a <a href="/wiki/CCD_imager" class="mw-redirect" title="CCD imager">CCD imager</a> where response voltage is linear in intensity.<a href="#cite_note-41">[41]</a> Thus, a camera <a href="/wiki/Signal-to-noise_ratio" title="Signal-to-noise ratio">signal-to-noise ratio</a> or <a href="/wiki/Dynamic_range" title="Dynamic range">dynamic range</a> quoted as 40 dB represents a ratio of 100:1 between optical signal intensity and optical-equivalent dark-noise intensity, not a 10,000:1 intensity (power) ratio as 40 dB might suggest.<a href="#cite_note-42">[42]</a> Sometimes the 20 log ratio definition is applied to electron counts or photon counts directly, which are proportional to sensor signal amplitude without the need to consider whether the voltage response to intensity is linear.<a href="#cite_note-43">[43]</a> However, as mentioned above, the 10 log intensity convention prevails more generally in physical optics, including fiber optics, so the terminology can become murky between the conventions of digital photographic technology and physics. Most commonly, quantities called "dynamic range" or "signal-to-noise" (of the camera) would be specified in 20 log dB, but in related contexts (e.g. attenuation, gain, intensifier SNR, or rejection ratio) the term should be interpreted cautiously, as confusion of the two units can result in very large misunderstandings of the value. Photographers typically use an alternative base-2 log unit, the <a href="/wiki/F-number#Stops.2C_f-stop_conventions.2C_and_exposure" title="F-number">stop</a>, to describe light intensity ratios or dynamic range. <div class="mw-heading mw-heading2"><h2 id="Suffixes_and_reference_values">Suffixes and reference values </h2>[<a href="/w/index.php?title=Decibel&action=edit&section=20" title="Edit section: Suffixes and reference values">edit</a>]</div> Suffixes are commonly attached to the basic dB unit in order to indicate the reference value by which the ratio is calculated. For example, dBm indicates power measurement relative to 1 milliwatt. In cases where the unit value of the reference is stated, the decibel value is known as "absolute". If the unit value of the reference is not explicitly stated, as in the dB gain of an amplifier, then the decibel value is considered relative. This form of attaching suffixes to dB is widespread in practice, albeit being against the rules promulgated by standards bodies (ISO and IEC),<a href="#cite_note-NIST2008-15">[15]</a> given the "unacceptability of attaching information to units"<a href="#cite_note-44">[a]</a> and the "unacceptability of mixing information with units".<a href="#cite_note-45">[b]</a> The <a href="/wiki/IEC_60027-3" class="mw-redirect" title="IEC 60027-3">IEC 60027-3</a> standard recommends the following format:<a href="#cite_note-IEC60027-3-14">[14]</a> Lx (re xref) or as Lx/xref, where x is the quantity symbol and xref is the value of the reference quantity, e.g., LE (re 1 μV/m) = 20 dB or LE/(1 μV/m) = 20 dB for the <a href="/wiki/Electric_field_strength" class="mw-redirect" title="Electric field strength">electric field strength</a> E relative to 1 μV/m reference value. If the measurement result 20 dB is presented separately, it can be specified using the information in parentheses, which is then part of the surrounding text and not a part of the unit: 20 dB (re: 1 μV/m) or 20 dB (1 μV/m). Outside of documents adhering to SI units, the practice is very common as illustrated by the following examples. There is no general rule, with various discipline-specific practices. Sometimes the suffix is a unit symbol ("W","K","m"), sometimes it is a transliteration of a unit symbol ("uV" instead of μV for microvolt), sometimes it is an acronym for the unit's name ("sm" for square meter, "m" for milliwatt), other times it is a mnemonic for the type of quantity being calculated ("i" for antenna gain with respect to an isotropic antenna, "λ" for anything normalized by the EM wavelength), or otherwise a general attribute or identifier about the nature of the quantity ("A" for <a href="/wiki/A-weighting" title="A-weighting">A-weighted</a> sound pressure level). The suffix is often connected with a <a href="/wiki/Hyphen" title="Hyphen">hyphen</a>, as in "dB‑Hz", or with a space, as in "dB HL", or enclosed in parentheses, as in "dB(HL)", or with no intervening character, as in "dBm" (which is non-compliant with international standards). <div class="mw-heading mw-heading2"><h2 id="List_of_suffixes">List of suffixes</h2>[<a href="/w/index.php?title=Decibel&action=edit&section=21" title="Edit section: List of suffixes">edit</a>]</div> <div class="mw-heading mw-heading3"><h3 id="Voltage">Voltage</h3>[<a href="/w/index.php?title=Decibel&action=edit&section=22" title="Edit section: Voltage">edit</a>]</div> Since the decibel is defined with respect to <a href="/wiki/Power_(physics)" title="Power (physics)">power</a>, not <a href="/wiki/Amplitude" title="Amplitude">amplitude</a>, conversions of voltage ratios to decibels must square the amplitude, or use the factor of 20 instead of 10, as discussed above. <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Relationship_between_dBu_and_dBm.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c7/Relationship_between_dBu_and_dBm.png/280px-Relationship_between_dBu_and_dBm.png" decoding="async" width="280" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c7/Relationship_between_dBu_and_dBm.png/420px-Relationship_between_dBu_and_dBm.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c7/Relationship_between_dBu_and_dBm.png/560px-Relationship_between_dBu_and_dBm.png 2x" data-file-width="1866" data-file-height="533" /></a><figcaption>A schematic showing the relationship between <a href="/wiki/DBu" class="mw-redirect" title="DBu">dB u</a> (the <a href="/wiki/Voltage_source" title="Voltage source">voltage source</a>) and <a href="/wiki/DBm" title="DBm">dB m</a> (the power dissipated as <a href="/wiki/Heat" title="Heat">heat</a> by the 600 Ω <a href="/wiki/Resistor" title="Resistor">resistor</a>)</figcaption></figure> <dl><dt>dB V</dt> <dd>dB(V<a href="/wiki/Root_mean_square" title="Root mean square">RMS</a>) – <a href="/wiki/Volt" title="Volt">voltage</a> relative to 1 volt, regardless of impedance.<a href="#cite_note-clqgmk-3">[3]</a> This is used to measure microphone sensitivity, and also to specify the consumer <a href="/wiki/Line_level" title="Line level">line-level</a> of −10 dBV, in order to reduce manufacturing costs relative to equipment using a +4 dBu line-level signal.<a href="#cite_note-46">[44]</a></dd></dl> <dl><dt>dB u or dB v</dt> <dd><a href="/wiki/Root_mean_square" title="Root mean square">RMS</a> <a href="/wiki/Volt" title="Volt">voltage</a> relative to <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V={\sqrt {600\ \Omega \ \cdot \ 0.001\ {\mathsf {W}}\;}}\approx 0.7746\ {\mathsf {V}}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>600</mn> <mtext> </mtext> <mi mathvariant="normal">Ω</mi> <mtext> </mtext> <mo>⋅</mo> <mtext> </mtext> <mn>0.001</mn> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">W</mi> </mrow> </mrow> <mspace width="thickmathspace" /> </msqrt> </mrow> <mo>≈</mo> <mn>0.7746</mn> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">V</mi> </mrow> </mrow> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V={\sqrt {600\ \Omega \ \cdot \ 0.001\ {\mathsf {W}}\;}}\approx 0.7746\ {\mathsf {V}}\ }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c65df97d078f6b211d14f0f798f11ceb2becd225" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:36.393ex; height:3.009ex;" alt="{\displaystyle V={\sqrt {600\ \Omega \ \cdot \ 0.001\ {\mathsf {W}}\;}}\approx 0.7746\ {\mathsf {V}}\ }"> (i.e. the voltage that would dissipate 1 mW into a 600 Ω load). An <a href="/wiki/Root_mean_square" title="Root mean square">RMS</a> voltage of 1 V therefore corresponds to <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ 20\cdot \log _{10}\left({\frac {\ 1\ V_{\mathsf {RMS}}\ }{{\sqrt {0.6\ }}\ V}}\right)=2.218\ {\mathsf {dB_{u}}}~.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mn>20</mn> <mo>⋅</mo> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mtext> </mtext> <mn>1</mn> <mtext> </mtext> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">R</mi> <mi mathvariant="sans-serif">M</mi> <mi mathvariant="sans-serif">S</mi> </mrow> </mrow> </msub> <mtext> </mtext> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>0.6</mn> <mtext> </mtext> </msqrt> </mrow> <mtext> </mtext> <mi>V</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>2.218</mn> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">d</mi> <msub> <mi mathvariant="sans-serif">B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">u</mi> </mrow> </msub> </mrow> </mrow> <mtext> </mtext> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ 20\cdot \log _{10}\left({\frac {\ 1\ V_{\mathsf {RMS}}\ }{{\sqrt {0.6\ }}\ V}}\right)=2.218\ {\mathsf {dB_{u}}}~.