{"id":61540,"date":"2021-02-05T12:29:22","date_gmt":"2021-02-05T10:29:22","guid":{"rendered":"https:\/\/wpcalc.com\/?p=61540"},"modified":"2026-10-23T10:29:04","modified_gmt":"2026-10-23T07:29:04","slug":"potential-energy","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/physics\/potential-energy\/","title":{"rendered":"Potential Energy Calculator \u2013 PE = mgh"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 id=\"calculator-title\" class=\"text-lg font-display font-bold\">Calculate Potential Energy<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"61540\" data-favorite-title=\"Potential Energy\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/physics\/potential-energy\/\" data-favorite-excerpt=\"Calculate gravitational potential energy from mass, height, and gravitational acceleration. Enter the values in kg, m, and m\/s\u00b2 to get the result in joules instantly.\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-physic\">\n    <span class=\"icon icon-shape-star-empty\" aria-hidden=\"true\"><\/span>\n  <\/button>\n  <div class=\"calcdash-favorite__tip\" aria-hidden=\"true\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n  <span class=\"sr-only\" role=\"status\" id=\"favorite-status\"><\/span>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/en\/physics\/potential-energy\/\" method=\"POST\" class=\"calculator\" id=\"calculator-61540\" data-post=\"61540\"><fieldset class=\"fieldset-input is-1\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field\" id=\"input-1\"><label for=\"field-1\">What do you want to find?<\/label><div class=\"grid grid-cols-1\"><select id=\"field-1\" name=\"what_do_you_want_to_find\"><option value=\"pe\" selected>Potential energy (Ep)<\/option><option value=\"mass\">Mass (m)<\/option><option value=\"height\">Height (h)<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><div class=\"field has-term\" id=\"input-2\" hidden><label for=\"field-2\">Potential energy<\/label><div class=\"term\">Ep<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"potential_energy\" id=\"field-2\" aria-describedby=\"calc-info-2\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 490.5\" min=\"0\" value=\"490.5\"\/><div class=\"grid grid-cols-1\"><select id=\"field-3\" name=\"unit\" aria-label=\"Unit\"><option value=\"J\" selected>J<\/option><option value=\"kJ\">kJ<\/option><option value=\"cal\">cal<\/option><option value=\"ftlb\">ft\u00b7lb<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-2\">Gravitational potential energy relative to the chosen reference level.<\/small><\/div><div class=\"field\" id=\"input-3\"><label for=\"field-4\">Mass (m)<\/label><div class=\"field-group\"><input type=\"text\" name=\"mass_m\" id=\"field-4\" aria-describedby=\"calc-info-4\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 10\" min=\"0\" value=\"10\"\/><div class=\"grid grid-cols-1\"><select id=\"field-5\" name=\"unit\" aria-label=\"Unit\"><option value=\"kg\" selected>kg<\/option><option value=\"g\">g<\/option><option value=\"lb\">lb<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-4\">Mass of the object.<\/small><\/div><div class=\"field\" id=\"input-4\"><label for=\"field-6\">Height (h)<\/label><div class=\"field-group\"><input type=\"text\" name=\"height_h\" id=\"field-6\" aria-describedby=\"calc-info-6\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 5\" min=\"0\" value=\"5\"\/><div class=\"grid grid-cols-1\"><select id=\"field-7\" name=\"unit\" aria-label=\"Unit\"><option value=\"m\" selected>m<\/option><option value=\"cm\">cm<\/option><option value=\"ft\">ft<\/option><option value=\"in\">in<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-6\">Vertical height of the object above the reference level (where the potential energy is zero).<\/small><\/div><div class=\"field has-term\" id=\"input-5\"><label for=\"field-8\">Gravity (g)<\/label><div class=\"term\">g<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"gravity_g\" id=\"field-8\" aria-describedby=\"calc-unit-8 calc-info-8\" placeholder=\"e.g. 9.81\" step=\"any\" value=\"9.81\"\/><div class=\"unit\" id=\"calc-unit-8\">m\/s\u00b2<\/div><small id=\"calc-info-8\">Gravitational acceleration. Earth \u2248 9.81 m\/s\u00b2, the Moon \u2248 1.62, Mars \u2248 3.71, the Sun&#039;s surface \u2248 274.<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"61540\">Calculate<\/button><button type=\"reset\">Reset<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Calculate automatically<\/label><small>If enabled, the result will update automatically when you change any value.