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</li> <li id="toc-Firearms" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Firearms"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4</span> <span>Firearms</span> </div> </a> <ul id="toc-Firearms-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Human_vision" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Human_vision"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.5</span> <span>Human vision</span> </div> </a> <ul id="toc-Human_vision-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Materials" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Materials"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.6</span> <span>Materials</span> </div> </a> <ul id="toc-Materials-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Manufacturing" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Manufacturing"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.7</span> <span>Manufacturing</span> </div> </a> <ul id="toc-Manufacturing-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" 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Available in 14 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-14" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">14 languages</span> </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%82%D9%8A%D9%82%D8%A9_%D8%A7%D9%84%D9%82%D9%88%D8%B3_%D9%88%D8%AB%D8%A7%D9%86%D9%8A%D8%AA%D9%87" title="دقيقة القوس وثانيته – Arabic" lang="ar" hreflang="ar" data-title="دقيقة القوس وثانيته" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%86%E0%A6%B0%E0%A7%8D%E0%A6%95%E0%A6%AE%E0%A6%BF%E0%A6%A8%E0%A6%BF%E0%A6%9F_%E0%A6%8F%E0%A6%AC%E0%A6%82_%E0%A6%86%E0%A6%B0%E0%A7%8D%E0%A6%95%E0%A6%B8%E0%A7%87%E0%A6%95%E0%A7%87%E0%A6%A8%E0%A7%8D%E0%A6%A1" title="আর্কমিনিট এবং আর্কসেকেন্ড – Bangla" lang="bn" hreflang="bn" data-title="আর্কমিনিট এবং আর্কসেকেন্ড" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Minuto_y_segundo_de_arco" title="Minuto y segundo de arco – Spanish" lang="es" hreflang="es" data-title="Minuto y segundo de arco" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AF%D9%82%DB%8C%D9%82%D9%87_%D9%88_%D8%AB%D8%A7%D9%86%DB%8C%D9%87_%D9%82%D9%88%D8%B3%DB%8C" title="دقیقه و ثانیه قوسی – Persian" lang="fa" hreflang="fa" data-title="دقیقه و ثانیه قوسی" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Sous-unit%C3%A9s_du_degr%C3%A9" title="Sous-unités du degré – French" lang="fr" hreflang="fr" data-title="Sous-unités du degré" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%9A%E0%A4%BE%E0%A4%AA_%E0%A4%95%E0%A5%87_%E0%A4%AE%E0%A4%BF%E0%A4%A8%E0%A4%9F_%E0%A4%94%E0%A4%B0_%E0%A4%B8%E0%A5%88%E0%A4%95%E0%A4%BF%E0%A4%82%E0%A4%A1" title="चाप के मिनट और सैकिंड – Hindi" lang="hi" hreflang="hi" data-title="चाप के मिनट और सैकिंड" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Menit_dan_detik_busur" title="Menit dan detik busur – Indonesian" lang="id" hreflang="id" data-title="Menit dan detik busur" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Bogam%C3%ADn%C3%BAta_og_bogasek%C3%BAnda" title="Bogamínúta og bogasekúnda – Icelandic" lang="is" hreflang="is" data-title="Bogamínúta og bogasekúnda" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Dakika_ya_tao" title="Dakika ya tao – Swahili" lang="sw" hreflang="sw" data-title="Dakika ya tao" data-language-autonym="Kiswahili" data-language-local-name="Swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Minit_dan_saat_arka" title="Minit dan saat arka – Malay" lang="ms" hreflang="ms" data-title="Minit dan saat arka" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%9A%E0%A8%BE%E0%A8%AA_%E0%A8%A6%E0%A9%87_%E0%A8%AE%E0%A8%BF%E0%A9%B0%E0%A8%9F_%E0%A8%85%E0%A8%A4%E0%A9%87_%E0%A8%B8%E0%A8%95%E0%A8%BF%E0%A9%B0%E0%A8%9F" title="ਚਾਪ ਦੇ ਮਿੰਟ ਅਤੇ ਸਕਿੰਟ – Punjabi" lang="pa" hreflang="pa" data-title="ਚਾਪ ਦੇ ਮਿੰਟ ਅਤੇ ਸਕਿੰਟ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Kotna_minuta_in_sekunda" title="Kotna minuta in sekunda – Slovenian" lang="sl" hreflang="sl" data-title="Kotna minuta in sekunda" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%A5%E0%B8%B4%E0%B8%9B%E0%B8%94%E0%B8%B2%E0%B9%81%E0%B8%A5%E0%B8%B0%E0%B8%9E%E0%B8%B4%E0%B8%A5%E0%B8%B4%E0%B8%9B%E0%B8%94%E0%B8%B2" title="ลิปดาและพิลิปดา – Thai" lang="th" hreflang="th" data-title="ลิปดาและพิลิปดา" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-uk badge-Q70893996 mw-list-item" title=""><a href="https://uk.wikipedia.org/wiki/%D0%9A%D1%83%D1%82%D0%BE%D0%B2%D0%B0_%D0%BC%D1%96%D0%BD%D1%83%D1%82%D0%B0_%D1%96_%D1%81%D0%B5%D0%BA%D1%83%D0%BD%D0%B4%D0%B0" title="Кутова мінута і секунда – Ukrainian" lang="uk" hreflang="uk" data-title="Кутова мінута і секунда" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q12097402#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></span></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 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Unsourced material may be challenged and removed.<br /><small><span class="plainlinks"><i>Find sources:</i> <a rel="nofollow" class="external text" href="https://www.google.com/search?as_eq=wikipedia&q=%22Minute+and+second+of+arc%22">"Minute and second of arc"</a> – <a rel="nofollow" class="external text" href="https://www.google.com/search?tbm=nws&q=%22Minute+and+second+of+arc%22+-wikipedia&tbs=ar:1">news</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?&q=%22Minute+and+second+of+arc%22&tbs=bkt:s&tbm=bks">newspapers</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?tbs=bks:1&q=%22Minute+and+second+of+arc%22+-wikipedia">books</a> <b>·</b> <a rel="nofollow" class="external text" href="https://scholar.google.com/scholar?q=%22Minute+and+second+of+arc%22">scholar</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.jstor.org/action/doBasicSearch?Query=%22Minute+and+second+of+arc%22&acc=on&wc=on">JSTOR</a></span></small></span> <span class="date-container"><i>(<span class="date">March 2022</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p class="mw-empty-elt"> </p> <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">Arcminute</th></tr><tr><td colspan="2" class="infobox-image notheme" style="background-color: #f8f9fa;"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:Arcminute_and_football.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Arcminute_and_football.png/220px-Arcminute_and_football.png" decoding="async" width="220" height="73" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Arcminute_and_football.png/330px-Arcminute_and_football.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/73/Arcminute_and_football.png/440px-Arcminute_and_football.png 2x" data-file-width="1440" data-file-height="480" /></a></span><div class="infobox-caption">An illustration of the size of an arcminute (not to scale). A standard <a href="/wiki/Ball_(association_football)" title="Ball (association football)">association football (soccer) ball</a> (with a diameter of 22 cm or 8.7 in) subtends an angle of 1 arcminute at a distance of approximately 756 m (827 yd).