}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9fe31d40a63eafc6454bea2524dee6ca977b4cbb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:35.633ex; height:6.509ex;" alt="{\displaystyle \ 20\cdot \log _{10}\left({\frac {\ 1\ V_{\mathsf {RMS}}\ }{{\sqrt {0.6\ }}\ V}}\right)=2.218\ {\mathsf {dB_{u}}}~.}"><a href="#cite_note-clqgmk-3">[3]</a> Originally dB v , it was changed to dB u to avoid confusion with dB V.<a href="#cite_note-47">[45]</a> The v comes from volt, while u comes from the <a href="/wiki/Volume_unit" class="mw-redirect" title="Volume unit">volume unit</a> displayed on a <a href="/wiki/VU_meter" title="VU meter">VU meter</a>.<a href="#cite_note-48">[46]</a><div class="paragraphbreak" style="margin-top:0.5em"></div>dB u can be used as a measure of voltage, regardless of impedance, but is derived from a 600 Ω load dissipating 0 dB m (1 mW). The reference voltage comes from the computation <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ 7{\mathsf {V}}={\sqrt {R\cdot P\ }}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mn>7</mn> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">V</mi> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>R</mi> <mo>⋅</mo> <mi>P</mi> <mtext> </mtext> </msqrt> </mrow> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ 7{\mathsf {V}}={\sqrt {R\cdot P\ }}\ }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5ea3de4f2eef584bd6b4c6324cfe8586ce081136" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.678ex; height:3.009ex;" alt="{\displaystyle \ 7{\mathsf {V}}={\sqrt {R\cdot P\ }}\ }"> where <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ R\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>R</mi> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ R\ }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bb46873223ab58ba83c959c590be4a27cf67bd6b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.925ex; height:2.176ex;" alt="{\displaystyle \ R\ }"> is the resistance and <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ P\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>P</mi> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ P\ }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fed61bf9e97b9304dbbb99ffbb2cd93cdd0b4b23" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.907ex; height:2.176ex;" alt="{\displaystyle \ P\ }"> is the power.</dd></dl> <dl><dd>In <a href="/wiki/Professional_audio" title="Professional audio">professional audio</a>, equipment may be calibrated to indicate a "0" on the VU meters some finite time after a signal has been applied at an amplitude of +4 dBu. Consumer equipment typically uses a lower "nominal" signal level of −10 dB V .<a href="#cite_note-49">[47]</a> Therefore, many devices offer dual voltage operation (with different gain or "trim" settings) for interoperability reasons. A switch or adjustment that covers at least the range between +4 dB u and −10 dB V is common in professional equipment.</dd></dl> <dl><dt>dB m0s</dt> <dd>Defined by Recommendation ITU-R V.574 ; dB mV: dB(mVRMS) – <a href="/wiki/Root_mean_square" title="Root mean square">root mean square</a> <a href="/wiki/Volt" title="Volt">voltage</a> relative to 1 millivolt across 75 Ω.<a href="#cite_note-50">[48]</a> Widely used in <a href="/wiki/Cable_television" title="Cable television">cable television</a> networks, where the nominal strength of a single TV signal at the receiver terminals is about 0 dB mV. Cable TV uses 75 Ω coaxial cable, so 0 dB mV corresponds to −78.75 dB W ( −48.75 dB m ) or approximately 13 nW.</dd></dl> <dl><dt>dB μV or dB uV</dt> <dd>dB(μV<a href="/wiki/Root_mean_square" title="Root mean square">RMS</a>) – <a href="/wiki/Volt" title="Volt">voltage</a> relative to 1 microvolt. Widely used in television and aerial amplifier specifications. 60 dBμV = 0 dB mV.</dd></dl> <div class="mw-heading mw-heading3"><h3 id="Acoustics_2">Acoustics</h3>[<a href="/w/index.php?title=Decibel&action=edit&section=23" title="Edit section: Acoustics">edit</a>]</div> Probably the most common usage of "decibels" in reference to sound level is dB SPL, <a href="/wiki/Sound_pressure_level" class="mw-redirect" title="Sound pressure level">sound pressure level</a> referenced to the nominal threshold of human hearing:<a href="#cite_note-51">[49]</a> The measures of pressure (a root-power quantity) use the factor of 20, and the measures of power (e.g. dB SIL and dB SWL) use the factor of 10. <dl><dt>dB SPL</dt> <dd>dB SPL (<a href="/wiki/Sound_pressure_level" class="mw-redirect" title="Sound pressure level">sound pressure level</a>) – for sound in air and other gases, relative to 20 micropascals (μPa), or 2×10−5 Pa, approximately the quietest sound a human can hear. For <a href="/wiki/Underwater_acoustics" title="Underwater acoustics">sound in water</a> and other liquids, a reference pressure of 1 μPa is used.<a href="#cite_note-52">[50]</a><div class="paragraphbreak" style="margin-top:0.5em"></div> An RMS sound pressure of one pascal corresponds to a level of 94 dB SPL.</dd> <dt>dB SIL</dt> <dd>dB <a href="/wiki/Sound_intensity_level" class="mw-redirect" title="Sound intensity level">sound intensity level</a> – relative to 10−12 W/m2, which is roughly the <a href="/wiki/Threshold_of_human_hearing" class="mw-redirect" title="Threshold of human hearing">threshold of human hearing</a> in air.</dd> <dt>dB SWL</dt> <dd>dB <a href="/wiki/Sound_power_level" class="mw-redirect" title="Sound power level">sound power level</a> – relative to 10−12 W.</dd> <dt>dB A, dB B, and dB C</dt> <dd>These symbols are often used to denote the use of different <a href="/wiki/Weighting_filter" title="Weighting filter">weighting filters</a>, used to approximate the human ear's <a href="/wiki/Stimulus_(psychology)" title="Stimulus (psychology)">response</a> to sound, although the measurement is still in dB (SPL). These measurements usually refer to noise and its effects on humans and other animals, and they are widely used in industry while discussing noise control issues, regulations and environmental standards. Other variations that may be seen are dB A or <a href="/wiki/A-weighting" title="A-weighting">dB(A)</a>. According to standards from the International Electro-technical Committee (<a href="/wiki/IEC_61672" class="mw-redirect" title="IEC 61672">IEC 61672-2013</a>)<a href="#cite_note-53">[51]</a> and the American National Standards Institute, <a href="/w/index.php?title=ANSI_S1.4&action=edit&redlink=1" class="new" title="ANSI S1.4 (page does not exist)">ANSI S1.4</a>,<a href="#cite_note-54">[52]</a> the preferred usage is to write L A = x dB . Nevertheless, the units dB A and dB(A) are still commonly used as a shorthand for A‑weighted measurements. Compare <a href="/wiki/DBc" title="DBc">dB c</a>, used in telecommunications.</dd> <dt>dB HL</dt> <dd>dB <a href="/wiki/Hearing_level" title="Hearing level">hearing level</a> is used in <a href="/wiki/Audiogram" title="Audiogram">audiograms</a> as a measure of hearing loss. The reference level varies with frequency according to a <a href="/wiki/Minimum_audibility_curve" title="Minimum audibility curve">minimum audibility curve</a> as defined in ANSI and other standards, such that the resulting audiogram shows deviation from what is regarded as 'normal' hearing.[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>]</dd> <dt>dB Q</dt> <dd>sometimes used to denote weighted noise level, commonly using the <a href="/wiki/ITU-R_468_noise_weighting" title="ITU-R 468 noise weighting">ITU-R 468 noise weighting</a>[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>]</dd> <dt>dB pp</dt> <dd>relative to the peak to peak sound pressure.<a href="#cite_note-55">[53]</a></dd> <dt>dB G</dt> <dd>G‑weighted spectrum<a href="#cite_note-56">[54]</a></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Audio_electronics">Audio electronics</h3>[<a href="/w/index.php?title=Decibel&action=edit&section=24" title="Edit section: Audio electronics">edit</a>]</div> See also dB V and dB u above. <dl><dt><a href="/wiki/DBm" title="DBm">dB m</a></dt> <dd>dB(mW) – power relative to 1 <a href="/wiki/Milliwatt" class="mw-redirect" title="Milliwatt">milliwatt</a>. In audio and telephony, dB m is typically referenced relative to a 600 Ω impedance,<a href="#cite_note-57">[55]</a> which corresponds to a voltage level of 0.775 volts or 775 millivolts.</dd> <dt><a href="/wiki/DBm0" title="DBm0">dB m0</a></dt> <dd>Power in dB m (described above) measured at a <a href="/wiki/Zero_transmission_level_point" class="mw-redirect" title="Zero transmission level point">zero transmission level point</a>.