{"id":65137,"date":"2026-05-02T10:58:27","date_gmt":"2026-05-02T07:58:27","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=65137"},"modified":"2026-10-01T13:49:19","modified_gmt":"2026-10-01T10:49:19","slug":"elastic-potential-energy-calculator","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/physics\/elastic-potential-energy-calculator\/","title":{"rendered":"Elastic Potential Energy Calculator"},"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 Stored Spring Energy<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"65137\" data-favorite-title=\"Elastic Potential Energy Calculator\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/physics\/elastic-potential-energy-calculator\/\" data-favorite-excerpt=\"Calculate the elastic potential energy stored in a spring from its spring constant and displacement, or solve for k or x when the energy is known. Supports N\/m, N\/cm, m, cm and mm units.\" 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\/elastic-potential-energy-calculator\/\" method=\"POST\" class=\"calculator\" id=\"calculator-65137\" data-post=\"65137\"><fieldset class=\"fieldset-input is-2\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field is-single\" id=\"input-1\"><label for=\"field-1\">I want to calculate<\/label><div class=\"grid grid-cols-1\"><select id=\"field-1\" name=\"i_want_to_calculate\"><option value=\"pe\">Elastic Potential Energy (PE)<\/option><option value=\"k\">Spring Constant (k)<\/option><option value=\"x\">Displacement (x)<\/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 is-single\" id=\"input-2\"><label for=\"field-2\">Spring Constant (k)<\/label><div class=\"field-group\"><input type=\"text\" name=\"spring_constant_k\" id=\"field-2\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"100\"\/><div class=\"grid grid-cols-1\"><select id=\"field-3\" name=\"unit\" aria-label=\"Unit\"><option value=\"n\/m\">N\/m<\/option><option value=\"n\/cm\">N\/cm<\/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><div class=\"field\" id=\"input-3\"><label for=\"field-4\">Displacement (x)<\/label><div class=\"field-group\"><input type=\"text\" name=\"displacement_x\" id=\"field-4\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"0.1\"\/><div class=\"grid grid-cols-1\"><select id=\"field-5\" name=\"unit\" aria-label=\"Unit\"><option value=\"m\">m<\/option><option value=\"cm\">cm<\/option><option value=\"mm\">mm<\/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><div class=\"field is-single\" id=\"input-4\" hidden><label for=\"field-6\">Elastic Potential Energy (PE)<\/label><input type=\"text\" name=\"elastic_potential_energy_pe\" id=\"field-6\" aria-describedby=\"calc-unit-6\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"1\"\/><div class=\"unit\" id=\"calc-unit-6\">J<\/div><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"65137\">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> Your 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><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=\"65137\" 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\">0<\/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>Elastic 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 = \\frac{1}{2} k x^2 \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(PE\\) \u2014 elastic potential energy (J)<\/li>\n<li>\\(k\\) \u2014 spring constant (N\/m)<\/li>\n<li>\\(x\\) \u2014 displacement from the equilibrium position (m)<\/li>\n<\/ul>\n<p>This formula, derived from Hooke's law, gives the energy stored in a spring that is stretched or compressed by a distance \\(x\\) from its natural length. The same relation can be rearranged to solve for the other two variables:<\/p>\n<p>\\[ k = \\frac{2 \\cdot PE}{x^2} \\qquad x = \\sqrt{\\frac{2 \\cdot PE}{k}} \\]<\/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>Elastic Potential Energy \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> a spring with a spring constant of \\(k = 100\\ \\text{N\/m}\\) is stretched by \\(x = 0.1\\ \\text{m}\\) from its equilibrium position. How much elastic potential energy is stored?<\/p>\n<p>\\[ PE = \\frac{1}{2} \\times 100 \\times (0.1)^2 \\]<\/p>\n<p>\\[ PE = 50 \\times 0.01 = 0.5\\ \\text{J} \\]<\/p>\n<p><strong>Result:<\/strong> the spring stores <strong>0.5 joules<\/strong> of elastic potential energy.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to Use the Calculator<\/h2>\n<ol>\n<li>In the <strong>\"I want to calculate\"<\/strong> dropdown, choose whether you want the elastic potential energy (PE), the spring constant (k), or the displacement (x). The field you are solving for is filled in automatically.