</div></td></tr><tr><th colspan="2" class="infobox-header">General information</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">Non-SI units mentioned in the SI</td></tr><tr><th scope="row" class="infobox-label">Unit of</th><td class="infobox-data"><a href="/wiki/Angle" title="Angle">Angle</a></td></tr><tr><th scope="row" class="infobox-label">Symbol</th><td class="infobox-data"><a href="/wiki/Prime_(symbol)" title="Prime (symbol)">′</a>, arcmin</td></tr><tr><th scope="row" class="infobox-label">In units</th><td class="infobox-data"><a href="/wiki/Dimensionless_quantity" title="Dimensionless quantity">Dimensionless</a> with an <a href="/wiki/Arc_length" title="Arc length">arc length</a> of approx. ≈ <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><span class="sfrac">⁠<span class="tion"><span class="num">0.2909</span><span class="sr-only">/</span><span class="den">1000</span></span>⁠</span> of the radius, i.e. 0.2909 <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">mm</span><span class="sr-only">/</span><span class="den">m</span></span>⁠</span></td></tr><tr><th colspan="2" class="infobox-header">Conversions </th></tr><tr class="nowrap"><td>1 <a href="/wiki/Prime_(symbol)" title="Prime (symbol)">′</a> <i>in ...</i></td><td><i>... is equal to ...</i></td></tr><tr style="display:none"><th colspan="2"> </th></tr><tr><th scope="row" class="infobox-label"><span class="nowrap">   </span><a href="/wiki/Degree_(angle)" title="Degree (angle)">degrees</a></th><td class="infobox-data"><span class="nowrap">   </span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">60</span></span>⁠</span>° = 0.01<span style="text-decoration:overline;">6</span>°</td></tr><tr><th scope="row" class="infobox-label"><span class="nowrap">   </span><a href="/wiki/Arcsecond" class="mw-redirect" title="Arcsecond">arcseconds</a></th><td class="infobox-data"><span class="nowrap">   </span>60″</td></tr><tr><th scope="row" class="infobox-label"><span class="nowrap">   </span><a href="/wiki/Radian" title="Radian">radians</a></th><td class="infobox-data"><span class="nowrap">   </span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num"><span class="texhtml mvar" style="font-style:italic;">π</span></span><span class="sr-only">/</span><span class="den">10800</span></span>⁠</span> ≈ 0.000290888 rad</td></tr><tr><th scope="row" class="infobox-label"><span class="nowrap">   </span><a href="/wiki/Milliradian" title="Milliradian">milliradians</a></th><td class="infobox-data"><span class="nowrap">   </span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num"><span class="texhtml mvar" style="font-style:italic;">π</span>·1000</span><span class="sr-only">/</span><span class="den">10800</span></span>⁠</span> ≈ 0.2909 mrad</td></tr><tr><th scope="row" class="infobox-label"><span class="nowrap">   </span><a href="/wiki/Gon_(unit)" class="mw-redirect" title="Gon (unit)">gons</a></th><td class="infobox-data"><span class="nowrap">   </span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">9</span><span class="sr-only">/</span><span class="den">600</span></span>⁠</span><sup>g</sup> = 0.015<sup>g</sup></td></tr><tr><th scope="row" class="infobox-label"><span class="nowrap">   </span><a href="/wiki/Turn_(unit)" class="mw-redirect" title="Turn (unit)">turns</a></th><td class="infobox-data"><span class="nowrap">   </span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">21600</span></span>⁠</span></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> <p>A <b>minute of arc</b>, <b>arcminute</b> (<b>arcmin</b>), <b>arc minute</b>, or <b>minute arc</b>, denoted by the symbol <span class="nounderlines" style="border: 1px solid var(--border-color-muted,#ddd); color: var(--color-base); background-color: var( --background-color-neutral-subtle, #fdfdfd); padding: 1px 1px;">′</span>, is a unit of <a href="/wiki/Angular_unit" class="mw-redirect" title="Angular unit">angular</a> measurement equal to <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">60</span></span>⁠</span> of one <a href="/wiki/Degree_(angle)" title="Degree (angle)">degree</a>.<sup id="cite_ref-:2_1-0" class="reference"><a href="#cite_note-:2-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Since one degree is <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">360</span></span>⁠</span> of a <a href="/wiki/Turn_(geometry)" class="mw-redirect" title="Turn (geometry)">turn, or complete rotation</a>, one arcminute is <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den"><span class="nowrap"><span data-sort-value="7004216000000000000♠"></span>21<span style="margin-left:.25em;">600</span></span></span></span>⁠</span> of a turn. The <a href="/wiki/Nautical_miles" class="mw-redirect" title="Nautical miles">nautical mile</a> (nmi) was originally defined as the <a href="/wiki/Meridian_arc" title="Meridian arc">arc length</a> of a minute of latitude on a spherical Earth, so the actual <a href="/wiki/Earth%27s_circumference" title="Earth's circumference">Earth's circumference</a> is very near <span class="nowrap"><span data-sort-value="7007400032000000000♠"></span>21<span style="margin-left:.25em;">600</span> nmi</span>. A minute of arc is <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num"><span class="texhtml mvar" style="font-style:italic;">π</span></span><span class="sr-only">/</span><span class="den"><span class="nowrap"><span data-sort-value="7004108000000000000♠"></span>10<span style="margin-left:.25em;">800</span></span></span></span>⁠</span> of a <a href="/wiki/Radian" title="Radian">radian</a>. </p><p>A <b>second of arc</b>, <b>arcsecond</b> (arcsec), or <b>arc second</b>, denoted by the symbol <span class="nounderlines" style="border: 1px solid var(--border-color-muted,#ddd); color: var(--color-base); background-color: var( --background-color-neutral-subtle, #fdfdfd); padding: 1px 1px;">″</span>,<sup id="cite_ref-:3_2-0" class="reference"><a href="#cite_note-:3-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> is <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">60</span></span>⁠</span> of an arcminute, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den"><span class="nowrap"><span data-sort-value="7003360000000000000♠"></span>3600</span></span></span>⁠</span> of a degree,<sup id="cite_ref-:2_1-1" class="reference"><a href="#cite_note-:2-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den"><span class="nowrap"><span data-sort-value="7006129600000000000♠"></span>1<span style="margin-left:.25em;">296</span><span style="margin-left:.25em;">000</span></span></span></span>⁠</span> of a turn, and <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num"><span class="texhtml mvar" style="font-style:italic;">π</span></span><span class="sr-only">/</span><span class="den"><span class="nowrap"><span data-sort-value="7005648000000000000♠"></span>648<span style="margin-left:.25em;">000</span></span></span></span>⁠</span> (about <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den"><span class="nowrap"><span data-sort-value="7005206264800000000♠"></span>206<span style="margin-left:.25em;">264</span>.8</span></span></span>⁠</span>) of a radian. </p><p>These units originated in <a href="/wiki/Babylonian_astronomy" title="Babylonian astronomy">Babylonian astronomy</a> as <a href="/wiki/Sexagesimal" title="Sexagesimal">sexagesimal</a> (base 60) subdivisions of the degree; they are used in fields that involve very small angles, such as <a href="/wiki/Astronomy" title="Astronomy">astronomy</a>, <a href="/wiki/Optometry" title="Optometry">optometry</a>, <a href="/wiki/Ophthalmology" title="Ophthalmology">ophthalmology</a>, <a href="/wiki/Optics" title="Optics">optics</a>, <a href="/wiki/Navigation" title="Navigation">navigation</a>, <a href="/wiki/Land_surveying" class="mw-redirect" title="Land surveying">land surveying</a>, and <a href="/wiki/Marksmanship" class="mw-redirect" title="Marksmanship">marksmanship</a>. </p><p>To express even smaller angles, standard <a href="/wiki/SI_prefixes" class="mw-redirect" title="SI prefixes">SI prefixes</a> can be employed; the <b>milliarcsecond</b> (mas) and <b>microarcsecond</b> (μas), for instance, are commonly used in astronomy. For a three-dimensional area such as on a sphere, <i><a href="/wiki/Square_arcminutes" class="mw-redirect" title="Square arcminutes">square arcminutes</a></i> or <i>seconds</i> may be used. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Symbols_and_abbreviations">Symbols and abbreviations</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Minute_and_second_of_arc&action=edit&section=1" title="Edit section: Symbols and abbreviations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/Prime_(symbol)" title="Prime (symbol)">prime symbol</a> <span class="nounderlines" style="border: 1px solid var(--border-color-muted,#ddd); color: var(--color-base); background-color: var( --background-color-neutral-subtle, #fdfdfd); padding: 1px 1px;">′</span> (<span title="′"><a href="/wiki/Unicode#Upluslink" title="Unicode">U+</a>2032</span>) designates the arcminute,<sup id="cite_ref-:3_2-1" class="reference"><a href="#cite_note-:3-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> though a single quote <span class="nounderlines" style="border: 1px solid var(--border-color-muted,#ddd); color: var(--color-base); background-color: var( --background-color-neutral-subtle, #fdfdfd); padding: 1px 1px;">'</span> (U+0027) is commonly used where only <a href="/wiki/ASCII" title="ASCII">ASCII</a> characters are permitted. One arcminute is thus written as 1′. It is also abbreviated as <b>arcmin</b> or <b>amin</b>. </p><p>Similarly, <a href="/wiki/Double_prime" class="mw-redirect" title="Double prime">double prime</a> <span class="nounderlines" style="border: 1px solid var(--border-color-muted,#ddd); color: var(--color-base); background-color: var( --background-color-neutral-subtle, #fdfdfd); padding: 1px 1px;">″</span> (U+2033) designates the arcsecond,<sup id="cite_ref-:3_2-2" class="reference"><a href="#cite_note-:3-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> though a double quote <span class="nounderlines" style="border: 1px solid var(--border-color-muted,#ddd); color: var(--color-base); background-color: var( --background-color-neutral-subtle, #fdfdfd); padding: 1px 1px;">"</span> (U+0022) is commonly used where only <a href="/wiki/ASCII" title="ASCII">ASCII</a> characters are permitted. One arcsecond is thus written as 1″. It is also abbreviated as <b>arcsec</b> or <b>asec</b>. </p> <table class="wikitable" style="margin:0 auto;"> <caption><a href="/wiki/Sexagesimal" title="Sexagesimal">Sexagesimal</a> system of <a href="/wiki/Angle" title="Angle">angular measurement</a> </caption> <tbody><tr> <th>Unit </th> <th>Value </th> <th colspan="2">Symbol </th> <th>Abbreviations </th> <th>In radians, approx. </th></tr> <tr> <th scope="row"><a href="/wiki/Degree_(angle)" title="Degree (angle)">Degree</a> </th> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">360</span></span>⁠</span> turn</td> <td>°</td> <td><a href="/wiki/Degree_symbol" title="Degree symbol">Degree</a></td> <td>deg</td> <td align="right"><span class="nowrap"><span data-sort-value="7001174532925000000♠"></span>17.453<span style="margin-left:.25em;">2925</span> <a href="/wiki/Milliradian" title="Milliradian">mrad</a></span> </td></tr> <tr> <th scope="row">Arcminute </th> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">60</span></span>⁠</span> degree</td> <td>′</td> <td><a href="/wiki/Prime_(symbol)" title="Prime (symbol)">Prime</a></td> <td>arcmin, amin, am, MOA</td> <td align="right"><span class="nowrap"><span data-sort-value="6994290888208700000♠"></span>290.888<span style="margin-left:.25em;">2087</span> μrad</span> </td></tr> <tr> <th scope="row">Arcsecond </th> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">60</span></span>⁠</span> arcminute = <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">3600</span></span>⁠</span> degree</td> <td>″</td> <td>Double prime</td> <td>arcsec, asec, as</td> <td align="right"><span class="nowrap"><span data-sort-value="6992484813680000000♠"></span>4.848<span style="margin-left:.25em;">1368</span> μrad</span> </td></tr> <tr> <th scope="row">Milliarcsecond </th> <td>0.001 arcsecond = <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">3600000</span></span>⁠</span> degree</td> <td></td> <td></td> <td>mas</td> <td align="right"><span class="nowrap"><span data-sort-value="6989484813680000000♠"></span>4.848<span style="margin-left:.25em;">1368</span> nrad</span> </td></tr> <tr> <th scope="row">Microarcsecond </th> <td>0.001 mas = <span class="nowrap"><span data-sort-value="6994100000000000000♠"></span>0.000<span style="margin-left:.25em;">001</span></span> arcsecond</td> <td></td> <td></td> <td>μas</td> <td align="right"><span class="nowrap"><span data-sort-value="6986484813679999999♠"></span>4.848<span style="margin-left:.25em;">1368</span> prad</span> </td></tr></tbody></table> <p>In <a href="/wiki/Celestial_navigation" title="Celestial navigation">celestial navigation</a>, seconds of arc are rarely used in calculations, the preference usually being for degrees, minutes, and decimals of a minute, for example, written as 42° 25.32′ or 42° 25.322′.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> This notation has been carried over into <a href="/wiki/Global_Positioning_System" title="Global Positioning System">marine GPS</a> and aviation GPS receivers, which normally display latitude and longitude in the latter format by default.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Common_examples">Common examples</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Minute_and_second_of_arc&action=edit&section=2" title="Edit section: Common examples"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The average <a href="/wiki/Angular_diameter" title="Angular diameter">apparent diameter</a> of the <a href="/wiki/Full_moon" title="Full moon">full Moon</a> is about 31 arcminutes, or 0.52°. </p><p>One arcminute is the approximate distance two contours can be separated by, and still be distinguished by, a person with <a href="/wiki/Visual_acuity" title="Visual acuity">20/20 vision</a>. </p><p>One arcsecond is the approximate <a href="/wiki/Subtended_angle" title="Subtended angle">angle subtended</a> by a <a href="/wiki/Dime_(United_States_coin)" title="Dime (United States coin)">U.S. dime coin</a> (18 mm) at a distance of 4 kilometres (about 2.5 mi).<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> An arcsecond is also the angle subtended by </p> <ul><li>an object of diameter <span class="nowrap"><span data-sort-value="7005725270000000000♠"></span>725.27 km</span> at a distance of one <a href="/wiki/Astronomical_unit" title="Astronomical unit">astronomical unit</a>,</li> <li>an object of diameter <span class="nowrap"><span data-sort-value="7010458669160000000♠"></span>45<span style="margin-left:.25em;">866</span><span style="margin-left:.25em;">916</span> km</span> at one <a href="/wiki/Light-year" title="Light-year">light-year</a>,</li> <li>an object of diameter one astronomical unit (<span class="nowrap"><span data-sort-value="7011149597870700000♠"></span>149<span style="margin-left:.25em;">597</span><span style="margin-left:.25em;">870</span>.7 km</span>) at a distance of one <a href="/wiki/Parsec" title="Parsec">parsec</a>, per the definition of the latter.