</dd> <dt><a href="/wiki/DBFS" title="DBFS">dB FS</a></dt> <dd>dB(<a href="/wiki/Full_scale" title="Full scale">full scale</a>) – the <a href="/wiki/Amplitude" title="Amplitude">amplitude</a> of a signal compared with the maximum which a device can handle before <a href="/wiki/Clipping_(signal_processing)" title="Clipping (signal processing)">clipping</a> occurs. Full-scale may be defined as the power level of a full-scale <a href="/wiki/Sine_wave" title="Sine wave">sinusoid</a> or alternatively a full-scale <a href="/wiki/Square_wave" title="Square wave">square wave</a>. A signal measured with reference to a full-scale sine-wave appears 3 dB weaker when referenced to a full-scale square wave, thus: 0 dBFS(fullscale sine wave) = −3 dB FS (fullscale square wave).</dd> <dt>dB VU</dt> <dd>dB <a href="/wiki/Volume_unit" class="mw-redirect" title="Volume unit">volume unit</a><a href="#cite_note-58">[56]</a></dd> <dt>dB TP</dt> <dd>dB(true peak) – <a href="/wiki/Peak_amplitude" class="mw-redirect" title="Peak amplitude">peak amplitude</a> of a signal compared with the maximum which a device can handle before clipping occurs.<a href="#cite_note-59">[57]</a> In digital systems, 0 dB TP would equal the highest level (number) the processor is capable of representing. Measured values are always negative or zero, since they are less than or equal to full-scale.</dd></dl> <div class="mw-heading mw-heading3"><h3 id="Radar">Radar</h3>[<a href="/w/index.php?title=Decibel&action=edit&section=25" title="Edit section: Radar">edit</a>]</div> <dl><dt><a href="/wiki/DBZ_(meteorology)" title="DBZ (meteorology)">dB Z</a></dt> <dd>dB(Z) – decibel relative to Z = 1 mm6 ⋅m−3 :<a href="#cite_note-60">[58]</a> energy of reflectivity (weather radar), related to the amount of transmitted power returned to the radar receiver. Values above 20 dB Z usually indicate falling precipitation.<a href="#cite_note-61">[59]</a></dd> <dt>dB sm</dt> <dd>dB(m²) – decibel relative to one square meter: measure of the <a href="/wiki/Radar_cross_section" title="Radar cross section">radar cross section</a> (RCS) of a target. The power reflected by the target is proportional to its RCS. "Stealth" aircraft and insects have negative RCS measured in dB sm , large flat plates or non-stealthy aircraft have positive values.<a href="#cite_note-62">[60]</a></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Radio_power,_energy,_and_field_strength">Radio power, energy, and field strength</h3>[<a href="/w/index.php?title=Decibel&action=edit&section=26" title="Edit section: Radio power, energy, and field strength">edit</a>]</div> <dl><dt><a href="/wiki/DBc" title="DBc">dB c</a></dt> <dd>relative to carrier – in <a href="/wiki/Telecommunications" title="Telecommunications">telecommunications</a>, this indicates the relative levels of noise or sideband power, compared with the carrier power. Compare dB C, used in acoustics.</dd> <dt>dB pp</dt> <dd>relative to the maximum value of the peak power.</dd> <dt>dB J</dt> <dd>energy relative to 1 <a href="/wiki/Joule" title="Joule">joule</a>. 1 joule = 1 watt second = 1 watt per hertz, so <a href="/wiki/Power_spectral_density" class="mw-redirect" title="Power spectral density">power spectral density</a> can be expressed in dB J .</dd> <dt><a href="/wiki/DBm" title="DBm">dB m</a></dt> <dd>dB(mW) – power relative to 1 <a href="/wiki/Milliwatt" class="mw-redirect" title="Milliwatt">milliwatt</a>. In the radio field, dB m is usually referenced to a 50 Ω load, with the resultant voltage being 0.224 volts.<a href="#cite_note-63">[61]</a></dd> <dt>dB μV/m , dB uV/m , or dB μ </dt> <dd><a href="#cite_note-dBμ-64">[62]</a> dB(μV/m) – <a href="/wiki/Electric_field_strength" class="mw-redirect" title="Electric field strength">electric field strength</a> relative to 1 <a href="/wiki/Microvolt" class="mw-redirect" title="Microvolt">microvolt</a> per <a href="/wiki/Meter" class="mw-redirect" title="Meter">meter</a>. The unit is often used to specify the signal strength of a <a href="/wiki/Television" title="Television">television</a> <a href="/wiki/Broadcast" class="mw-redirect" title="Broadcast">broadcast</a> at a receiving site (the signal measured at the antenna output is reported in dBμ V).</dd> <dt>dB f</dt> <dd>dB(fW) – power relative to 1 <a href="/wiki/Femtowatt" class="mw-redirect" title="Femtowatt">femtowatt</a>.</dd> <dt>dB W</dt> <dd>dB(W) – power relative to 1 <a href="/wiki/Watt" title="Watt">watt</a>.</dd> <dt>dB k</dt> <dd>dB(kW) – power relative to 1 <a href="/wiki/Kilowatt" class="mw-redirect" title="Kilowatt">kilowatt</a>.</dd> <dt>dB e</dt> <dd>dB electrical.</dd> <dt>dB o</dt> <dd>dB optical. A change of 1 dB o in optical power can result in a change of up to 2 dB e in electrical signal power in a system that is thermal noise limited.<a href="#cite_note-65">[63]</a></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Antenna_measurements">Antenna measurements</h3>[<a href="/w/index.php?title=Decibel&action=edit&section=27" title="Edit section: Antenna measurements">edit</a>]</div> <dl><dt>dB i</dt> <dd>dB(isotropic) – the <a href="/wiki/Antenna_gain" class="mw-redirect" title="Antenna gain">gain</a> of an antenna compared with the gain of a theoretical <a href="/wiki/Isotropic_antenna" class="mw-redirect" title="Isotropic antenna">isotropic antenna</a>, which uniformly distributes energy in all directions. <a href="/wiki/Linear_polarization" title="Linear polarization">Linear polarization</a> of the EM field is assumed unless noted otherwise.</dd> <dt>dB d</dt> <dd>dB(dipole) – the <a href="/wiki/Antenna_gain" class="mw-redirect" title="Antenna gain">gain</a> of an <a href="/wiki/Antenna_(electronics)" class="mw-redirect" title="Antenna (electronics)">antenna</a> compared with the gain a half-wave <a href="/wiki/Dipole_antenna" title="Dipole antenna">dipole antenna</a>. 0 dBd = 2.15 dBi</dd> <dt>dB iC</dt> <dd>dB(isotropic circular) – the gain of an antenna compared to the gain of a theoretical <a href="/wiki/Circular_polarization" title="Circular polarization">circularly polarized</a> isotropic antenna. There is no fixed conversion rule between dBiC and dBi, as it depends on the receiving antenna and the field polarization.</dd> <dt>dB q</dt> <dd>dB(quarterwave) – the <a href="/wiki/Antenna_gain" class="mw-redirect" title="Antenna gain">gain</a> of an antenna compared to the gain of a quarter wavelength whip. Rarely used, except in some marketing material; 0 dBq = −0.85 dBi </dd> <dt>dB sm</dt> <dd>dB m², dB(m²) – decibels relative to one square meter: A measure of the <a href="/wiki/Antenna_effective_area" class="mw-redirect" title="Antenna effective area">effective area</a> for capturing signals of the antenna.<a href="#cite_note-66">[64]</a></dd> <dt>dB m⁻¹</dt> <dd>dB(m−1) – decibels relative to reciprocal of meter: measure of the <a href="/wiki/Antenna_factor" title="Antenna factor">antenna factor</a>.</dd></dl> <div class="mw-heading mw-heading3"><h3 id="Other_measurements">Other measurements</h3>[<a href="/w/index.php?title=Decibel&action=edit&section=28" title="Edit section: Other measurements">edit</a>]</div> <dl><dt>dB Hz or dB‑Hz</dt> <dd>dB(Hz) – bandwidth relative to one hertz. E.g., 20 dB‑Hz corresponds to a bandwidth of 100 Hz. Commonly used in <a href="/wiki/Link_budget" title="Link budget">link budget</a> calculations. Also used in <a href="/wiki/Carrier-to-receiver_noise_density" class="mw-redirect" title="Carrier-to-receiver noise density">carrier-to-noise-density ratio</a> (not to be confused with <a href="/wiki/Carrier-to-noise_ratio" title="Carrier-to-noise ratio">carrier-to-noise ratio</a>, in dB).