Measurement | Definition, Types, Instruments, & Facts

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Ludwig</a></dd> <dd><a href="/biography/Henry-Maudslay" topicid="369915">Henry Maudslay</a></dd> <dd><a href="/biography/Jagadish-Chandra-Bose" topicid="74631">Sir Jagadish Chandra Bose</a></dd> <dd><a href="/biography/Edmund-Gunter" topicid="249527">Edmund Gunter</a></dd> <dd><a href="/biography/Edward-Weston-American-engineer-and-industrialist" topicid="641135">Edward Weston</a></dd> </dl> <button class="js-more-btn d-none btn btn-unstyled font-12 bg-gray-50" aria-label="Toggle more/less fact data"> <em class="js-content link-blue">(Show more)</em> </button> </div> </div> <div class=""> <div class="js-fact mb-10 line-clamp clamp-3"> <dl> <dt>Related Topics: </dt> <dd><a href="/technology/radiation-measurement" topicid="1357248">radiation measurement</a></dd> <dd><a href="/science/psychological-testing" topicid="481664">psychological testing</a></dd> <dd><a href="/science/measurement-system" topicid="1286365">measurement system</a></dd> <dd><a href="/money/productivity" topicid="478036">productivity</a></dd> <dd><a href="/technology/oscilloscope" topicid="2132244">oscilloscope</a></dd> </dl> <button class="js-more-btn d-none btn btn-unstyled font-12 bg-gray-50" aria-label="Toggle more/less fact data"> <em class="js-content link-blue">(Show more)</em> </button> </div> <div class="text-center"> <a class="btn btn-sm btn-link p-0" href="/facts/measurement"> See all related content </a> </div> </div> </div> </div><span class="marker before-article"></span><section data-level="1" id="ref1"><span class="marker PREMOD1 mod-inline"></span><p class="topic-paragraph"><strong><span id="ref280725"></span>measurement</strong>, the process of associating numbers with physical quantities and phenomena. Measurement is fundamental to the sciences; to <a href="https://www.britannica.com/technology/engineering" class="md-crosslink autoxref " data-show-preview="true">engineering</a>, construction, and other technical fields; and to almost all everyday activities. For that reason the elements, conditions, <a class="md-dictionary-link md-dictionary-tt-off eb" data-term="limitations" href="https://www.britannica.com/dictionary/limitations" data-type="EB">limitations</a>, and theoretical foundations of measurement have been much studied. See also <a href="https://www.britannica.com/science/measurement-system" class="md-crosslink " data-show-preview="true">measurement system</a> for a comparison of different systems and the history of their development.</p><span class="marker MOD1 mod-inline"></span><span class="marker PREMOD2 mod-inline"></span><p class="topic-paragraph">Measurements may be made by unaided human senses, in which case they are often called estimates, or, more commonly, by the use of instruments, which may range in complexity from simple rules for measuring lengths to highly sophisticated systems designed to detect and measure quantities entirely beyond the capabilities of the senses, such as radio waves from a distant star or the magnetic moment of a <a href="https://www.britannica.com/science/subatomic-particle" class="md-crosslink autoxref " data-show-preview="true">subatomic particle</a>. (See <a href="https://www.britannica.com/technology/instrumentation-technology" class="md-crosslink " data-show-preview="true">instrumentation</a>.)</p><span class="marker MOD2 mod-inline"></span><span class="marker PREMOD3 mod-inline"></span><p class="topic-paragraph">Measurement begins with a definition of the quantity that is to be measured, and it always involves a comparison with some known quantity of the same kind. If the object or quantity to be measured is not accessible for direct comparison, it is converted or “transduced” into an <a class="md-dictionary-link md-dictionary-tt-off mw" data-term="analogous" href="https://www.merriam-webster.com/dictionary/analogous" data-type="MW">analogous</a> measurement signal. Since measurement always involves some interaction between the object and the observer or observing instrument, there is always an exchange of energy, which, although in everyday applications is negligible, can become considerable in some types of measurement and thereby limit accuracy.