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup></li></ul> <p>One milliarcsecond is about the size of a half dollar, seen from a distance equal to that between the <a href="/wiki/Washington_Monument" title="Washington Monument">Washington Monument</a> and the <a href="/wiki/Eiffel_Tower" title="Eiffel Tower">Eiffel Tower</a>. </p><p>One microarcsecond is about the size of a period at the end of a sentence in the Apollo mission manuals left on the Moon as seen from Earth. </p><p>One nanoarcsecond is about the size of a penny on <a href="/wiki/Neptune" title="Neptune">Neptune</a>'s moon <a href="/wiki/Triton_(moon)" title="Triton (moon)">Triton</a> as observed from Earth. </p><p>Also notable examples of size in arcseconds are: </p> <ul><li><a href="/wiki/Hubble_Space_Telescope" title="Hubble Space Telescope">Hubble Space Telescope</a> has calculational resolution of 0.05 arcseconds and actual resolution of almost 0.1 arcseconds, which is close to the <a href="/wiki/Diffraction_limit" class="mw-redirect" title="Diffraction limit">diffraction limit</a>.<sup id="cite_ref-:0_8-0" class="reference"><a href="#cite_note-:0-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup></li> <li>At crescent phase, <a href="/wiki/Venus" title="Venus">Venus</a> measures between 60.2 and 66 seconds of arc.<sup id="cite_ref-:0_8-1" class="reference"><a href="#cite_note-:0-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup></li></ul> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Minute_and_second_of_arc&action=edit&section=3" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The concepts of degrees, minutes, and seconds—as they relate to the measure of both angles and time—derive from <a href="/wiki/Babylonia" title="Babylonia">Babylonian</a> <a href="/wiki/Babylonian_astronomy" title="Babylonian astronomy">astronomy</a> and time-keeping. Influenced by the <a href="/wiki/Sumer" title="Sumer">Sumerians</a>, the ancient Babylonians divided the Sun's perceived motion across the sky over the course of one <a href="/wiki/Solar_day" class="mw-redirect" title="Solar day">full day</a> into 360 degrees.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability"><span title="The material near this tag failed verification of its source citation(s). (December 2023)">failed verification</span></a></i>]</sup> Each degree was subdivided into 60 minutes and each minute into 60 seconds.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> Thus, one Babylonian degree was equal to four minutes in modern terminology, one Babylonian minute to four modern seconds, and one Babylonian second to <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">15</span></span>⁠</span> (approximately 0.067) of a modern second. </p> <div class="mw-heading mw-heading2"><h2 id="Uses">Uses</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Minute_and_second_of_arc&action=edit&section=4" title="Edit section: Uses"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Astronomy">Astronomy</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Minute_and_second_of_arc&action=edit&section=5" title="Edit section: Astronomy"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Comparison_angular_diameter_solar_system.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f8/Comparison_angular_diameter_solar_system.svg/330px-Comparison_angular_diameter_solar_system.svg.png" decoding="async" width="330" height="330" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f8/Comparison_angular_diameter_solar_system.svg/495px-Comparison_angular_diameter_solar_system.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f8/Comparison_angular_diameter_solar_system.svg/660px-Comparison_angular_diameter_solar_system.svg.png 2x" data-file-width="512" data-file-height="512" /></a><figcaption>Comparison of angular diameter of the Sun, Moon, planets and the International Space Station. True representation of the sizes is achieved when the image is viewed at a distance of 103 times the width of the "Moon: max." circle. For example, if the "Moon: max." circle is 10 cm wide on a computer display, viewing it from 10.3 m (11.3 yards) away will show true representation of the sizes.</figcaption></figure> <p>Since antiquity, the arcminute and arcsecond have been used in <a href="/wiki/Astronomy" title="Astronomy">astronomy</a>: in the <a href="/wiki/Ecliptic_coordinate_system" title="Ecliptic coordinate system">ecliptic coordinate system</a> as latitude (β) and longitude (λ); in the <a href="/wiki/Horizontal_coordinate_system" title="Horizontal coordinate system">horizon system</a> as altitude (Alt) and <a href="/wiki/Azimuth" title="Azimuth">azimuth</a> (Az); and in the <a href="/wiki/Equatorial_coordinate_system" title="Equatorial coordinate system">equatorial coordinate system</a> as <a href="/wiki/Declination" title="Declination">declination</a> (δ). All are measured in degrees, arcminutes, and arcseconds. The principal exception is <a href="/wiki/Right_ascension" title="Right ascension">right ascension</a> (RA) in equatorial coordinates, which is measured in time units of hours, minutes, and seconds. </p><p>Contrary to what one might assume, minutes and seconds of arc do not directly relate to minutes and seconds of time, in either the rotational frame of the Earth around its own axis (day), or the Earth's rotational frame around the Sun (year). The Earth's rotational rate around its own axis is 15 minutes of arc per minute of time (360 degrees / 24 hours in day); the Earth's rotational rate around the Sun (not entirely constant) is roughly 24 minutes of time per minute of arc (from 24 hours in day), which tracks the annual progression of the Zodiac. Both of these factor in what astronomical objects you can see from surface telescopes (time of year) and when you can best see them (time of day), but neither are in unit correspondence. For simplicity, the explanations given assume a degree/day in the Earth's annual rotation around the Sun, which is off by roughly 1%. The same ratios hold for seconds, due to the consistent factor of 60 on both sides. </p><p>The arcsecond is also often used to describe small astronomical angles such as the angular diameters of planets (e.g. the angular diameter of Venus which varies between 10″ and 60″); the <a href="/wiki/Proper_motion" title="Proper motion">proper motion</a> of stars; the separation of components of <a href="/wiki/Binary_star_system" class="mw-redirect" title="Binary star system">binary star systems</a>; and <a href="/wiki/Parallax" title="Parallax">parallax</a>, the small change of position of a star or Solar System body as the Earth revolves about the Sun. These small angles may also be written in milliarcseconds (mas), or thousandths of an arcsecond. The unit of distance called the <a href="/wiki/Parsec" title="Parsec">parsec</a>, abbreviated from the <b>par</b>allax angle of one arc <b>sec</b>ond, was developed for such parallax measurements. The distance from the Sun to a celestial object is the <a href="/wiki/Multiplicative_inverse" title="Multiplicative inverse">reciprocal</a> of the angle, measured in arcseconds, of the object's apparent movement caused by parallax. </p><p>The <a href="/wiki/European_Space_Agency" title="European Space Agency">European Space Agency</a>'s <a href="/wiki/Astrometry" title="Astrometry">astrometric</a> satellite <a href="/wiki/Gaia_mission" class="mw-redirect" title="Gaia mission">Gaia</a>, launched in 2013, can approximate star positions to 7 microarcseconds (μas).