</dd> <dt><a href="/wiki/DBFS" title="DBFS">dB ov or dB O</a></dt> <dd>dB(overload) – the <a href="/wiki/Amplitude" title="Amplitude">amplitude</a> of a signal (usually audio) compared with the maximum which a device can handle before <a href="/wiki/Clipping_(signal_processing)" title="Clipping (signal processing)">clipping</a> occurs. Similar to dB FS, but also applicable to analog systems. According to ITU-T Rec. G.100.1 the level in dB ov of a digital system is defined as: <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ L_{\mathsf {ov}}=10\log _{10}\left({\frac {P}{\ P_{\mathsf {max}}\ }}\right)\ [{\mathsf {dB_{ov}}}]\ ,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">o</mi> <mi mathvariant="sans-serif">v</mi> </mrow> </mrow> </msub> <mo>=</mo> <mn>10</mn> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>P</mi> <mrow> <mtext> </mtext> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">m</mi> <mi mathvariant="sans-serif">a</mi> <mi mathvariant="sans-serif">x</mi> </mrow> </mrow> </msub> <mtext> </mtext> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mtext> </mtext> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">d</mi> <msub> <mi mathvariant="sans-serif">B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">o</mi> <mi mathvariant="sans-serif">v</mi> </mrow> </msub> </mrow> </mrow> <mo stretchy="false">]</mo> <mtext> </mtext> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ L_{\mathsf {ov}}=10\log _{10}\left({\frac {P}{\ P_{\mathsf {max}}\ }}\right)\ [{\mathsf {dB_{ov}}}]\ ,}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d6d67f7325af5c9dd1590f22ebf7291327e6ce1b" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:32.297ex; height:6.176ex;" alt="{\displaystyle \ L_{\mathsf {ov}}=10\log _{10}\left({\frac {P}{\ P_{\mathsf {max}}\ }}\right)\ [{\mathsf {dB_{ov}}}]\ ,}"> with the maximum signal power <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ P_{\mathsf {max}}=1.0\ ,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">m</mi> <mi mathvariant="sans-serif">a</mi> <mi mathvariant="sans-serif">x</mi> </mrow> </mrow> </msub> <mo>=</mo> <mn>1.0</mn> <mtext> </mtext> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ P_{\mathsf {max}}=1.0\ ,}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eab8455435d04e6432805e3e7680c56715b2dc68" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.456ex; height:2.509ex;" alt="{\displaystyle \ P_{\mathsf {max}}=1.0\ ,}"> for a rectangular signal with the maximum amplitude <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ x_{\mathsf {over}}~.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">o</mi> <mi mathvariant="sans-serif">v</mi> <mi mathvariant="sans-serif">e</mi> <mi mathvariant="sans-serif">r</mi> </mrow> </mrow> </msub> <mtext> </mtext> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ x_{\mathsf {over}}~.}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d0611df7607d11b4b40e4b59096a89782d1131f2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.242ex; height:2.009ex;" alt="{\displaystyle \ x_{\mathsf {over}}~.}"> The level of a tone with a digital amplitude (peak value) of <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ x_{\mathsf {over}}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">o</mi> <mi mathvariant="sans-serif">v</mi> <mi mathvariant="sans-serif">e</mi> <mi mathvariant="sans-serif">r</mi> </mrow> </mrow> </msub> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ x_{\mathsf {over}}\ }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/026f682d7d84d2a9f070898f12e3e40c53848d0b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.596ex; height:2.009ex;" alt="{\displaystyle \ x_{\mathsf {over}}\ }"> is therefore <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ L_{\mathsf {ov}}=-3.01\ {\mathsf {dB_{ov}}}~.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">o</mi> <mi mathvariant="sans-serif">v</mi> </mrow> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mn>3.01</mn> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">d</mi> <msub> <mi mathvariant="sans-serif">B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">o</mi> <mi mathvariant="sans-serif">v</mi> </mrow> </msub> </mrow> </mrow> <mtext> </mtext> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ L_{\mathsf {ov}}=-3.01\ {\mathsf {dB_{ov}}}~.}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5263b7471937e3c14a167e4be5567671ff5d8126" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:19.389ex; height:2.509ex;" alt="{\displaystyle \ L_{\mathsf {ov}}=-3.01\ {\mathsf {dB_{ov}}}~.}"><a href="#cite_note-67">[65]</a></dd> <dt>dB r</dt> <dd>dB(relative) – simply a relative difference from something else, which is made apparent in context. The difference of a filter's response to nominal levels, for instance.</dd> <dt><a href="/wiki/DBrn" title="DBrn">dB rn</a></dt> <dd>dB above <a href="/wiki/Reference_noise" title="Reference noise">reference noise</a>. See also dB rnC</dd> <dt>dB rnC</dt> <dd>dB(rnC) represents an audio level measurement, typically in a telephone circuit, relative to a −90 dB m reference level, with the measurement of this level frequency-weighted by a standard C-message weighting filter. The C-message weighting filter was chiefly used in North America. The <a href="/wiki/Psophometric_weighting" title="Psophometric weighting">psophometric</a> filter is used for this purpose on international circuits.<a href="#cite_note-68">[c]</a><a href="#cite_note-69">[66]</a></dd> <dt>dB K</dt> <dd>dB(K) – decibels relative to 1 <a href="/wiki/Kelvin" title="Kelvin">K</a>; used to express <a href="/wiki/Noise_temperature" title="Noise temperature">noise temperature</a>.<a href="#cite_note-70">[67]</a></dd> <dt>dB K⁻¹ or dB/K</dt> <dd>dB(K⁻¹) – decibels relative to 1 K⁻¹.<a href="#cite_note-71">[68]</a> — not decibels per Kelvin: Used for the <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035">⁠ G / T ⁠ <a href="/wiki/G/T" class="mw-redirect" title="G/T">(G/T) factor</a>, a <a href="/wiki/Figure_of_merit" title="Figure of merit">figure of merit</a> used in <a href="/wiki/Satellite_communications" class="mw-redirect" title="Satellite communications">satellite communications</a>, relating the <a href="/wiki/Antenna_gain" class="mw-redirect" title="Antenna gain">antenna gain</a> G to the <a href="/wiki/Receiver_(radio)" class="mw-redirect" title="Receiver (radio)">receiver</a> system noise equivalent temperature T.<a href="#cite_note-72">[69]</a><a href="#cite_note-73">[70]</a></dd></dl> <div class="mw-heading mw-heading3"><h3 id="List_of_suffixes_in_alphabetical_order">List of suffixes in alphabetical order</h3>[<a href="/w/index.php?title=Decibel&action=edit&section=29" title="Edit section: List of suffixes in alphabetical order">edit</a>]</div> <div class="mw-heading mw-heading4"><h4 id="Unpunctuated_suffixes">Unpunctuated suffixes</h4>[<a href="/w/index.php?title=Decibel&action=edit&section=30" title="Edit section: Unpunctuated suffixes">edit</a>]</div> <dl><dt>dB A</dt> <dd>see <a href="/wiki/DB(A)" class="mw-redirect" title="DB(A)">dB(A)</a>.</dd> <dt>dB a</dt> <dd>see <a href="/wiki/DBrn_adjusted" class="mw-redirect" title="DBrn adjusted">dB rn adjusted</a>.</dd> <dt>dB B</dt> <dd>see <a href="/wiki/DB(B)" class="mw-redirect" title="DB(B)">dB(B)</a>.</dd> <dt><a href="/wiki/DBc" title="DBc">dB c</a></dt> <dd>relative to carrier – in <a href="/wiki/Telecommunications" title="Telecommunications">telecommunications</a>, this indicates the relative levels of noise or sideband power, compared with the carrier power.</dd> <dt>dB C</dt> <dd>see <a href="/wiki/DB(C)" class="mw-redirect" title="DB(C)">dB(C)</a>.</dd> <dt>dB D</dt> <dd>see <a href="/wiki/DB(D)" class="mw-redirect" title="DB(D)">dB(D)</a>.</dd> <dt>dB d</dt> <dd>dB(dipole) – the forward gain of an <a href="/wiki/Antenna_(electronics)" class="mw-redirect" title="Antenna (electronics)">antenna</a> compared with a half-wave <a href="/wiki/Dipole_antenna" title="Dipole antenna">dipole antenna</a>. 0 dBd = 2.15 dB i</dd> <dt>dB e</dt> <dd>dB electrical.</dd> <dt>dB f</dt> <dd>dB(fW) – power relative to 1 <a href="/wiki/Femtowatt" class="mw-redirect" title="Femtowatt">femtowatt</a>.</dd> <dt><a href="/wiki/DBFS" title="DBFS">dB FS</a></dt> <dd>dB(<a href="/wiki/Full_scale" title="Full scale">full scale</a>) – the <a href="/wiki/Amplitude" title="Amplitude">amplitude</a> of a signal compared with the maximum which a device can handle before <a href="/wiki/Clipping_(signal_processing)" title="Clipping (signal processing)">clipping</a> occurs. Full-scale may be defined as the power level of a full-scale <a href="/wiki/Sine_wave" title="Sine wave">sinusoid</a> or alternatively a full-scale <a href="/wiki/Square_wave" title="Square wave">square wave</a>. A signal measured with reference to a full-scale sine-wave appears 3 dB weaker when referenced to a full-scale square wave, thus: 0 dB FS (fullscale sine wave) = −3 dB FS (full-scale square wave).</dd> <dt>dB G</dt> <dd><a href="/wiki/G-weighted" class="mw-redirect" title="G-weighted">G-weighted</a> spectrum</dd> <dt>dB i</dt> <dd>dB(isotropic) – the forward <a href="/wiki/Antenna_gain" class="mw-redirect" title="Antenna gain">gain of an antenna</a> compared with the hypothetical <a href="/wiki/Isotropic_antenna" class="mw-redirect" title="Isotropic antenna">isotropic antenna</a>, which uniformly distributes energy in all directions. <a href="/wiki/Linear_polarization" title="Linear polarization">Linear polarization</a> of the EM field is assumed unless noted otherwise.</dd> <dt>dB iC</dt> <dd>dB(isotropic circular) – the forward gain of an antenna compared to a <a href="/wiki/Circular_polarization" title="Circular polarization">circularly polarized</a> isotropic antenna. There is no fixed conversion rule between dB iC and dB i , as it depends on the receiving antenna and the field polarization.