</p><a class="link-module shadow-sm d-block qa-quiz-module" href="/quiz/fun-facts-of-measurement-math" data-link-module-iframe-link=""> <img loading="lazy" src="https://cdn.britannica.com/68/166068-131-03976F7B/barometer-Barometer-Technology-measurement-readout-pressure-mathematics.jpg" alt="barometer. Antique Barometer with readout. Technology measurement, mathematics, measure atmospheric pressure" class="rounded-sm mr-15" width="70" /> <div class="line-clamp clamp-5"> <div class="module-title bg-green">Britannica Quiz</div> <div class="font-weight-semi-bold mt-5">Fun Facts of Measurement & Math</div> </div> </a><span class="marker MOD3 mod-inline"></span></section><span class="marker h2"></span><section data-level="1" id="ref233663"><h2 class="h1">Measurement instruments and systems</h2><span class="marker PREMOD4 mod-inline"></span><p class="topic-paragraph">In general, measuring systems <a class="md-dictionary-link md-dictionary-tt-off mw" data-term="comprise" href="https://www.merriam-webster.com/dictionary/comprise" data-type="MW">comprise</a> a number of functional elements. One element is required to discriminate the object and sense its dimensions or frequency. This information is then transmitted throughout the system by physical signals. If the object is itself active, such as water flow, it may <a href="https://www.britannica.com/science/power-physics" class="md-crosslink autoxref " data-show-preview="true">power</a> the signal; if passive, it must trigger the signal by interaction either with an energetic probe, such as a light source or <a href="https://www.britannica.com/technology/X-ray-tube" class="md-crosslink autoxref " data-show-preview="true">X-ray tube</a>, or with a carrier signal. Eventually the physical signal is compared with a reference signal of known quantity that has been subdivided or multiplied to suit the range of measurement required. The reference signal is derived from objects of known quantity by a process called<span id="ref280726"></span> calibration. The comparison may be an <a class="md-dictionary-link md-dictionary-tt-off mw" data-term="analog" href="https://www.merriam-webster.com/dictionary/analog" data-type="MW">analog</a> process in which signals in a continuous dimension are brought to equality. An <a class="md-dictionary-link md-dictionary-tt-off mw" data-term="alternative" href="https://www.merriam-webster.com/dictionary/alternative" data-type="MW">alternative</a> comparison process is <a href="https://www.britannica.com/science/quantum" class="md-crosslink autoxref " data-show-preview="true">quantization</a> by counting, i.e., dividing the signal into parts of equal and known size and adding up the number of parts.</p><span class="marker MOD4 mod-inline"></span><span class="marker PREMOD5 mod-inline"></span><p class="topic-paragraph">Other functions of measurement systems <a class="md-dictionary-link md-dictionary-tt-off mw" data-term="facilitate" href="https://www.merriam-webster.com/dictionary/facilitate" data-type="MW">facilitate</a> the basic process described above. Amplification ensures that the physical signal is strong enough to complete the measurement. In order to reduce <a class="md-dictionary-link md-dictionary-tt-off mw" data-term="degradation" href="https://www.merriam-webster.com/dictionary/degradation" data-type="MW">degradation</a> of the measurement as it progresses through the system, the signal may be converted to coded or digital form. Magnification, enlarging the measurement signal without increasing its power, is often necessary to match the output of one element of the system with the input of another, such as matching the size of the readout <a href="https://www.britannica.com/science/metre-measurement" class="md-crosslink autoxref " data-show-preview="true">meter</a> with the discerning power of the <a href="https://www.britannica.com/science/human-eye" class="md-crosslink autoxref " data-show-preview="true">human eye</a>.</p><span class="marker MOD5 mod-inline"></span><span class="marker PREMOD6 mod-inline"></span><p class="topic-paragraph">One important type of measurement is the analysis of <a href="https://www.britannica.com/science/theory-of-resonance" class="md-crosslink " data-show-preview="true">resonance</a>, or the frequency of variation within a physical system. This is determined by <a href="https://www.britannica.com/science/harmonic-analysis" class="md-crosslink autoxref " data-show-preview="true">harmonic analysis</a>, commonly exhibited in the sorting of signals by a radio receiver. <span id="ref280727"></span><a href="https://www.britannica.com/science/computation" class="md-crosslink ">Computation</a> is another important measurement process, in which measurement signals are <a class="md-dictionary-link md-dictionary-tt-off eb" data-term="manipulated" href="https://www.britannica.com/dictionary/manipulated" data-type="EB">manipulated</a> mathematically, typically by some form of analog or <a href="https://www.britannica.com/technology/digital-computer" class="md-crosslink autoxref " data-show-preview="true">digital computer</a>. Computers may also provide a control function in monitoring system performance.