<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p><p>Apart from the Sun, the star with the largest <a href="/wiki/Angular_diameter" title="Angular diameter">angular diameter</a> from Earth is <a href="/wiki/R_Doradus" title="R Doradus">R Doradus</a>, a <a href="/wiki/Red_giant" title="Red giant">red giant</a> with a diameter of 0.05″. Because of the effects of atmospheric <a href="/wiki/Astronomical_seeing" title="Astronomical seeing">blurring</a>, ground-based <a href="/wiki/Telescope" title="Telescope">telescopes</a> will smear the image of a star to an angular diameter of about 0.5″; in poor conditions this increases to 1.5″ or even more. The dwarf planet <a href="/wiki/Pluto" title="Pluto">Pluto</a> has proven difficult to resolve because its <a href="/wiki/Angular_diameter" title="Angular diameter">angular diameter</a> is about 0.1″.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> Techniques exist for improving seeing on the ground. <a href="/wiki/Adaptive_optics" title="Adaptive optics">Adaptive optics</a>, for example, can produce images around 0.05″ on a 10 m class telescope. </p><p>Space telescopes are not affected by the Earth's atmosphere but are <a href="/wiki/Diffraction_limit#Diffraction_limit_of_telescopes" class="mw-redirect" title="Diffraction limit">diffraction limited</a>. For example, the <a href="/wiki/Hubble_Space_Telescope" title="Hubble Space Telescope">Hubble Space Telescope</a> can reach an angular size of stars down to about 0.1″. </p> <div class="mw-heading mw-heading3"><h3 id="Cartography">Cartography</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Minute_and_second_of_arc&action=edit&section=6" title="Edit section: Cartography"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Minutes (′) and seconds (″) of arc are also used in <a href="/wiki/Cartography" title="Cartography">cartography</a> and <a href="/wiki/Navigation" title="Navigation">navigation</a>. At <a href="/wiki/Sea_level" title="Sea level">sea level</a> one minute of arc along the <a href="/wiki/Equator" title="Equator">equator</a> equals exactly one <a href="/wiki/Geographical_mile" title="Geographical mile">geographical mile</a> (not to be confused with international mile or statute mile) along the Earth's equator or approximately one <a href="/wiki/Nautical_mile" title="Nautical mile">nautical mile</a> (1,852 <a href="/wiki/Metre" title="Metre">metres</a>; 1.151 <a href="/wiki/Mile" title="Mile">miles</a>).<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> A second of arc, one sixtieth of this amount, is roughly 30 metres (98 feet). The exact distance varies along <a href="/wiki/Meridian_arc" title="Meridian arc">meridian arcs</a> or any other <a href="/wiki/Great_circle" title="Great circle">great circle</a> arcs because the <a href="/wiki/Figure_of_the_Earth" title="Figure of the Earth">figure of the Earth</a> is slightly <a href="/wiki/Oblate_spheroid" class="mw-redirect" title="Oblate spheroid">oblate</a> (bulges a third of a percent at the equator). </p><p>Positions are traditionally given using degrees, minutes, and seconds of arcs for <a href="/wiki/Latitude" title="Latitude">latitude</a>, the arc north or south of the equator, and for <a href="/wiki/Longitude" title="Longitude">longitude</a>, the arc east or west of the <a href="/wiki/Prime_Meridian" class="mw-redirect" title="Prime Meridian">Prime Meridian</a>. Any position on or above the Earth's <a href="/wiki/Reference_ellipsoid" class="mw-redirect" title="Reference ellipsoid">reference ellipsoid</a> can be precisely given with this method. However, when it is inconvenient to use <a href="/wiki/Radix" title="Radix">base</a>-60 for minutes and seconds, positions are frequently expressed as decimal fractional degrees to an equal amount of precision. Degrees given to three decimal places (<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den"><span class="nowrap"><span data-sort-value="7003100000000000000♠"></span>1000</span></span></span>⁠</span> of a degree) have about <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">4</span></span>⁠</span> the precision of degrees-minutes-seconds (<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den"><span class="nowrap"><span data-sort-value="7003360000000000000♠"></span>3600</span></span></span>⁠</span> of a degree) and specify locations within about 120 metres (390 feet). For navigational purposes positions are given in degrees and decimal minutes, for instance The Needles lighthouse is at 50º 39.734’N 001º 35.500’W.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Property_cadastral_surveying">Property cadastral surveying</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Minute_and_second_of_arc&action=edit&section=7" title="Edit section: Property cadastral surveying"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Related to cartography, property boundary <a href="/wiki/Surveying" title="Surveying">surveying</a> using the <a href="/wiki/Metes_and_bounds" title="Metes and bounds">metes and bounds</a> system and <a href="/wiki/Cadastral_surveying" title="Cadastral surveying">cadastral surveying</a> relies on fractions of a degree to describe property lines' angles in reference to <a href="/wiki/Cardinal_direction" title="Cardinal direction">cardinal directions</a>. A boundary "mete" is described with a beginning reference point, the cardinal direction North or South followed by an angle less than 90 degrees and a second cardinal direction, and a linear distance. The boundary runs the specified linear distance from the beginning point, the direction of the distance being determined by rotating the first cardinal direction the specified angle toward the second cardinal direction. For example, <i>North 65° 39′ 18″ West 85.69 feet</i> would describe a line running from the starting point 85.69 feet in a direction 65° 39′ 18″ (or 65.655°) away from north toward the west. </p> <div class="mw-heading mw-heading3"><h3 id="Firearms">Firearms</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Minute_and_second_of_arc&action=edit&section=8" title="Edit section: Firearms"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Ballistic_table_for_7.62x51_mm_NATO_(mrad_and_moa).png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/60/Ballistic_table_for_7.62x51_mm_NATO_%28mrad_and_moa%29.png/220px-Ballistic_table_for_7.62x51_mm_NATO_%28mrad_and_moa%29.png" decoding="async" width="220" height="287" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/60/Ballistic_table_for_7.62x51_mm_NATO_%28mrad_and_moa%29.png/330px-Ballistic_table_for_7.62x51_mm_NATO_%28mrad_and_moa%29.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/60/Ballistic_table_for_7.62x51_mm_NATO_%28mrad_and_moa%29.png/440px-Ballistic_table_for_7.62x51_mm_NATO_%28mrad_and_moa%29.png 2x" data-file-width="1598" data-file-height="2087" /></a><figcaption>Example ballistic table for a given <a href="/wiki/7.62%C3%9751mm_NATO" title="7.62×51mm NATO">7.62×51mm NATO</a> load. Bullet drop and wind drift are shown both in <a href="/wiki/Milliradian" title="Milliradian">mrad</a> and minute of angle.