</dd> <dt>dB J</dt> <dd>energy relative to 1 <a href="/wiki/Joule" title="Joule">joule</a>: 1 joule = 1 watt-second = 1 watt per hertz, so <a href="/wiki/Power_spectral_density" class="mw-redirect" title="Power spectral density">power spectral density</a> can be expressed in dB J .</dd> <dt>dB k</dt> <dd>dB(kW) – power relative to 1 <a href="/wiki/Kilowatt" class="mw-redirect" title="Kilowatt">kilowatt</a>.</dd> <dt>dB K</dt> <dd>dB(K) – decibels relative to <a href="/wiki/Kelvin" title="Kelvin">kelvin</a>: Used to express <a href="/wiki/Noise_temperature" title="Noise temperature">noise temperature</a>.</dd> <dt><a href="/wiki/DBm" title="DBm">dB m</a></dt> <dd>dB(mW) – power relative to 1 <a href="/wiki/Milliwatt" class="mw-redirect" title="Milliwatt">milliwatt</a>.</dd> <dt>dB m² or dB sm</dt> <dd>dB(m²) – decibel relative to one square meter</dd> <dt><a href="/wiki/DBm0" title="DBm0">dB m0</a></dt> <dd>Power in dB m measured at a zero transmission level point.</dd> <dt>dB m0s</dt> <dd>Defined by Recommendation ITU-R V.574.</dd> <dt>dB mV</dt> <dd>dB(mV<a href="/wiki/Root_mean_square" title="Root mean square">RMS</a>) – <a href="/wiki/Volt" title="Volt">voltage</a> relative to 1 millivolt across 75 Ω.</dd> <dt>dB o</dt> <dd>dB optical. A change of 1 dB o in optical power can result in a change of up to 2 dB e in electrical signal power in system that is thermal noise limited.</dd> <dt>dB O</dt> <dd>see dB ov</dd> <dt>dB ov or dB O</dt> <dd>dB(overload) – the <a href="/wiki/Amplitude" title="Amplitude">amplitude</a> of a signal (usually audio) compared with the maximum which a device can handle before <a href="/wiki/Clipping_(signal_processing)" title="Clipping (signal processing)">clipping</a> occurs.</dd> <dt>dB pp</dt> <dd>relative to the peak to peak <a href="/wiki/Sound_pressure" title="Sound pressure">sound pressure</a>.</dd> <dt>dB pp</dt> <dd>relative to the maximum value of the peak <a href="/wiki/Electrical_power" class="mw-redirect" title="Electrical power">electrical power</a>.</dd> <dt>dB q</dt> <dd>dB(quarterwave) – the forward gain of an antenna compared to a quarter wavelength whip. Rarely used, except in some marketing material. 0 dBq = −0.85 dB i</dd> <dt>dB r</dt> <dd>dB(relative) – simply a relative difference from something else, which is made apparent in context. The difference of a filter's response to nominal levels, for instance.</dd> <dt><a href="/wiki/DBrn" title="DBrn">dB rn</a></dt> <dd>dB above <a href="/wiki/Reference_noise" title="Reference noise">reference noise</a>. See also dB rnC</dd> <dt>dB rnC</dt> <dd>dB rnC represents an audio level measurement, typically in a telephone circuit, relative to the <a href="/wiki/Circuit_noise_level" title="Circuit noise level">circuit noise level</a>, with the measurement of this level frequency-weighted by a standard C-message weighting filter. The C-message weighting filter was chiefly used in North America.</dd> <dt>dB sm</dt> <dd>see dB m²</dd> <dt>dB TP</dt> <dd>dB(true peak) – <a href="/wiki/Peak_amplitude" class="mw-redirect" title="Peak amplitude">peak amplitude</a> of a signal compared with the maximum which a device can handle before clipping occurs.</dd> <dt>dB u or dB v</dt> <dd><a href="/wiki/Root_mean_square" title="Root mean square">RMS</a> <a href="/wiki/Volt" title="Volt">voltage</a> relative to <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ {\sqrt {0.6\;}}\ {\mathsf {V}}\ \approx 0.7746\ {\mathsf {V}}\ \approx -2.218\ {\mathsf {dB_{V}}}~.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>0.6</mn> <mspace width="thickmathspace" /> </msqrt> </mrow> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">V</mi> </mrow> </mrow> <mtext> </mtext> <mo>≈</mo> <mn>0.7746</mn> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">V</mi> </mrow> </mrow> <mtext> </mtext> <mo>≈</mo> <mo>−</mo> <mn>2.218</mn> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">d</mi> <msub> <mi mathvariant="sans-serif">B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">V</mi> </mrow> </msub> </mrow> </mrow> <mtext> </mtext> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ {\sqrt {0.6\;}}\ {\mathsf {V}}\ \approx 0.7746\ {\mathsf {V}}\ \approx -2.218\ {\mathsf {dB_{V}}}~.}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2995bece0b7a9cd1002c69394847b4396b0837a2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:37.206ex; height:2.843ex;" alt="{\displaystyle \ {\sqrt {0.6\;}}\ {\mathsf {V}}\ \approx 0.7746\ {\mathsf {V}}\ \approx -2.218\ {\mathsf {dB_{V}}}~.}"></dd> <dt>dB u0s</dt> <dd>Defined by Recommendation ITU-R V.574.</dd> <dt>dB uV</dt> <dd>see dB μV</dd> <dt>dB uV/m</dt> <dd>see dB μV/m</dd> <dt>dB v</dt> <dd>see dB u</dd> <dt>dB V</dt> <dd>dB(V<a href="/wiki/Root_mean_square" title="Root mean square">RMS</a>) – <a href="/wiki/Volt" title="Volt">voltage</a> relative to 1 volt, regardless of impedance.</dd> <dt>dB VU</dt> <dd>dB(VU) dB <a href="/wiki/Volume_unit" class="mw-redirect" title="Volume unit">volume unit</a></dd> <dt>dB W</dt> <dd>dB(W) – power relative to 1 <a href="/wiki/Watt" title="Watt">watt</a>.</dd> <dt>dB W·m⁻²·Hz⁻¹</dt> <dd><a href="/wiki/Jansky#dBW·m−2·Hz−1" title="Jansky">spectral density</a> relative to 1 W·m⁻²·Hz⁻¹<a href="#cite_note-74">[71]</a></dd> <dt><a href="/wiki/DBZ_(meteorology)" title="DBZ (meteorology)">dB Z</a></dt> <dd>dB(Z) – decibel relative to Z = 1 mm6⋅m−3</dd> <dt>dB μ</dt> <dd>see dB μV/m</dd> <dt>dB μV or dB uV</dt> <dd>dB(μV<a href="/wiki/Root_mean_square" title="Root mean square">RMS</a>) – <a href="/wiki/Volt" title="Volt">voltage</a> relative to 1 <a href="/wiki/Root_mean_square" title="Root mean square">root mean square</a> microvolt.</dd> <dt>dB μV/m , dB uV/m , or dB μ </dt> <dd>dB(μV/m) – <a href="/wiki/Electric_field_strength" class="mw-redirect" title="Electric field strength">electric field strength</a> relative to 1 <a href="/wiki/Microvolt" class="mw-redirect" title="Microvolt">microvolt</a> per <a href="/wiki/Meter" class="mw-redirect" title="Meter">meter</a>.</dd></dl> <div class="mw-heading mw-heading4"><h4 id="Suffixes_preceded_by_a_space">Suffixes preceded by a space</h4>[<a href="/w/index.php?title=Decibel&action=edit&section=31" title="Edit section: Suffixes preceded by a space">edit</a>]</div> <dl><dt>dB HL</dt> <dd>dB hearing level is used in <a href="/wiki/Audiogram" title="Audiogram">audiograms</a> as a measure of hearing loss.</dd> <dt>dB Q</dt> <dd>sometimes used to denote weighted noise level</dd> <dt>dB SIL</dt> <dd>dB <a href="/wiki/Sound_intensity_level" class="mw-redirect" title="Sound intensity level">sound intensity level</a> – relative to 10−12 W/m2</dd> <dt>dB SPL</dt> <dd>dB SPL (<a href="/wiki/Sound_pressure_level" class="mw-redirect" title="Sound pressure level">sound pressure level</a>) – for sound in air and other gases, relative to 20 μPa in air or 1 μPa in water</dd> <dt>dB SWL</dt> <dd>dB <a href="/wiki/Sound_power_level" class="mw-redirect" title="Sound power level">sound power level</a> – relative to 10−12 W.</dd></dl> <div class="mw-heading mw-heading4"><h4 id="Suffixes_within_parentheses">Suffixes within parentheses</h4>[<a href="/w/index.php?title=Decibel&action=edit&section=32" title="Edit section: Suffixes within parentheses">edit</a>]</div> <dl><dt><a href="/wiki/DB(A)" class="mw-redirect" title="DB(A)">dB(A)</a>, <a href="/wiki/DB(B)" class="mw-redirect" title="DB(B)">dB(B)</a>, <a href="/wiki/DB(C)" class="mw-redirect" title="DB(C)">dB(C)</a>, <a href="/wiki/DB(D)" class="mw-redirect" title="DB(D)">dB(D)</a>, <a href="/wiki/DB(G)" class="mw-redirect" title="DB(G)">dB(G)</a>, and <a href="/wiki/DB(Z)" class="mw-redirect" title="DB(Z)">dB(Z)</a></dt> <dd>These symbols are often used to denote the use of different <a href="/wiki/Weighting_filter" title="Weighting filter">weighting filters</a>, used to approximate the human ear's <a href="/wiki/Stimulus_(psychology)" title="Stimulus (psychology)">response</a> to sound, although the measurement is still in dB (SPL). These measurements usually refer to noise and its effects on humans and other animals, and they are widely used in industry while discussing noise control issues, regulations and environmental standards. Other variations that may be seen are dBA or <a href="/wiki/A-weighting" title="A-weighting">dBA</a>.