</p><span class="marker MOD6 mod-inline"></span><span class="marker PREMOD7 mod-inline"></span><p class="topic-paragraph">Measuring systems may also include devices for transmitting signals over great distances (see <a href="https://www.britannica.com/technology/telemetry" class="md-crosslink " data-show-preview="true">telemetry</a>). All measuring systems, even highly automated ones, include some method of displaying the signal to an observer. Visual display systems may comprise a <a class="md-dictionary-link md-dictionary-tt-off mw" data-term="calibrated" href="https://www.merriam-webster.com/dictionary/calibrated" data-type="MW">calibrated</a> chart and a pointer, an <a class="md-dictionary-link md-dictionary-tt-off mw" data-term="integrated" href="https://www.merriam-webster.com/dictionary/integrated" data-type="MW">integrated</a> display on a <a href="https://www.britannica.com/technology/cathode-ray-tube" class="md-crosslink autoxref " data-show-preview="true">cathode-ray tube</a>, or a digital readout. Measurement systems often include elements for recording. A common type utilizes a writing stylus that records measurements on a moving chart. Electrical recorders may include feedback reading devices for greater accuracy.</p><div class="module-spacing"> <DIV class="marketing-INLINE_SUBSCRIPTION marketing-content" data-marketing-id="INLINE_SUBSCRIPTION"><style> .student-promo-banner-wrapper { container-type: inline-size; margin-bottom: 15px; } @container (min-width: 475px) { .student-promo-banner { flex-direction: row; } .student-promo-banner-img-wrapper { margin-bottom: 0; margin-right: 10px; justify-content: flex-start; } .student-promo-banner-text-wrapper { text-align: left; margin-bottom: 0px; margin-left: 10px; } .student-promo-banner-button-wrapper { margin-right: 0; } }</style> <div class="student-promo-banner-wrapper"> <div class="student-promo-banner d-flex flex-column align-items-center bg-blue rounded p-20"> <div class="student-promo-banner-img-wrapper mb-20 mr-0 d-flex justify-content-center"> <img class="rounded" style="max-width: 100px; min-width: 80px" src="https://cdn.britannica.com/marketing/BlueThistle.webp" /> </div> <div class="student-promo-banner-text-wrapper ml-0 mb-10 text-center text-white"> <div class="h2 mb-10">Get Unlimited Access</div> <div class="h4 font-weight-semi-bold">Try Britannica Premium for free and discover more.</div> </div> <div class="student-promo-banner-button-wrapper d-flex justify-content-center align-items-center ml-auto mr-auto"> <a class="btn btn-m btn-orange" href="https://premium.britannica.com/premium-membership/?utm_source=premium&utm_medium=inline-cta&utm_campaign=black-friday-2024">Subscribe</a> </div> </div> </div> </DIV></div><span class="marker MOD7 mod-inline"></span><span class="marker PREMOD8 mod-inline"></span><p class="topic-paragraph">The actual performance of measuring instruments is affected by numerous external and internal factors. Among external factors are noise and interference, both of which tend to mask or distort the measurement signal. Internal factors include linearity, resolution, <a href="https://www.britannica.com/science/precision-measurement" class="md-crosslink autoxref " data-show-preview="true">precision</a>, and accuracy, all of which are characteristic of a given instrument or system, and <a class="md-dictionary-link md-dictionary-tt-off mw" data-term="dynamic" href="https://www.merriam-webster.com/dictionary/dynamic" data-type="MW">dynamic</a> response, drift, and <a href="https://www.britannica.com/science/hysteresis" class="md-crosslink " data-show-preview="true">hysteresis</a>, which are effects produced in the process of measurement itself. The general question of error in measurement raises the topic of measurement theory.</p><span class="marker MOD8 mod-inline"></span></section><span class="marker h3"></span><section data-level="1" id="ref233664"><h2 class="h1">Measurement theory</h2><span class="marker PREMOD9 mod-inline"></span><p class="topic-paragraph">Measurement theory is the study of how numbers are assigned to objects and phenomena, and its concerns include the kinds of things that can be measured, how different measures relate to each other, and the problem of <span id="ref280729"></span><a href="https://www.britannica.com/science/error-mathematics" class="md-crosslink " data-show-preview="true">error</a> in the measurement process. Any general theory of measurement must come to grips with three basic problems: error; representation, which is the justification of number assignment; and uniqueness, which is the degree to which the kind of representation chosen approaches being the only one possible for the object or phenomenon in question.