</figcaption></figure> <p>The arcminute is commonly found in the <a href="/wiki/Firearm" title="Firearm">firearms</a> industry and literature, particularly concerning the <a href="/wiki/Accuracy_and_precision" title="Accuracy and precision">precision</a> of <a href="/wiki/Rifle" title="Rifle">rifles</a>, though the industry refers to it as <b>minute of angle</b> (MOA). It is especially popular as a unit of measurement with shooters familiar with the <a href="/wiki/Imperial_measurement_system" class="mw-redirect" title="Imperial measurement system">imperial measurement system</a> because 1 MOA <a href="/wiki/Subtension" class="mw-redirect" title="Subtension">subtends</a> a circle with a diameter of 1.047 <a href="/wiki/Inch" title="Inch">inches</a> (which is often rounded to just 1 inch) at 100 <a href="/wiki/Yard" title="Yard">yards</a> (2.66 cm at 91 m or 2.908 cm at 100 m), a traditional distance on American <a href="/wiki/Shooting_range" title="Shooting range">target ranges</a>. The <a href="/wiki/Subtension" class="mw-redirect" title="Subtension">subtension</a> is linear with the distance, for example, at 500 yards, 1 MOA subtends 5.235 inches, and at 1000 yards 1 MOA subtends 10.47 inches. Since many modern <a href="/wiki/Telescopic_sight" title="Telescopic sight">telescopic sights</a> are adjustable in half (<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">2</span></span>⁠</span>), quarter (<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">4</span></span>⁠</span>) or eighth (<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">8</span></span>⁠</span>) MOA increments, also known as <i>clicks</i>, <a href="/wiki/Zeroing" class="mw-redirect" title="Zeroing">zeroing</a> and adjustments are made by counting 2, 4 and 8 clicks per MOA respectively. </p><p>For example, if the point of impact is 3 inches high and 1.5 inches left of the point of aim at 100 yards (which for instance could be measured by using a <a href="/wiki/Spotting_scope" title="Spotting scope">spotting scope</a> with a calibrated reticle, or a target delineated for such purposes), the scope needs to be adjusted 3 MOA down, and 1.5 MOA right. Such adjustments are trivial when the scope's adjustment dials have a MOA scale printed on them, and even figuring the right number of clicks is relatively easy on scopes that <i>click</i> in fractions of MOA. This makes zeroing and adjustments much easier: </p> <ul><li>To adjust a <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><span class="frac"><span class="num">1</span>⁄<span class="den">2</span></span> MOA scope 3 MOA down and 1.5 MOA right, the scope needs to be adjusted 3 × 2 = 6 clicks down and 1.5 x 2 = 3 clicks right</li> <li>To adjust a <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">1</span>⁄<span class="den">4</span></span> MOA scope 3 MOA down and 1.5 MOA right, the scope needs to be adjusted 3 x 4 = 12 clicks down and 1.5 × 4 = 6 clicks right</li> <li>To adjust a <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">1</span>⁄<span class="den">8</span></span> MOA scope 3 MOA down and 1.5 MOA right, the scope needs to be adjusted 3 x 8 = 24 clicks down and 1.5 × 8 = 12 clicks right</li></ul> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:MOA_and_mrad_comparison.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/MOA_and_mrad_comparison.png/220px-MOA_and_mrad_comparison.png" decoding="async" width="220" height="111" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/MOA_and_mrad_comparison.png/330px-MOA_and_mrad_comparison.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/87/MOA_and_mrad_comparison.png/440px-MOA_and_mrad_comparison.png 2x" data-file-width="798" data-file-height="402" /></a><figcaption>Comparison of minute of arc (MOA) and <a href="/wiki/Milliradian" title="Milliradian">milliradian</a> (mrad).</figcaption></figure> <p>Another common system of measurement in firearm scopes is the <a href="/wiki/Milliradian" title="Milliradian">milliradian</a> (mrad). Zeroing an mrad based scope is easy for users familiar with <a href="/wiki/Decimal" title="Decimal">base ten</a> systems. The most common adjustment value in mrad based scopes is <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">10</span></span>⁠</span> mrad (which approximates <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">1</span>⁄<span class="den">3</span></span> MOA). </p> <ul><li>To adjust a <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">10</span></span>⁠</span> mrad scope 0.9 mrad down and 0.4 mrad right, the scope needs to be adjusted 9 clicks down and 4 clicks right (which equals approximately 3 and 1.5 MOA respectively).</li></ul> <p>One thing to be aware of is that some MOA scopes, including some higher-end models, are calibrated such that an adjustment of 1 MOA on the scope knobs corresponds to exactly 1 inch of impact adjustment on a target at 100 yards, rather than the mathematically correct 1.047 inches. This is commonly known as the Shooter's MOA (SMOA) or Inches Per Hundred Yards (IPHY). While the difference between one true MOA and one SMOA is less than half of an inch even at 1000 yards,<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> this error compounds significantly on longer range shots that may require adjustment upwards of 20–30 MOA to compensate for the bullet drop. If a shot requires an adjustment of 20 MOA or more, the difference between true MOA and SMOA will add up to 1 inch or more. In competitive target shooting, this might mean the difference between a hit and a miss. </p><p>The physical group size equivalent to <i>m</i> minutes of arc can be calculated as follows: group size = tan(<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num"><i>m</i></span><span class="sr-only">/</span><span class="den">60</span></span>⁠</span>) × distance. In the example previously given, for 1 minute of arc, and substituting 3,600 inches for 100 yards, 3,600 tan(<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">60</span></span>⁠</span>) ≈ 1.047 inches. In <a href="/wiki/Metric_units" class="mw-redirect" title="Metric units">metric units</a> 1 MOA at 100 metres ≈ 2.908 centimetres. </p><p>Sometimes, a precision-oriented firearm's performance will be measured in MOA. This simply means that under ideal conditions (i.e. no wind, high-grade ammo, clean barrel, and a stable mounting platform such as a vise or a benchrest used to eliminate shooter error), the gun is capable of producing a <a href="/wiki/Shot_grouping" title="Shot grouping">group of shots</a> whose center points (center-to-center) fit into a circle, the average diameter of circles in several groups can be subtended by that amount of arc. For example, a <i>1 MOA rifle</i> should be capable, under ideal conditions, of repeatably shooting 1-inch groups at 100 yards. Most higher-end rifles are warrantied by their manufacturer to shoot under a given MOA threshold (typically 1 MOA or better) with specific ammunition and no error on the shooter's part. For example, Remington's <a href="/wiki/M24_Sniper_Weapon_System" class="mw-redirect" title="M24 Sniper Weapon System">M24 Sniper Weapon System</a> is required to shoot 0.8 MOA or better, or be rejected from sale by <a href="/wiki/Quality_control" title="Quality control">quality control</a>. </p><p>Rifle manufacturers and gun magazines often refer to this capability as <i>sub-MOA</i>, meaning a gun consistently shooting groups under 1 MOA. This means that a single group of 3 to 5 shots at 100 yards, or the average of several groups, will measure less than 1 MOA between the two furthest shots in the group, i.e. all shots fall within 1 MOA. If larger samples are taken (i.e., more shots per group) then group size typically increases, however this will ultimately average out. If a rifle was truly a 1 MOA rifle, it would be just as likely that two consecutive shots land exactly on top of each other as that they land 1 MOA apart. For 5-shot groups, based on 95% <a href="/wiki/Confidence_interval" title="Confidence interval">confidence</a>, a rifle that normally shoots 1 MOA can be expected to shoot groups between 0.58 MOA and 1.47 MOA, although the majority of these groups will be under 1 MOA. What this means in practice is if a rifle that shoots 1-inch groups on average at 100 yards shoots a group measuring 0.7 inches followed by a group that is 1.3 inches, this is not statistically abnormal.