</dd></dl> <div class="mw-heading mw-heading4"><h4 id="Other_suffixes">Other suffixes</h4>[<a href="/w/index.php?title=Decibel&action=edit&section=33" title="Edit section: Other suffixes">edit</a>]</div> <dl><dt>dB Hz or dB-Hz</dt> <dd>dB(Hz) – bandwidth relative to one <a href="/wiki/Hertz_(unit)" class="mw-redirect" title="Hertz (unit)">Hertz</a></dd> <dt>dB K⁻¹ or dB /K</dt> <dd>dB(K⁻¹) – decibels relative to <a href="/wiki/Multiplicative_inverse" title="Multiplicative inverse">reciprocal</a> of <a href="/wiki/Kelvin" title="Kelvin">kelvin</a></dd> <dt>dB m⁻¹</dt> <dd>dB(m⁻¹) – decibel relative to reciprocal of meter: measure of the <a href="/wiki/Antenna_factor" title="Antenna factor">antenna factor</a></dd></dl> <dl><dt>mB m</dt> <dd> mB(mW) – power relative to 1 <a href="/wiki/Milliwatt" class="mw-redirect" title="Milliwatt">milliwatt</a>, in millibels (one hundredth of a decibel). 100 mB m = 1 dB m . This unit is in the Wi-Fi drivers of the <a href="/wiki/Linux" title="Linux">Linux</a> kernel<a href="#cite_note-75">[72]</a> and the regulatory domain sections.<a href="#cite_note-76">[73]</a></dd></dl> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2>[<a href="/w/index.php?title=Decibel&action=edit&section=34" title="Edit section: See also">edit</a>]</div> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 8;"> <ul><li><a href="/wiki/Apparent_magnitude" title="Apparent magnitude">Apparent magnitude</a></li> <li><a href="/wiki/Cent_(music)" title="Cent (music)">Cent (music)</a></li> <li><a href="/wiki/Day%E2%80%93evening%E2%80%93night_noise_level" title="Day–evening–night noise level">Day–evening–night noise level</a> (Lden) and <a href="/wiki/Day-night_average_sound_level" title="Day-night average sound level">day-night average sound level</a> (Ldl), European and American standards for expressing noise level over an entire day</li> <li><a href="/wiki/DB_drag_racing" title="DB drag racing">dB drag racing</a></li> <li><a href="/wiki/Decade_(log_scale)" title="Decade (log scale)">Decade (log scale)</a></li> <li><a href="/wiki/Loudness" title="Loudness">Loudness</a></li> <li><a href="/wiki/Neper" title="Neper">Neper</a></li> <li><a href="/wiki/One-third_octave#Base_10" title="One-third octave">One-third octave § Base 10</a></li> <li><a href="/wiki/PH" title="PH">pH</a></li> <li><a href="/wiki/Phon" title="Phon">Phon</a></li> <li><a href="/wiki/Richter_magnitude_scale" class="mw-redirect" title="Richter magnitude scale">Richter magnitude scale</a></li> <li><a href="/wiki/Sone" title="Sone">Sone</a></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2>[<a href="/w/index.php?title=Decibel&action=edit&section=35" title="Edit section: Notes">edit</a>]</div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-lower-alpha"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-44"><a href="#cite_ref-44">^</a> "When one gives the value of a quantity, it is incorrect to attach letters or other symbols to the unit in order to provide information about the quantity or its conditions of measurement. Instead, the letters or other symbols should be attached to the quantity."<a href="#cite_note-NIST2008-15">[15]</a>: 16  </li> <li id="cite_note-45"><a href="#cite_ref-45">^</a> "When one gives the value of a quantity, any information concerning the quantity or its conditions of measurement must be presented in such a way as not to be associated with the unit. This means that quantities must be defined so that they can be expressed solely in acceptable units..."<a href="#cite_note-NIST2008-15">[15]</a>: 17  </li> <li id="cite_note-68"><a href="#cite_ref-68">^</a> See <a href="/wiki/Psophometric_weighting" title="Psophometric weighting">psophometric weighting</a> to see a comparison of frequency response curves for the C-message weighting and psophometric weighting filters. </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2>[<a href="/w/index.php?title=Decibel&action=edit&section=36" title="Edit section: References">edit</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239543626"><div class="reflist reflist-columns references-column-width" style="column-width: 25em;"> <ol class="references"> <li id="cite_note-auto-1">^ <a href="#cite_ref-auto_1-0">a</a> <a href="#cite_ref-auto_1-1">b</a> <style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFMark2007" class="citation book cs1">Mark, James E. (2007). Physical Properties of Polymers Handbook. Springer. p. 1025. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2007ppph.book.....M">2007ppph.book.....M</a>. <q>[…] the decibel represents a reduction in power of 1.258 times […]</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Physical+Properties+of+Polymers+Handbook&rft.pages=1025&rft.pub=Springer&rft.date=2007&rft_id=info%3Abibcode%2F2007ppph.book.....M&rft.aulast=Mark&rft.aufirst=James+E.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADecibel" class="Z3988"> </li> <li id="cite_note-auto1-2">^ <a href="#cite_ref-auto1_2-0">a</a> <a href="#cite_ref-auto1_2-1">b</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFYost1985" class="citation book cs1">Yost, William (1985). <a rel="nofollow" class="external text" href="https://archive.org/details/fundamentalsofhe00yost">Fundamentals of Hearing: An Introduction</a> (Second ed.). Holt, Rinehart and Winston. p. <a rel="nofollow" class="external text" href="https://archive.org/details/fundamentalsofhe00yost/page/206">206</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-12-772690-8" title="Special:BookSources/978-0-12-772690-8"><bdi>978-0-12-772690-8</bdi></a>. <q>[...] a pressure ratio of 1.122 equals + 1.0 dB [...]</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fundamentals+of+Hearing%3A+An+Introduction&rft.pages=206&rft.edition=Second&rft.pub=Holt%2C+Rinehart+and+Winston&rft.date=1985&rft.isbn=978-0-12-772690-8&rft.aulast=Yost&rft.aufirst=William&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Ffundamentalsofhe00yost&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADecibel" class="Z3988"> </li> <li id="cite_note-clqgmk-3">^ <a href="#cite_ref-clqgmk_3-0">a</a> <a href="#cite_ref-clqgmk_3-1">b</a> <a href="#cite_ref-clqgmk_3-2">c</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://designtools.analog.com/dt/dbconvert/dbconvert.html">"VRMS / dBm / dBu / dBV calculator"</a>. Utilities. Analog Devices. Retrieved 16 September 2016 – via designtools.analog.com.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=V%3Csub%3ERMS%3C%2Fsub%3E+%2F+dBm+%2F+dBu+%2F+dBV+calculator&rft.pub=Analog+Devices&rft_id=http%3A%2F%2Fdesigntools.analog.com%2Fdt%2Fdbconvert%2Fdbconvert.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADecibel" class="Z3988"> </li> <li id="cite_note-4"><a href="#cite_ref-4">^</a> <a rel="nofollow" class="external text" href="http://physics.nist.gov/cuu/pdf/sp811.pdf">Thompson and Taylor 2008, Guide for the Use of the International System of Units (SI), NIST Special Publication SP811</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160603203340/http://physics.nist.gov/cuu/pdf/sp811.pdf">Archived</a> 2016-06-03 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> </li> <li id="cite_note-5"><a href="#cite_ref-5">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1">IEEE Standard 100: a dictionary of IEEE standards and terms (7th ed.). New York: The Institute of Electrical and Electronics Engineering. 2000. p. 288. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7381-2601-2" title="Special:BookSources/978-0-7381-2601-2"><bdi>978-0-7381-2601-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=IEEE+Standard+100%3A+a+dictionary+of+IEEE+standards+and+terms&rft.place=New+York&rft.pages=288&rft.edition=7th&rft.pub=The+Institute+of+Electrical+and+Electronics+Engineering&rft.date=2000&rft.isbn=978-0-7381-2601-2&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADecibel" class="Z3988"> </li> <li id="cite_note-6"><a href="#cite_ref-6">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJohnson1944" class="citation book cs1">Johnson, Kenneth Simonds (1944). 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U.S. <a href="/wiki/National_Weather_Service" title="National Weather Service">National Weather Service</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20190331123302/https://www.weather.gov/jetstream/radarfaq#reflcolor">Archived</a> from the original on 31 March 2019. Retrieved 8 August 2019.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=weather.gov&rft.atitle=Frequently+Asked+Questions&rft_id=https%3A%2F%2Fwww.weather.gov%2Fjetstream%2Fradarfaq%23reflcolor&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADecibel" class="Z3988"> </li> <li id="cite_note-62"><a href="#cite_ref-62">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://everything2.com/title/dBsm">"dBsm"</a>. Definition. 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Newnes. pp. 45–46. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0750648448" title="Special:BookSources/978-0750648448"><bdi>978-0750648448</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=RF+Components+and+Circuits&rft.pages=%3Cspan+class%3D%22nowrap%22%3E45-%3C%2Fspan%3E46&rft.pub=Newnes&rft.date=2002&rft.isbn=978-0750648448&rft.aulast=Carr&rft.aufirst=Joseph&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADecibel" class="Z3988"> </li> <li id="cite_note-dBμ-64"><a href="#cite_ref-dBμ_64-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://radio-timetraveller.blogspot.com/2015/02/the-db-versus-dbu-mystery-signal.html">"The dBμ vs. dBu mystery: Signal strength vs. field strength?"</a>. Radio Time Traveller (radio-timetraveller.blogspot.com) (blog). 24 February 2015. Retrieved 13 October 2016 – via blogspot.com.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Radio+Time+Traveller+%28radio-timetraveller.blogspot.com%29&rft.atitle=The+dB%CE%BC+vs.+dBu+mystery%3A+Signal+strength+vs.+field+strength%3F&rft.date=2015-02-24&rft_id=http%3A%2F%2Fradio-timetraveller.blogspot.com%2F2015%2F02%2Fthe-db-versus-dbu-mystery-signal.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADecibel" class="Z3988"> </li> <li id="cite_note-65"><a href="#cite_ref-65">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFChandMagillSwaminathanDaugherty1999" class="citation journal cs1">Chand, N.; Magill, P.D.; Swaminathan, S.V.; Daugherty, T.H. (1999). "Delivery of digital video and other multimedia services ( > 1 Gb/s bandwidth) in passband above the 155 Mb/s baseband services on a FTTx full service access network". Journal of Lightwave Technology. 17 (12): 2449–2460. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2F50.809663">10.1109/50.809663</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Lightwave+Technology&rft.atitle=Delivery+of+digital+video+and+other+multimedia+services+%3Cspan+class%3D%22nowrap%22%3E%28+%3E+1+Gb%2Fs%3C%2Fspan%3E+bandwidth%29+in+passband+above+the+155+Mb%2Fs+baseband+services+on+a+FTTx+full+service+access+network&rft.volume=17&rft.issue=12&rft.pages=%3Cspan+class%3D%22nowrap%22%3E2449-%3C%2Fspan%3E2460&rft.date=1999&rft_id=info%3Adoi%2F10.1109%2F50.809663&rft.aulast=Chand&rft.aufirst=N.&rft.au=Magill%2C+P.D.&rft.au=Swaminathan%2C+S.V.&rft.au=Daugherty%2C+T.H.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADecibel" class="Z3988"> </li> <li id="cite_note-66"><a href="#cite_ref-66">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAdamy2004" class="citation book cs1">Adamy, David (2004). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=-AkfVZskc64C">EW 102: A second course in electronic warfare</a>. Artech House Radar Library. Boston, MA: Artech House. p. <a rel="nofollow" class="external text" href="https://books.google.com/books?id=-AkfVZskc64C&pg=PA118">118</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9781-58053687-5" title="Special:BookSources/9781-58053687-5"><bdi>9781-58053687-5</bdi></a>. Retrieved 16 September 2013 – via Google.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=EW+102%3A+A+second+course+in+electronic+warfare&rft.place=Boston%2C+MA&rft.series=Artech+House+Radar+Library&rft.pages=118&rft.pub=Artech+House&rft.date=2004&rft.isbn=9781-58053687-5&rft.aulast=Adamy&rft.aufirst=David&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D-AkfVZskc64C&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADecibel" class="Z3988"> </li> <li id="cite_note-67"><a href="#cite_ref-67">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation report cs1"><a rel="nofollow" class="external text" href="https://www.itu.int/rec/dologin_pub.asp?lang=e&id=T-REC-G.100.1-201506-I!!PDF-E&type=items">The use of the decibel and of relative levels in speech band telecommunications</a> (tech spec). Geneva, CH: <a href="/wiki/International_Telecommunication_Union" title="International Telecommunication Union">International Telecommunication Union</a> (ITU). June 2015. ITU-T Rec. G.100.1.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=report&rft.btitle=The+use+of+the+decibel+and+of+relative+levels+in+speech+band+telecommunications&rft.place=Geneva%2C+CH&rft.pub=International+Telecommunication+Union+%28ITU%29&rft.date=2015-06&rft_id=https%3A%2F%2Fwww.itu.int%2Frec%2Fdologin_pub.asp%3Flang%3De%26id%3DT-REC-G.100.1-201506-I%21%21PDF-E%26type%3Ditems&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADecibel" class="Z3988"> </li> <li id="cite_note-69"><a href="#cite_ref-69">^</a> Definition of dB rnC is given in <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRey1983" class="citation book cs1">Rey, R.F., ed. (1983). Engineering and Operations in the Bell System (2nd ed.). Murray Hill, NJ: AT&T Bell Laboratories. p. 230. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-932764-04-5" title="Special:BookSources/0-932764-04-5"><bdi>0-932764-04-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Engineering+and+Operations+in+the+Bell+System&rft.place=Murray+Hill%2C+NJ&rft.pages=230&rft.edition=2nd&rft.pub=AT%26T+Bell+Laboratories&rft.date=1983&rft.isbn=0-932764-04-5&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADecibel" class="Z3988"> </li> <li id="cite_note-70"><a href="#cite_ref-70">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRao2013" class="citation book cs1">Rao, K.N. Raja (31 January 2013). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=pjEubAt5dk0C">Satellite Communication: Concepts and applications</a>. p. <a rel="nofollow" class="external text" href="https://books.google.com/books?id=pjEubAt5dk0C&pg=PA126">126</a>. Retrieved 16 September 2013 – via Google.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Satellite+Communication%3A+Concepts+and+applications&rft.pages=126&rft.date=2013-01-31&rft.aulast=Rao&rft.aufirst=K.N.+Raja&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DpjEubAt5dk0C&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADecibel" class="Z3988"> </li> <li id="cite_note-71"><a href="#cite_ref-71">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFArabi" class="citation book cs1">Arabi, Ali Akbar. <a rel="nofollow" class="external text" href="https://books.google.com/books?id=DVoqmlX6048C">Comprehensive Glossary of Telecom Abbreviations and Acronyms</a>. p. <a rel="nofollow" class="external text" href="https://books.google.com/books?id=DVoqmlX6048C&pg=PA79">79</a>. Retrieved 16 September 2013 – via Google.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Comprehensive+Glossary+of+Telecom+Abbreviations+and+Acronyms&rft.pages=79&rft.aulast=Arabi&rft.aufirst=Ali+Akbar&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DDVoqmlX6048C&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADecibel" class="Z3988"> </li> <li id="cite_note-72"><a href="#cite_ref-72">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLong1999" class="citation book cs1">Long, Mark E. (1999). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=L4yQ0iztvQEC">The Digital Satellite TV Handbook</a>. Woburn, MA: Newnes Press. p. <a rel="nofollow" class="external text" href="https://books.google.com/books?id=L4yQ0iztvQEC&pg=PA93">93</a>. Retrieved 16 September 2013.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Digital+Satellite+TV+Handbook&rft.place=Woburn%2C+MA&rft.pages=93&rft.pub=Newnes+Press&rft.date=1999&rft.aulast=Long&rft.aufirst=Mark+E.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DL4yQ0iztvQEC&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADecibel" class="Z3988"> </li> <li id="cite_note-73"><a href="#cite_ref-73">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFvan_Valkenburg2001" class="citation book cs1">van Valkenburg, Mac E. (19 October 2001). Middleton, Wendy M. (ed.). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=U9RzPGwlic4C">Reference Data for Engineers: Radio, electronics, computers, and communications</a>. Technology & Engineering. Woburn, MA: Newness Press. p. <a rel="nofollow" class="external text" href="https://books.google.com/books?id=U9RzPGwlic4C&pg=PASA27-PA14">27·14</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780-08051596-0" title="Special:BookSources/9780-08051596-0"><bdi>9780-08051596-0</bdi></a>. Retrieved 16 September 2013 – via Google.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Reference+Data+for+Engineers%3A+Radio%2C+electronics%2C+computers%2C+and+communications&rft.place=Woburn%2C+MA&rft.series=Technology+%26+Engineering&rft.pages=27%C2%B714&rft.pub=Newness+Press&rft.date=2001-10-19&rft.isbn=9780-08051596-0&rft.aulast=van+Valkenburg&rft.aufirst=Mac+E.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DU9RzPGwlic4C&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADecibel" class="Z3988"> </li> <li id="cite_note-74"><a href="#cite_ref-74">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.iucaf.org/sschool/mike/Units_and_Calculations.ppt">"Units and calculations"</a>. iucaf.org. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160303223821/http://www.iucaf.org/sschool/mike/Units_and_Calculations.ppt">Archived</a> from the original on 3 March 2016. Retrieved 24 August 2013.