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Gravitational Potential Energy Results<\/h3><div class=\"result-box\"><div class=\"field-result is-column\" id=\"output-1\"><span class=\"field-title\"><span>Result<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-2\"><span class=\"field-title\"><span>Step-by-step solution<\/span><\/span><span class=\"field-value\" id=\"result-2\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><\/div><div class=\"result-actions\"><button type=\"button\" class=\"copy-link\"><svg viewBox=\"0 0 20 20\" fill=\"currentColor\" aria-hidden=\"true\"><path d=\"M12.232 4.232a2.5 2.5 0 0 1 3.536 3.536l-1.225 1.224a.75.75 0 0 0 1.061 1.06l1.224-1.224a4 4 0 0 0-5.656-5.656l-3 3a4 4 0 0 0 .225 5.865.75.75 0 0 0 .977-1.138 2.5 2.5 0 0 1-.142-3.667l3-3Z\"\/><path d=\"M11.603 7.963a.75.75 0 0 0-.977 1.138 2.5 2.5 0 0 1 .142 3.667l-3 3a2.5 2.5 0 0 1-3.536-3.536l1.225-1.224a.75.75 0 0 0-1.061-1.06l-1.224 1.224a4 4 0 1 0 5.656 5.656l3-3a4 4 0 0 0-.225-5.865Z\"\/><\/svg><span class=\"copy-link__text\">Copy link to this calculation<\/span><\/button><span class=\"sr-only\" role=\"status\" id=\"copy-link-status\"><\/span><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Leave a Comment<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"61540\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">How did this result make you feel?<\/p><div role=\"group\" aria-labelledby=\"calc-reactions-title\" class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Like <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">Helpful <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"confused\"><span class=\"reaction-count\" data-reaction-count=\"confused\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Confused <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"disappointed\"><span class=\"reaction-count\" data-reaction-count=\"disappointed\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">Disappointed <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">1<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\u274c <\/span><span class=\"reaction-description font-medium\">Inaccurate <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><div class=\"calcdash-ad not-prose calcdash-ad--calc_result calcdash-ad--in-article\"><ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-1721569815777345\" data-ad-slot=\"6317458308\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\"><\/ins><script>(adsbygoogle = window.adsbygoogle || []).push({});<\/script><\/div>\n<style id=\"wpcoderpro-inline-1\">.formula-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>Potential Energy Formula<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Formula<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n\\[ PE = m \\cdot g \\cdot h \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(PE\\) \u2014 potential energy (joules, J)<\/li>\n<li>\\(m\\) \u2014 mass of the object (kg)<\/li>\n<li>\\(g\\) \u2014 gravitational acceleration (m\/s\u00b2, about 9.8 on Earth)<\/li>\n<li>\\(h\\) \u2014 height above the reference level (m)<\/li>\n<\/ul>\n<p>The formula expresses the energy an object stores simply because it sits at a height \\(h\\) above a chosen reference level in a gravitational field. That energy equals the work needed to lift the object to that height, and it is released as kinetic energy when the object falls.<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-459\">.calculation-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>Potential Energy \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> a 10 kg crate is lifted onto a shelf 5 m above the floor. Using the default gravitational acceleration of 9.8 m\/s\u00b2:<\/p>\n<p>\\[ PE = m \\cdot g \\cdot h = 10 \\times 9.8 \\times 5 = 490 \\text{ J} \\]<\/p>\n<p><strong>Result:<\/strong> the crate stores 490 J of gravitational potential energy.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to Use the Potential Energy Calculator<\/h2>\n<ol>\n<li>Enter the object's <strong>Mass<\/strong> in kilograms (kg).<\/li>\n<li>Enter the <strong>Height<\/strong> of the object above your reference level (usually the ground) in meters (m).<\/li>\n<li>Enter the <strong>Acceleration of Gravity<\/strong> in m\/s\u00b2. The default is 9.8 for Earth's surface; change it for other planets or altitudes.<\/li>\n<li>Read the <strong>Potential Energy<\/strong> result, displayed in joules (J).<\/li>\n<\/ol>\n<h2>What Is Potential Energy?