<\/li>\n<li>Enter the <strong>Spring Constant (k)<\/strong> and select its unit \u2014 <strong>N\/m<\/strong> or <strong>N\/cm<\/strong> (values in N\/cm are converted to N\/m internally).<\/li>\n<li>Enter the <strong>Displacement (x)<\/strong> and pick its unit \u2014 <strong>m<\/strong>, <strong>cm<\/strong>, or <strong>mm<\/strong> (converted to meters automatically).<\/li>\n<li>If you are solving for k or x, enter the known <strong>Elastic Potential Energy (PE)<\/strong> in joules instead of the corresponding input.<\/li>\n<li>Read the result under <strong>Result<\/strong>: the energy is given in joules (J), the spring constant in N\/m, and the displacement in meters.<\/li>\n<\/ol>\n<h2>What Is Elastic Potential Energy?<\/h2>\n<p>Elastic potential energy is the energy stored in an object when it is stretched or compressed \u2014 think of a compressed spring, a drawn bow, or a stretched rubber band. As long as the deformation stays within the elastic limit, the object returns to its original shape when the force is removed, releasing the stored energy. This behavior is described by <a href=\"https:\/\/wpcalc.com\/en\/physics\/hookes-law-calculator\/\">Hooke's law<\/a>, which states that the restoring force is proportional to the displacement: \\(F = kx\\).<\/p>\n<p>The spring constant \\(k\\) measures stiffness: a stiff spring might have \\(k = 10{,}000\\ \\text{N\/m}\\), while a soft one might be \\(k = 50\\ \\text{N\/m}\\). The larger the spring constant, the more force is needed for the same displacement, and the more energy is stored. Notice that energy grows with the <em>square<\/em> of the displacement \u2014 doubling the stretch stores four times as much energy, which is why over-stretched springs can be dangerous.<\/p>\n<p>Because the spring force varies with displacement, the stored energy equals the work done against it: the average force \\(\\frac{kx}{2}\\) acting over the distance \\(x\\) gives \\(PE = \\frac{1}{2}kx^2\\). This is the linear-elastic analogue of <a href=\"https:\/\/wpcalc.com\/en\/physics\/rotational-kinetic-energy-calculator\/\">rotational kinetic energy<\/a> and other squared-variable energy formulas in physics.<\/p>\n<p>The result tells you how much energy is available for release. When a compressed spring pushes a block, that elastic energy converts into kinetic energy; in a dart gun or a car's suspension, the same principle smooths impacts. Comparing the stored energy with other energies in a system (for example, in <a href=\"https:\/\/wpcalc.com\/en\/physics\/projectile-motion-calculator\/\">projectile motion<\/a> problems where a spring launches a projectile) is a standard way to solve mechanics problems.<\/p>\n<h2>Assumptions and Limitations<\/h2>\n<ul>\n<li><strong>Linear elasticity (Hooke's law):<\/strong> the formula is only valid while force and displacement stay proportional. Beyond the elastic limit the material deforms permanently and the calculation no longer applies.<\/li>\n<li><strong>Ideal spring:<\/strong> the spring's own mass, internal friction, and damping are neglected; real springs lose some energy as heat when they compress or recoil.<\/li>\n<li><strong>Displacement from equilibrium:<\/strong> \\(x\\) must be measured from the spring's natural (unstressed) length \u2014 not from an arbitrary position. For a vertically hung spring carrying a weight, measure the additional stretch, not the total length.<\/li>\n<li><strong>Unit consistency:<\/strong> the calculator converts N\/cm to N\/m and cm\/mm to m automatically, but if you use the formula by hand, keep \\(k\\) in N\/m and \\(x\\) in meters so that \\(PE\\) comes out in joules.<\/li>\n<li><strong>Sign doesn't matter:<\/strong> since \\(x\\) is squared, compression and stretching by the same distance store the same energy; you can enter either as a positive value.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Calculate the elastic potential energy stored in a spring from its spring constant and displacement, or solve for k or x when the energy is known. Supports N\/m, N\/cm, m, cm and mm units.<\/p>\n","protected":false},"author":3168,"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-65137","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\/65137","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\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/comments?post=65137"}],"version-history":[{"count":5,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/65137\/revisions"}],"predecessor-version":[{"id":67031,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/65137\/revisions\/67031"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=65137"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=65137"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=65137"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}