E = mc² | Equation, Explanation, & Proof

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class="md-content"> <div class="md-article-container template-desktop"> <div class="infinite-scroll-container article last"> <article class="article-content container-lg qa-content px-0 pt-0 pb-40 py-lg-20 content " data-topic-id="1666493"> <div class="grid gx-0"> <div class="col-auto"> <div class="topic-left-rail md-article-drawer position-relative d-flex border-right-sm border-left-sm open"> <div class="drawer d-flex flex-column open"> <div class="left-rail-section-content"> <div class="topic-left-rail-header text-truncate bg-gray-50 position-relative text-right d-flex align-items-center"> <div class="tlr-title px-20 py-15 text-left"> <em class="material-icons text-gray-400 d-lg-none" data-icon="toc"></em> <a class="font-serif font-weight-bold text-black link-blue" href="https://www.britannica.com/science/E-mc2-equation">E = mc<sup>2</sup></a> </div> <button aria-label="Close" class="js-sections-close-button btn-link btn-sm btn d-lg-none position-absolute top-0 p-10 right-0" > <em 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Author of <em>Empire of Light, Universal Foam, Hollywood Science, Slow Light</em>, and others. </div> </a> <div data-popper-arrow></div> </div> <span class="btn btn-link editor-link p-0 qa-byline-link gtm-byline font-12 byline-contributor text-decoration-underline"> Sidney Perkowitz</span></div> <div class="font-serif font-12 text-gray-700"> <span class="qa-fact-checked-by">Fact-checked by</span> <div class="editor-popover popover p-0"> <a class="d-block p-20 font-12" href="/editor/The-Editors-of-Encyclopaedia-Britannica/4419" > <div class="editor-title font-16 font-weight-bold">The Editors of Encyclopaedia Britannica</div> <div class="editor-description font-12 font-serif mt-5 text-black">Encyclopaedia Britannica's editors oversee subject areas in which they have extensive knowledge, whether from years of experience gained by working on that content or via study for an advanced degree. They write new content and verify and edit content received from contributors.</div> </a> <div data-popper-arrow></div> </div> <span class="btn btn-link editor-link p-0 qa-byline-link font-12 "> The Editors of Encyclopaedia Britannica</span></div> <div class="last-updated font-12 font-serif"> <span class="text-gray-700"> Last Updated: <time datetime="2024-10-21T00:00:00CDT" >Oct 21, 2024</time> •</span> <a class="byline-edit-history" href="https://www.britannica.com/science/E-mc2-equation/additional-info#history" rel="nofollow">Article History</a> </div></div> </div> <button class="d-flex d-lg-none btn btn-outline-blue border rounded-sm shadow-sm mobile-toc-button gtm-mobile-toc-inline-button d-none d-sm-block js-sections-inline-button module-spacing btn d-lg-none"> <em class="material-icons mr-5 ml-n10 my-n5 md-icon" data-icon="toc"></em> Table of Contents </button> <div class="d-flex d-sm-none flex-row"> <button class="d-flex d-lg-none btn btn-outline-blue border rounded-sm shadow-sm mobile-toc-button gtm-mobile-toc-inline-button js-sections-inline-button module-spacing"> <em class="material-icons mr-5 ml-n10 my-n5 md-icon" data-icon="toc"></em> Table of Contents </button> <button class="ai-ask-button btn border-2 ai-ask-button btn border-2 module-spacing btn-sm js-inline-ai-ask-button btn-outline-red-400 border-red-400 p-10 ml-5"> Ask the Chatbot a Question </button> </div> <div class="js-qf-module qf-module px-40 px-sm-20 py-15 mx-auto module-spacing font-14 bg-gray-50 rounded"> <div class="facts-list mt-10"> <div class=""> <div class="js-fact mb-10 line-clamp clamp-3"> <dl> <dt>Key People: </dt> <dd><a href="/biography/Albert-Einstein" topicid="181349">Albert Einstein</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="/science/mass-physics" topicid="368127">mass</a></dd> <dd><a href="/science/kinetic-energy" topicid="318130">kinetic energy</a></dd> <dd><a href="/science/special-relativity" topicid="558565">special relativity</a></dd> <dd><a href="/science/speed-of-light" topicid="559095">speed of light</a></dd> <dd><a href="/science/mass-energy-equivalence" topicid="368202">mass-energy equivalence</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/E-mc2-equation"> 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="ref1070923"></span>E = mc<sup>2</sup></strong>, equation in German-born physicist <a href="https://www.britannica.com/biography/Albert-Einstein" class="md-crosslink " data-show-preview="true">Albert Einstein</a>’s theory of <a href="https://www.britannica.com/science/special-relativity" class="md-crosslink " data-show-preview="true">special relativity</a> that expresses the fact that mass and <a href="https://www.britannica.com/science/energy" class="md-crosslink autoxref " data-show-preview="true">energy</a> are the same physical <a class="md-dictionary-link md-dictionary-tt-off eb" data-term="entity" href="https://www.britannica.com/dictionary/entity" data-type="EB">entity</a> and can be changed into each other. In the equation, the increased relativistic <a href="https://www.britannica.com/science/mass-physics" class="md-crosslink " data-show-preview="true">mass</a> (<em>m</em>) of a body times the <a href="https://www.britannica.com/science/speed-of-light" class="md-crosslink " data-show-preview="true">speed of light</a> squared (<em>c</em><sup>2</sup>) is equal to the <a href="https://www.britannica.com/science/kinetic-energy" class="md-crosslink autoxref " data-show-preview="true">kinetic energy</a> (<em>E</em>) of that body.