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=iucaf.org&rft.atitle=Units+and+calculations&rft_id=http%3A%2F%2Fwww.iucaf.org%2Fsschool%2Fmike%2FUnits_and_Calculations.ppt&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADecibel" class="Z3988"> </li> <li id="cite_note-75"><a href="#cite_ref-75">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://wireless.kernel.org/en/users/Documentation/iw#Setting_TX_power">"Setting TX power"</a>. wireless.kernel.org. en:users:documentation:iw.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=wireless.kernel.org&rft.atitle=Setting+%3Cspan+class%3D%22smallcaps%22%3E%3Cspan+style%3D%22font-variant%3A+small-caps%3B+text-transform%3A+lowercase%3B%22%3ETX%3C%2Fspan%3E%3C%2Fspan%3E+power&rft_id=http%3A%2F%2Fwireless.kernel.org%2Fen%2Fusers%2FDocumentation%2Fiw%23Setting_TX_power&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADecibel" class="Z3988"> </li> <li id="cite_note-76"><a href="#cite_ref-76">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://penturalabs.wordpress.com/2013/05/16/is-your-wifi-ap-missing-channels-12-13/">"Is your Wi Fi ap missing channels 12 and 13 ?"</a>. Pentura Labs. 16 May 2013 – via wordpress.com.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Pentura+Labs&rft.atitle=Is+your+Wi+Fi+ap+missing+channels+12+and+13+%3F&rft.date=2013-05-16&rft_id=http%3A%2F%2Fpenturalabs.wordpress.com%2F2013%2F05%2F16%2Fis-your-wifi-ap-missing-channels-12-13%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADecibel" class="Z3988"> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2>[<a href="/w/index.php?title=Decibel&action=edit&section=37" title="Edit section: Further reading">edit</a>]</div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTuffentsammer1956" class="citation journal cs1 cs1-prop-foreign-lang-source">Tuffentsammer, Karl (1956). "Das Dezilog, eine Brücke zwischen Logarithmen, Dezibel, Neper und Normzahlen" [The decilog, a bridge between logarithms, decibel, neper and preferred numbers]. VDI-Zeitschrift (in German). 98: 267–274.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=VDI-Zeitschrift&rft.atitle=Das+Dezilog%2C+eine+Br%C3%BCcke+zwischen+Logarithmen%2C+Dezibel%2C+Neper+und+Normzahlen&rft.volume=98&rft.pages=%3Cspan+class%3D%22nowrap%22%3E267-%3C%2Fspan%3E274&rft.date=1956&rft.aulast=Tuffentsammer&rft.aufirst=Karl&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADecibel" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPaulin2007" class="citation book cs1 cs1-prop-foreign-lang-source">Paulin, Eugen (1 September 2007). <a rel="nofollow" class="external text" href="http://www.rechenschieber.org/Normzahlen.pdf">Logarithmen, Normzahlen, Dezibel, Neper, Phon - natürlich verwandt!</a> [Logarithms, preferred numbers, decibel, neper, phon - naturally related!] (PDF) (in German). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20161218223050/http://www.rechenschieber.org/Normzahlen.pdf">Archived</a> (PDF) from the original on 18 December 2016. Retrieved 18 December 2016.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Logarithmen%2C+Normzahlen%2C+Dezibel%2C+Neper%2C+Phon+-+nat%C3%BCrlich+verwandt%21&rft.date=2007-09-01&rft.aulast=Paulin&rft.aufirst=Eugen&rft_id=http%3A%2F%2Fwww.rechenschieber.org%2FNormzahlen.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADecibel" class="Z3988"></li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2>[<a href="/w/index.php?title=Decibel&action=edit&section=38" title="Edit section: External links">edit</a>]</div> <ul><li><a rel="nofollow" class="external text" href="http://www.phys.unsw.edu.au/jw/dB.html">What is a decibel? With sound files and animations</a></li> <li><a rel="nofollow" class="external text" href="http://www.sengpielaudio.com/calculator-soundlevel.htm">Conversion of sound level units: dBSPL or dBA to sound pressure p and sound intensity J</a></li> <li><a rel="nofollow" class="external text" href="https://www.osha.gov/pls/oshaweb/owadisp.show_document?p_table=STANDARDS&p_id=9735">OSHA Regulations on Occupational Noise Exposure</a></li> <li><a rel="nofollow" class="external text" href="http://learnemc.com/working-with-decibels">Working with Decibels</a> (RF signal and field strengths)</li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output .hlist dt:last-child::after,.mw-parser-output .hlist li:last-child::after{content:none}.mw-parser-output .hlist dd dd:first-child::before,.mw-parser-output .hlist dd dt:first-child::before,.mw-parser-output .hlist dd li:first-child::before,.mw-parser-output .hlist dt dd:first-child::before,.mw-parser-output .hlist dt dt:first-child::before,.mw-parser-output .hlist dt 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href="/wiki/Template:Decibel" title="Template:Decibel"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Decibel" title="Template talk:Decibel"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Decibel" title="Special:EditPage/Template:Decibel"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Decibel_suffixes_(dB)140" style="font-size:114%;margin:0 4em"><a class="mw-selflink selflink">Decibel</a> <a class="mw-selflink-fragment" href="#Suffixes">suffixes</a> (dB)</div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/DBm" title="DBm">dBm</a> (or dBmW)</li> <li><a href="/wiki/Decibel_watt" title="Decibel watt">dBW</a></li> <li><a class="mw-selflink-fragment" href="#Voltage">dBV</a></li> <li><a href="/wiki/Spectral_density#Explanation" title="Spectral density">dBm/Hz</a> <ul><li><a href="/wiki/Spectral_density#Power_spectral_density" title="Spectral density">PSD</a></li></ul></li> <li><a href="/wiki/A-weighting#Environmental_noise_measurement" title="A-weighting">dBA</a></li> <li><a href="/wiki/DBZ_(meteorology)" title="DBZ (meteorology)">dBZ</a> (radar)</li> <li><a class="mw-selflink-fragment" href="#Radar">dBsm</a></li> <li><a href="/wiki/DBc" title="DBc">dBc</a></li> <li><a class="mw-selflink-fragment" href="#Antenna_measurements">dBi</a></li> <li><a href="/wiki/DBFS" title="DBFS">dBFS</a></li> <li><a href="/wiki/DBrn" title="DBrn">dBrn</a></li> <li><a class="mw-selflink-fragment" href="#Other_measurements">dB-Hz</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <dl><dt>See also</dt> <dd><a href="/wiki/Logarithmic_unit" class="mw-redirect" title="Logarithmic unit">logarithmic unit</a></dd> <dd><a href="/wiki/Link_budget" title="Link budget">link budget</a></dd> <dd><a href="/wiki/Signal_noise" class="mw-redirect" title="Signal noise">signal noise</a></dd> <dd><a href="/wiki/Telecommunications" title="Telecommunications">telecommunications</a></dd></dl> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="SI_units303" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:SI_units" title="Template:SI units"><abbr title="View 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title="Kilogram">kilogram</a></li> <li><a href="/wiki/Metre" title="Metre">metre</a></li> <li><a href="/wiki/Mole_(unit)" title="Mole (unit)">mole</a></li> <li><a href="/wiki/Second" title="Second">second</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/SI_derived_unit" title="SI derived unit">Derived units with special names</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Becquerel" title="Becquerel">becquerel</a></li> <li><a href="/wiki/Coulomb" title="Coulomb">coulomb</a></li> <li><a href="/wiki/Celsius" title="Celsius">degree Celsius</a></li> <li><a href="/wiki/Farad" title="Farad">farad</a></li> <li><a href="/wiki/Gray_(unit)" title="Gray (unit)">gray</a></li> <li><a href="/wiki/Henry_(unit)" title="Henry (unit)">henry</a></li> <li><a href="/wiki/Hertz" title="Hertz">hertz</a></li> <li><a href="/wiki/Joule" title="Joule">joule</a></li> <li><a href="/wiki/Katal" title="Katal">katal</a></li> <li><a href="/wiki/Lumen_(unit)" title="Lumen (unit)">lumen</a></li> <li><a href="/wiki/Lux" title="Lux">lux</a></li> <li><a href="/wiki/Newton_(unit)" title="Newton (unit)">newton</a></li> <li><a href="/wiki/Ohm" title="Ohm">ohm</a></li> <li><a href="/wiki/Pascal_(unit)" title="Pascal (unit)">pascal</a></li> <li><a href="/wiki/Radian" title="Radian">radian</a></li> <li><a href="/wiki/Siemens_(unit)" title="Siemens (unit)">siemens</a></li> <li><a href="/wiki/Sievert" title="Sievert">sievert</a></li> <li><a href="/wiki/Steradian" title="Steradian">steradian</a></li> <li><a href="/wiki/Tesla_(unit)" title="Tesla (unit)">tesla</a></li> <li><a href="/wiki/Volt" title="Volt">volt</a></li> <li><a href="/wiki/Watt" title="Watt">watt</a></li> <li><a href="/wiki/Weber_(unit)" title="Weber (unit)">weber</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a 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