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </p><p>The <a href="/wiki/Metric_system" title="Metric system">metric system</a> counterpart of the MOA is the <a href="/wiki/Milliradian" title="Milliradian">milliradian</a> (mrad or 'mil'), being equal to <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">1</span>⁄<span class="den">1000</span></span> of the target range, laid out on a circle that has the observer as centre and the target range as radius. The number of milliradians on a full such circle therefore always is equal to 2 × <span class="texhtml mvar" style="font-style:italic;">π</span> × 1000, regardless the target range. Therefore, 1 MOA ≈ 0.2909 mrad. This means that an object which spans 1 mrad on the <a href="/wiki/Reticle" title="Reticle">reticle</a> is at a range that is in metres equal to the object's linear size in millimetres (e.g. an object of 100 mm subtending 1 mrad is 100 metres away).<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> So there is no conversion factor required, contrary to the MOA system. A reticle with markings (hashes or dots) spaced with a one mrad apart (or a fraction of a mrad) are collectively called a mrad reticle. If the markings are round they are called <b>mil-dots</b>. </p><p>In the table below conversions from mrad to metric values are exact (e.g. 0.1 mrad equals exactly 10 mm at 100 metres), while conversions of minutes of arc to both metric and imperial values are approximate. </p> <table class="wikitable" style="text-align: right;"> <caption>Conversion of various sight adjustment increment </caption> <tbody><tr> <th rowspan="2">Increment, <br />or click </th> <th rowspan="2">(<a href="/wiki/Minute_of_arc" class="mw-redirect" title="Minute of arc">mins <br />of arc</a>) </th> <th rowspan="2">(<a href="/wiki/Milliradian" title="Milliradian">milli-<br />radians</a>) </th> <th colspan="3">At 100<span class="nowrap"> </span>m </th> <th>At 100<span class="nowrap"> </span>yd </th></tr> <tr> <th>(<a href="/wiki/Millimeter" class="mw-redirect" title="Millimeter">mm</a>) </th> <th>(<a href="/wiki/Centimeter" class="mw-redirect" title="Centimeter">cm</a>) </th> <th>(<a href="/wiki/Inch" title="Inch">in</a>) </th> <th>(<a href="/wiki/Inch" title="Inch">in</a>) </th></tr> <tr> <td style="background: #BFD; color:black; vertical-align: middle; text-align: center;" class="yes2 table-yes2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">1</span>⁄<span class="den">12</span></span>′ </td> <td style="text-align: right;">0.083′ </td> <td>0.024 mrad </td> <td>2.42 mm </td> <td>0.242 cm </td> <td style="text-align: right;">0.0958 in </td> <td>0.087 in </td></tr> <tr> <td style="background: #BFD; color:black; vertical-align: middle; text-align: center;" class="yes2 table-yes2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">0.25</span>⁄<span class="den">10</span></span> mrad </td> <td>0.086′ </td> <td style="background: #BFD; color:black; vertical-align: middle; text-align: right;" class="yes2 table-yes2">0.025 mrad </td> <td style="background: #BFD; color:black; vertical-align: middle; text-align: right;" class="yes2 table-yes2">2.5 mm </td> <td style="background: #BFD; color:black; vertical-align: middle; text-align: right;" class="yes2 table-yes2">0.25 cm </td> <td style="text-align: right;">0.0985 in </td> <td>0.09 in </td></tr> <tr> <td style="background: #BFD; color:black; vertical-align: middle; text-align: center;" class="yes2 table-yes2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">1</span>⁄<span class="den">8</span></span>′ </td> <td style="background: #BFD; color:black; vertical-align: middle; text-align: right;" class="yes2 table-yes2">0.125′ </td> <td>0.036 mrad </td> <td>3.64 mm </td> <td>0.36 cm </td> <td style="text-align: right;">0.144 in </td> <td>0.131 in </td></tr> <tr> <td style="background: #BFD; color:black; vertical-align: middle; text-align: center;" class="yes2 table-yes2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">1</span>⁄<span class="den">6</span></span>′ </td> <td>0.167′ </td> <td>0.0485 mrad </td> <td>4.85 mm </td> <td>0.485 cm </td> <td>0.192 in </td> <td>0.175 in </td></tr> <tr> <td style="background: #BFD; color:black; vertical-align: middle; text-align: center;" class="yes2 table-yes2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">0.5</span>⁄<span class="den">10</span></span> mrad </td> <td>0.172′ </td> <td style="background: #BFD; color:black; vertical-align: middle; text-align: right;" class="yes2 table-yes2">0.05 mrad </td> <td style="background: #BFD; color:black; vertical-align: middle; text-align: right;" class="yes2 table-yes2">5 mm </td> <td style="background: #BFD; color:black; vertical-align: middle; text-align: right;" class="yes2 table-yes2">0.5 cm </td> <td>0.197 in </td> <td>0.18 in </td></tr> <tr> <td style="background: #BFD; color:black; vertical-align: middle; text-align: center;" class="yes2 table-yes2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">1</span>⁄<span class="den">4</span></span>′ </td> <td style="background: #BFD; color:black; vertical-align: middle; text-align: center;" class="yes2 table-yes2">0.25′ </td> <td>0.073 mrad </td> <td>7.27 mm </td> <td>0.73 cm </td> <td>0.29 in </td> <td>0.26 in </td></tr> <tr> <td style="background: #BFD; color:black; vertical-align: middle; text-align: center;" class="yes2 table-yes2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">1</span>⁄<span class="den">10</span></span> mrad </td> <td>0.344′ </td> <td style="background: #BFD; color:black; vertical-align: middle; text-align: center;" class="yes2 table-yes2">0.1 mrad </td> <td style="background: #BFD; color:black; vertical-align: middle; text-align: center;" class="yes2 table-yes2">10 mm </td> <td style="background: #BFD; color:black; vertical-align: middle; text-align: center;" class="yes2 table-yes2">1 cm </td> <td>0.39 in </td> <td>0.36 in </td></tr> <tr> <td style="background: #BFD; color:black; vertical-align: middle; text-align: center;" class="yes2 table-yes2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">1</span>⁄<span class="den">2</span></span>′ </td> <td style="background: #BFD; color:black; vertical-align: middle; text-align: center;" class="yes2 table-yes2">0.5′ </td> <td>0.145 mrad </td> <td>14.54 mm </td> <td>1.45 cm </td> <td>0.57 in </td> <td>0.52 in </td></tr> <tr> <td style="background: #BFD; color:black; vertical-align: middle; text-align: center;" class="yes2 table-yes2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">1.5</span>⁄<span class="den">10</span></span> mrad </td> <td>0.516′ </td> <td style="background: #BFD; color:black; vertical-align: middle; text-align: center;" class="yes2 table-yes2">0.15 mrad </td> <td style="background: #BFD; color:black; vertical-align: middle; text-align: center;" class="yes2 