</p><div class="one-good-fact-module"> </div><span class="marker MOD1 mod-inline"></span><span class="marker PREMOD2 mod-inline"></span><div class="assemblies"><div class="w-100"><figure class="md-assembly m-0 mb-md-0 card card-borderless print-false" data-assembly-id="255371" data-asm-type="video"><div class="md-assembly-wrapper card-media " data-type="video" video-id="222280"><a data-id="222280" class="gtm-assembly-link d-flex justify-content-center" style="--aspect-ratio: 16/9" href="/video/Your-Daily-Equation-01-E-mc2/-255371"><img src="https://cdn.britannica.com/80/222280-138-41E211F6/Your-Daily-Equation-01-E-mc2.jpg?w=800&h=450&c=crop" alt="Explaining E = mc2" loading="lazy"><script type="application/json"> { "sources": [ { "file" : "//content.jwplatform.com/manifests/ByZvrOFX.m3u8" } ], "image": "https://cdn.britannica.com/80/222280-138-41E211F6/Your-Daily-Equation-01-E-mc2.jpg" ,"tracks": [ { "file" : "//assets-jpcust.jwpsrv.com/tracks/uQqh3McI", "label": "English" } ] ,"adfile": "//content.jwplatform.com/manifests/None.m3u8" } </script><div class="btn btn-xl btn-white btn-circle position-absolute shadow" style="top: 50%; transform: translateY(-50%)"><em class="material-icons" data-icon="play_arrow"></em></div></a></div><figcaption class="card-body"><div class="md-assembly-caption text-muted font-14 font-serif line-clamp"><span><span class="md-assembly-title font-weight-bold mr-5 d-inline font-sans-serif md-video-caption" video-control="222280">Explaining E = mc<sup>2</sup></span><span>Brian Greene kicks off his <em>Daily Equation</em> video series with Albert Einstein's famous equation <em>E</em> = <em>m</em><em>c</em><sup>2</sup>.</span><button class="js-more-btn d-none btn btn-unstyled font-12 bg-white js-content" aria-label="Toggle more/less fact data"><span class="link-blue">(more)</span></button></span></div><a class="font-14 mt-10 d-inline-block" href="/science/E-mc2-equation/images-videos">See all videos for this article</a></figcaption></figure></div></div><p class="topic-paragraph">In physical theories prior to that of special relativity, mass and energy were viewed as distinct entities. Furthermore, the energy of a body at rest could be assigned an arbitrary value. In special relativity, however, the energy of a body at rest is determined to be <em>m</em><em>c</em><sup>2</sup>. Thus, each body of rest mass <em>m</em> possesses <em>m</em><em>c</em><sup>2</sup> of “rest energy,” which potentially is available for conversion to other forms of energy. The mass-energy relation, moreover, implies that, if energy is released from the body as a result of such a conversion, then the rest mass of the body will decrease. Such a conversion of rest energy to other forms of energy occurs in ordinary <a href="https://www.britannica.com/science/chemical-reaction" class="md-crosslink " data-show-preview="true">chemical reactions</a>, but much larger <a class="md-dictionary-link md-dictionary-tt-off eb" data-term="conversions" href="https://www.britannica.com/dictionary/conversions" data-type="EB">conversions</a> occur in <a href="https://www.britannica.com/science/nuclear-reaction" class="md-crosslink " data-show-preview="true">nuclear reactions</a>. This is particularly true in the case of <a href="https://www.britannica.com/science/nuclear-fusion" class="md-crosslink " data-show-preview="true">nuclear fusion</a> reactions that transform <a href="https://www.britannica.com/science/hydrogen" class="md-crosslink " data-show-preview="true">hydrogen</a> to <a href="https://www.britannica.com/science/helium-chemical-element" class="md-crosslink " data-show-preview="true">helium</a>, in which 0.7 percent of the original rest energy of the hydrogen is converted to other forms of energy. <a href="https://www.britannica.com/science/star-astronomy" class="md-crosslink " data-show-preview="true">Stars</a> like the <a href="https://www.britannica.com/place/Sun" class="md-crosslink " data-show-preview="true">Sun</a> shine from the energy released from the rest energy of hydrogen atoms that are fused to form helium.</p><span class="marker MOD2 mod-inline"></span></section> <span class="md-signature"><a href="/contributor/Sidney-Perkowitz/4558">Sidney Perkowitz</a></span> <span class="md-signature"><a href="/editor/The-Editors-of-Encyclopaedia-Britannica/4419">The Editors of Encyclopaedia Britannica</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":1666493,"pageLength":241,"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":"C","adLeg":"C","userType":"ANONYMOUS","pageType":"Topic","pageSubtype":null,"articleTemplateType":"SMALL","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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E = mc² | Equation, Explanation, & Proof | Britannica