</p><span class="marker MOD9 mod-inline"></span><span class="marker PREMOD10 mod-inline"></span><p class="topic-paragraph">Various systems of <span id="ref280728"></span><a href="https://www.britannica.com/topic/axiom" class="md-crosslink " data-show-preview="true">axioms</a>, or basic rules and assumptions, have been formulated as a basis for measurement theory. Some of the most important types of <a class="md-dictionary-link md-dictionary-tt-off eb" data-term="axioms" href="https://www.britannica.com/dictionary/axioms" data-type="EB">axioms</a> include axioms of order, axioms of extension, axioms of difference, axioms of conjointness, and axioms of <a href="https://www.britannica.com/science/geometry" class="md-crosslink autoxref " data-show-preview="true">geometry</a>. Axioms of order ensure that the order imposed on objects by the assignment of numbers is the same order attained in actual observation or measurement. Axioms of extension deal with the representation of such attributes as time duration, length, and mass, which can be combined, or concatenated, for multiple objects exhibiting the attribute in question. Axioms of difference govern the measuring of intervals. Axioms of conjointness postulate that attributes that cannot be measured empirically (for example, loudness, intelligence, or hunger) can be measured by observing the way their component <a class="md-dictionary-link md-dictionary-tt-off eb" data-term="dimensions" href="https://www.britannica.com/dictionary/dimensions" data-type="EB">dimensions</a> change in relation to each other. Axioms of geometry govern the representation of dimensionally complex attributes by pairs of numbers, triples of numbers, or even <em>n</em>-tuples of numbers.</p><span class="marker MOD10 mod-inline"></span><span class="marker PREMOD11 mod-inline"></span><p class="topic-paragraph">The problem of error is one of the central concerns of measurement theory. At one time it was believed that errors of measurement could eventually be eliminated through the refinement of scientific principles and equipment. This belief is no longer held by most scientists, and almost all physical measurements reported today are accompanied by some indication of the limitation of accuracy or the probable degree of error. Among the various types of error that must be taken into account are errors of observation (which include instrumental errors, personal errors, systematic errors, and random errors), errors of sampling, and direct and indirect errors (in which one <a class="md-dictionary-link md-dictionary-tt-off mw" data-term="erroneous" href="https://www.merriam-webster.com/dictionary/erroneous" data-type="MW">erroneous</a> measurement is used in computing other measurements).</p><span class="marker MOD11 mod-inline"></span><span class="marker PREMOD12 mod-inline"></span><p class="topic-paragraph">Measurement theory dates back to the 4th century <span class="text-smallcaps">bc</span>, when a theory of magnitudes developed by the Greek mathematicians <a href="https://www.britannica.com/biography/Eudoxus-of-Cnidus" class="md-crosslink " data-show-preview="true">Eudoxus of Cnidus</a> and Thaeatetus was included in <a href="https://www.britannica.com/biography/Euclid-Greek-mathematician" class="md-crosslink " data-show-preview="true">Euclid</a>’s <em>Elements</em>. The first systematic work on observational error was produced by the English mathematician Thomas Simpson in 1757, but the fundamental work on error theory was done by two 18th-century French astronomers, <a href="https://www.britannica.com/biography/Joseph-Louis-Lagrange-comte-de-lEmpire" class="md-crosslink " data-show-preview="true">Joseph-Louis Lagrange</a> and <a href="https://www.britannica.com/biography/Pierre-Simon-marquis-de-Laplace" class="md-crosslink " data-show-preview="true">Pierre-Simon Laplace</a>. The first attempt to incorporate measurement theory into the social sciences also occurred in the 18th century, when <a href="https://www.britannica.com/money/Jeremy-Bentham" class="md-crosslink " data-show-preview="true">Jeremy Bentham</a>, a British utilitarian moralist, attempted to create a theory for the measurement of value. Modern <a class="md-dictionary-link md-dictionary-tt-off mw" data-term="axiomatic" href="https://www.merriam-webster.com/dictionary/axiomatic" data-type="MW">axiomatic</a> theories of measurement derive from the work of two German scientists, <a href="https://www.britannica.com/biography/Hermann-von-Helmholtz" class="md-crosslink " data-show-preview="true">Hermann von Helmholtz</a> and Otto Hölder, and contemporary work on the application of measurement theory to psychology and economics derives in large part from the work of <a href="https://www.britannica.com/money/Oskar-Morgenstern" class="md-crosslink " data-show-preview="true">Oskar Morgenstern</a> and <a href="https://www.britannica.com/biography/John-von-Neumann" class="md-crosslink " data-show-preview="true">John von Neumann</a>.