table-yes2">15 mm </td> <td style="background: #BFD; color:black; vertical-align: middle; text-align: center;" class="yes2 table-yes2">1.5 cm </td> <td>0.59 in </td> <td>0.54 in </td></tr> <tr> <td style="background: #BFD; color:black; vertical-align: middle; text-align: center;" class="yes2 table-yes2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">2</span>⁄<span class="den">10</span></span> mrad </td> <td>0.688′ </td> <td style="background: #BFD; color:black; vertical-align: middle; text-align: center;" class="yes2 table-yes2">0.2 mrad </td> <td style="background: #BFD; color:black; vertical-align: middle; text-align: center;" class="yes2 table-yes2">20 mm </td> <td style="background: #BFD; color:black; vertical-align: middle; text-align: center;" class="yes2 table-yes2">2 cm </td> <td>0.79 in </td> <td>0.72 in </td></tr> <tr> <td style="background: #BFD; color:black; vertical-align: middle; text-align: center;" class="yes2 table-yes2">1′ </td> <td style="background: #BFD; color:black; vertical-align: middle; text-align: center;" class="yes2 table-yes2">1.0′ </td> <td style="text-align: right;">0.291 mrad </td> <td>29.1 mm </td> <td>2.91 cm </td> <td>1.15 in </td> <td>1.047 in </td></tr> <tr> <td style="background: #BFD; color:black; vertical-align: middle; text-align: center;" class="yes2 table-yes2">1 mrad </td> <td style="background: #BFD; color:black; vertical-align: middle; text-align: center;" class="yes2 table-yes2">3.438′ </td> <td style="background: #BFD; color:black; vertical-align: middle; text-align: center;" class="yes2 table-yes2">1 mrad </td> <td style="background: #BFD; color:black; vertical-align: middle; text-align: center;" class="yes2 table-yes2">100 mm </td> <td style="background: #BFD; color:black; vertical-align: middle; text-align: center;" class="yes2 table-yes2">10 cm </td> <td>3.9 in </td> <td>3.6 in </td></tr></tbody></table> <ul><li>1′ at 100 yards is about 1.047 inches<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup></li> <li>1′ ≈ 0.291 mrad (or 29.1 mm at 100 m, approximately 30 mm at 100 m)</li> <li>1 mrad ≈ 3.44′, so <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">10</span></span>⁠</span> mrad ≈ <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">3</span></span>⁠</span>′</li> <li>0.1 mrad equals exactly 1 cm at 100 m, or exactly 0.36 inches at 100 yards</li></ul> <div class="mw-heading mw-heading3"><h3 id="Human_vision">Human vision</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Minute_and_second_of_arc&action=edit&section=9" title="Edit section: Human vision"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In humans, <a href="/wiki/Normal_vision" class="mw-redirect" title="Normal vision">20/20 vision</a> is the ability to resolve a <a href="/wiki/Spatial_pattern" class="mw-redirect" title="Spatial pattern">spatial pattern</a> separated by a <a href="/wiki/Visual_angle" title="Visual angle">visual angle</a> of one minute of arc, from a distance of twenty <a href="/wiki/Foot_(unit)" title="Foot (unit)">feet</a>. A 20/20 letter subtends 5 minutes of arc total. </p> <div class="mw-heading mw-heading3"><h3 id="Materials">Materials</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Minute_and_second_of_arc&action=edit&section=10" title="Edit section: Materials"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The deviation from parallelism between two surfaces, for instance in <a href="/wiki/Optical_engineering" title="Optical engineering">optical engineering</a>, is usually measured in arcminutes or arcseconds. In addition, arcseconds are sometimes used in <a href="/wiki/Rocking_curve" class="mw-redirect" title="Rocking curve">rocking curve</a> (ω-scan) <a href="/wiki/X_ray_diffraction" class="mw-redirect" title="X ray diffraction">x ray diffraction</a> measurements of high-quality <a href="/wiki/Epitaxy" title="Epitaxy">epitaxial</a> thin films. </p> <div class="mw-heading mw-heading3"><h3 id="Manufacturing">Manufacturing</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Minute_and_second_of_arc&action=edit&section=11" title="Edit section: Manufacturing"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Some measurement devices make use of arcminutes and arcseconds to measure angles when the object being measured is too small for direct visual inspection. For instance, a toolmaker's <a href="/wiki/Optical_comparator" title="Optical comparator">optical comparator</a> will often include an option to measure in "minutes and seconds". </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Minute_and_second_of_arc&action=edit&section=12" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Gradian" title="Gradian">Gradian</a></li> <li><a href="/wiki/Degree_(angle)#Subdivisions" title="Degree (angle)">Degree (angle) § Subdivisions</a></li> <li><a href="/wiki/Sexagesimal#Modern_usage" title="Sexagesimal">Sexagesimal § Modern usage</a></li> <li><a href="/wiki/Square_minute" class="mw-redirect" title="Square minute">Square minute</a></li> <li><a href="/wiki/Square_second_of_arc" class="mw-redirect" title="Square second of arc">Square second</a></li> <li><a href="/wiki/Steradian" title="Steradian">Steradian</a></li> <li><a href="/wiki/Milliradian" title="Milliradian">Milliradian</a></li> <li><a href="/wiki/Nautical_mile" title="Nautical mile">Nautical mile</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Minute_and_second_of_arc&action=edit&section=13" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></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"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-:2-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-:2_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:2_1-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><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 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Retrieved <span class="nowrap">31 August</span> 2020</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=mathworld.wolfram.com&rft.atitle=Arc+Second&rft.aulast=Weisstein&rft.aufirst=Eric+W.&rft_id=https%3A%2F%2Fmathworld.wolfram.com%2FArcSecond.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMinute+and+second+of+arc" class="Z3988"></span></span> </li> <li id="cite_note-:3-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-:3_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:3_2-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:3_2-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.inchcalculator.com/convert/arcminute-to-degree/">"Minutes of Arc to Degree Conversion"</a>. <i>Inch Calculator</i><span class="reference-accessdate">. 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See <a href="/wiki/Talk:Minute_and_second_of_arc#Stop_quibbling" title="Talk:Minute and second of arc">Talk</a></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Minute_and_second_of_arc&action=edit&section=14" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://www.scribd.com/doc/251836084/Mils-MOA-and-the-Range-Estimation-Equations">MOA/ mils</a> By Robert Simeone</li> <li>A Guide to <a rel="nofollow" class="external text" href="https://binoscopes.com/blog/how-to-range-a-target-using-moa/">calculate distance using MOA Scope</a> by Steve Coffman</li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist 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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" 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