<\/h2>\n<p>Potential energy is the energy an object has because of its position or configuration rather than its motion. Gravitational potential energy \u2014 the type this calculator computes \u2014 comes from an object's height within a gravitational field. A book on a shelf, water behind a dam, and a lifted crane load all carry potential energy that can be converted into other forms, most commonly kinetic energy, when they are released.<\/p>\n<p>The value of \\(PE\\) depends on the choice of a reference level (where \\(h = 0\\)). Usually the ground or the floor is the natural choice, so the calculated energy tells you how much work gravity can do if the object falls back to that level. Physically, only <em>changes<\/em> in potential energy matter: raising the crate in the example from 0 m to 5 m required 490 J of work against gravity, and that same 490 J can be recovered during the descent.<\/p>\n<p>Interpreting the result is straightforward: a larger mass or a greater height means proportionally more stored energy. Doubling the height doubles the potential energy, and so does doubling the mass. If the object falls freely, all of this energy converts into kinetic energy just before impact (neglecting air resistance) \u2014 you can explore that conversion with our <a href=\"https:\/\/wpcalc.com\/en\/physics\/free-fall-calculator\/\">Free Fall Calculator<\/a> or see how gravity drives the motion with the <a href=\"https:\/\/wpcalc.com\/en\/physics\/projectile-motion-calculator\/\">Projectile Motion Calculator<\/a>.<\/p>\n<h2>Assumptions, Limitations, and Tips<\/h2>\n<ul>\n<li><strong>Uniform gravity:<\/strong> the formula assumes \\(g\\) is constant over the height involved. This is excellent near Earth's surface but breaks down for satellites or very tall structures.<\/li>\n<li><strong>Reference level:<\/strong> the result is measured relative to wherever you set \\(h = 0\\). Be consistent when comparing energies \u2014 always measure heights from the same level.<\/li>\n<li><strong>Gravitational acceleration varies:<\/strong> use 9.8 m\/s\u00b2 for Earth, 1.62 for the Moon, or 3.71 for Mars. The <a href=\"https:\/\/wpcalc.com\/en\/physics\/weight-on-other-planets-calculator\/\">Weight on Planets Calculator<\/a> shows how \\(g\\) differs across the solar system.<\/li>\n<li><strong>Only gravitational energy:<\/strong> this tool does not cover elastic potential energy (for springs, see the <a href=\"https:\/\/wpcalc.com\/en\/physics\/hookes-law-calculator\/\">Hooke's Law Calculator<\/a>) or other forms such as chemical or electrical potential energy.<\/li>\n<li><strong>No friction or losses:<\/strong> the calculation is idealized; real lifting systems lose energy to friction, so actual work input is higher than the computed \\(PE\\).<\/li>\n<\/ul>\n<h2>Typical Values of Gravitational Acceleration<\/h2>\n<table>\n<thead>\n<tr>\n<th>Location<\/th>\n<th>\\(g\\) (m\/s\u00b2)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Earth (average surface)<\/td>\n<td>9.8<\/td>\n<\/tr>\n<tr>\n<td>Moon<\/td>\n<td>1.62<\/td>\n<\/tr>\n<tr>\n<td>Mars<\/td>\n<td>3.71<\/td>\n<\/tr>\n<tr>\n<td>Jupiter<\/td>\n<td>24.79<\/td>\n<\/tr>\n<tr>\n<td>Space station orbit (microgravity)<\/td>\n<td>\u2248 0 (effective)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Simply enter the appropriate value in the <strong>Acceleration of Gravity<\/strong> field to compute potential energy on another world.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Calculate gravitational potential energy from mass, height, and gravitational acceleration. Enter the values in kg, m, and m\/s\u00b2 to get the result in joules instantly.<\/p>\n","protected":false},"author":70,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[62],"tags":[91],"class_list":["post-61540","post","type-post","status-publish","format-standard","hentry","category-physics","tag-energy-work"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/61540","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/users\/70"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/comments?post=61540"}],"version-history":[{"count":6,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/61540\/revisions"}],"predecessor-version":[{"id":67469,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/61540\/revisions\/67469"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=61540"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=61540"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=61540"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}