</p><div class="one-good-fact-module"> </div><span class="marker MOD12 mod-inline"></span><span class="marker PREMOD13 mod-inline"></span><p class="topic-paragraph">Since most social theories are speculative in nature, attempts to establish standard measuring sequences or techniques for them have met with limited success. Some of the problems involved in social measurement include the lack of universally accepted theoretical frameworks and thus of quantifiable measures, sampling errors, problems associated with the intrusion of the measurer on the object being measured, and the subjective nature of the information received from human subjects. Economics is probably the <a href="https://www.britannica.com/topic/social-science" class="md-crosslink autoxref " data-show-preview="true">social science</a> that has had the most success in adopting measurement theories, primarily because many economic variables (like price and quantity) can be measured easily and objectively. Demography has successfully employed measurement techniques as well, particularly in the area of <a class="md-dictionary-link md-dictionary-tt-off eb" data-term="mortality" href="https://www.britannica.com/dictionary/mortality" data-type="EB">mortality</a> tables.</p><span class="marker MOD13 mod-inline"></span></section><span class="md-signature">This article was most recently revised and updated by <a href="/editor/Adam-Augustyn/6394">Adam Augustyn</a>.</span><span class="marker end-of-content"></span><span class="marker after-article"></span></div> <div id="chatbot-root"></div> </div> </div> </div> <div class="ai-dialog-placeholder"></div> </div> </div> <aside class="col-md-da-320"></aside> </div> </div> </div> </div> </article></div> </div></div> </div> </main> <div id="md-footer"></div> <noscript><iframe src="//www.googletagmanager.com/ns.html?id=GTM-5W6NC8" height="0" width="0" style="display:none;visibility:hidden"></iframe></noscript> <script type="text/javascript" id="_informizely_script_tag"> var IzWidget = IzWidget || {}; (function (d) { var scriptElement = d.createElement('script'); scriptElement.type = 'text/javascript'; scriptElement.async = true; scriptElement.src = "https://insitez.blob.core.windows.net/site/f780f33e-a610-4ac2-af81-3eb184037547.js"; var node = d.getElementById('_informizely_script_tag'); node.parentNode.insertBefore(scriptElement, node); } )(document); </script>  <script> window.ap3c = window.ap3c || {}; var ap3c = window.ap3c; ap3c.cmd = ap3c.cmd || []; ap3c.cmd.push(function() { ap3c.init('ZO4siT4cLwnykPnzZWJtd3Byb2Q', 'https://engage.email.britannica.com/'); ap3c.track({v: 0}); }); ap3c.activity = function(act) { ap3c.act = (ap3c.act || []); ap3c.act.push(act); }; var s, t; s = document.createElement('script'); s.type = 'text/javascript'; s.src = "https://engage.email.britannica.com/app.js"; t = document.getElementsByTagName('script')[0]; t.parentNode.insertBefore(s, t); </script> <script class="marketing-page-info" type="application/json"> {"pageType":"Topic","templateName":"DESKTOP","pageNumber":1,"pagesTotal":1,"pageId":371701,"pageLength":1336,"initialLoad":true,"lastPageOfScroll":false} </script> <script class="marketing-content-info" type="application/json"> [] </script> <script src="https://cdn.britannica.com/mendel-resources/3-130/js/libs/jquery-3.5.0.min.js?v=3.130.14"></script> <script type="text/javascript" data-type="Init Mendel Code Splitting"> (function() { $.ajax({ dataType: 'script', cache: true, url: 'https://cdn.britannica.com/mendel-resources/3-130/dist/topic-page.js?v=3.130.14' }); })(); </script> <script class="analytics-metadata" type="application/json"> {"leg":"B","adLeg":"B","userType":"ANONYMOUS","pageType":"Topic","pageSubtype":null,"articleTemplateType":"LARGE","gisted":false,"pageNumber":1,"hasSummarizeButton":false,"hasAskButton":false} </script> <script type="text/javascript"> EBStat={accountId:-1,hostnameOverride:'webstats.eb.com',domain:'www.britannica.com', json:''}; </script> <script type="text/javascript"> ( function() { $.ajax( { dataType: 'script', cache: true, url: '//www.britannica.com/webstats/mendelstats.js?v=1' } ) .done( function() { try {writeStat(null,EBStat);} catch(err){} } ); })(); </script> <div id="bc-fixed-dialogue"></div> </body> </html>

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Measurement | Definition, Types, Instruments, & Facts | Britannica