{"id":65179,"date":"2026-05-02T11:19:08","date_gmt":"2026-05-02T08:19:08","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=65179"},"modified":"2026-05-02T11:20:05","modified_gmt":"2026-05-02T08:20:05","slug":"conservation-of-energy-calculator","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/physics\/conservation-of-energy-calculator\/","title":{"rendered":"Conservation of 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 class=\"text-lg font-display font-bold\">Conservation of Energy Calculator<\/h2><\/div><div class=\"relative group inline-block\">\n  <button class=\"favorite\" id=\"favorite\" data-favorite-id=\"65179\" data-favorite-title=\"Conservation of Energy\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/physics\/conservation-of-energy-calculator\/\" data-favorite-excerpt=\"This calculator computes the total mechanical energy at two different states using the principle of conservation of energy. Enter the mass, height, and velocity at state 1, along with the height at state 2, to find the velocity at state 2 and verify that total energy is conserved.\r\n\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-content-360deg\">\n    <span class=\"icon icon-shape-star-empty\"><\/span>\n  <\/button>\n  <div class=\"absolute right-full -translate-y-1\/2 top-1\/2 mr-2 w-max max-w-xs px-3 py-2 bg-gray-800 text-white text-xs rounded shadow-lg opacity-0 group-hover:opacity-100 transition-opacity duration-200 z-10 pointer-events-none\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/en\/physics\/conservation-of-energy-calculator\/\" method=\"POST\" class=\"calculator\" id=\"calculator-65179\" data-post=\"65179\"><fieldset class=\"fieldset-input is-2\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"is-single field\" id=\"input-1\"><span class=\"font-semibold\">State 1<\/span><\/div><div class=\"field is-single\" id=\"input-2\"><label for=\"field-2\">Mass (m)<\/label><div class=\"field-group\"><input type=\"number\" name=\"mass_m\" id=\"field-2\" step=\"any\" value=\"5\"\/><div class=\"grid grid-cols-1\"><select id=\"field-3\" name=\"unit\" aria-label=\"Unit\"><option value=\"kg\">kg<\/option><option value=\"g\">g<\/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-3\"><label for=\"field-4\">Height 1 (h\u2081)<\/label><div class=\"field-group\"><input type=\"number\" name=\"height_1_h\" id=\"field-4\" step=\"any\" value=\"10\"\/><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><\/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\"><label for=\"field-6\">Velocity 1 (v\u2081)<\/label><div class=\"field-group\"><input type=\"number\" name=\"velocity_1_v\" id=\"field-6\" step=\"any\" value=\"0\"\/><div class=\"grid grid-cols-1\"><select id=\"field-7\" name=\"unit\" aria-label=\"Unit\"><option value=\"m\/s\">m\/s<\/option><option value=\"km\/h\">km\/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><div class=\"is-single field\" id=\"input-5\"><span class=\"font-semibold\">State 2<\/span><\/div><div class=\"field is-single\" id=\"input-6\"><label for=\"field-9\">Height 2 (h\u2082)<\/label><div class=\"field-group\"><input type=\"number\" name=\"height_2_h\" id=\"field-9\" step=\"any\" value=\"0\"\/><div class=\"grid grid-cols-1\"><select id=\"field-10\" name=\"unit\" aria-label=\"Unit\"><option value=\"m\">m<\/option><option value=\"cm\">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 is-single\" id=\"input-7\" hidden><label for=\"field-11\">Velocity 2 (v\u2082)<\/label><div class=\"field-group\"><input type=\"number\" name=\"velocity_2_v\" id=\"field-11\" step=\"any\" value=\"14\"\/><div class=\"grid grid-cols-1\"><select id=\"field-12\" name=\"unit\" aria-label=\"Unit\"><option value=\"m\/s\">m\/s<\/option><option value=\"km\/h\">km\/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><div class=\"field is-single\" id=\"input-8\"><label for=\"field-13\">Gravitational Acceleration (g)<\/label><input type=\"number\" name=\"gravitational_acceleration_g\" id=\"field-13\" step=\"any\" value=\"9.81\"\/><div class=\"unit\">m\/s\u00b2<\/div><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"65179\">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>Total Energy (State 1)<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button class=\"copy-result\" data-tooltip=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-2\"><span class=\"field-title\"><span>Velocity at State 2 (v\u2082)<\/span><\/span><span class=\"field-value\" id=\"result-2\"><\/span><button class=\"copy-result\" data-tooltip=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-3\"><span class=\"field-title\"><span>Total Energy (State 2)<\/span><\/span><span class=\"field-value\" id=\"result-3\"><\/span><button class=\"copy-result\" data-tooltip=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\"><\/span><\/button><\/div><\/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=\"65179\" aria-live=\"polite\"><h2 class=\"text-sm text-gray-500 text-center mb-2\">How did this result make you feel?<\/h2><div class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button 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\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Like <\/span><\/button><button 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\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">Helpful <\/span><\/button><button 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\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Confused <\/span><\/button><button 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\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">Disappointed <\/span><\/button><button 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\">\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><ins class=\"adsbygoogle\"\n     style=\"display:block; text-align:center; margin: 32px 0;\"\n     data-ad-layout=\"in-article\"\n     data-ad-format=\"fluid\"\n     data-ad-client=\"ca-pub-1721569815777345\"\n     data-ad-slot=\"6317458308\"><\/ins>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script>\n<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>Conservation of 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$$\nKE_1 + PE_1 = KE_2 + PE_2 \\\\[1em]\n\\frac{1}{2}mv_1^2 + mgh_1 = \\frac{1}{2}mv_2^2 + mgh_2\n$$\n<\/div>\r\n\t<\/figure>\r\n\t<br \/>\n<strong>Where:<\/strong><\/p>\n<ul>\n<li>$$m$$ is the mass of the object.<\/li>\n<li>$$v_1$$ and $$v_2$$ are the velocities at state 1 and state 2.<\/li>\n<li>$$h_1$$ and $$h_2$$ are the heights at state 1 and state 2.<\/li>\n<li>$$g$$ is the gravitational acceleration (9.81 m\/s\u00b2).<\/li>\n<li>$$KE$$ is kinetic energy and $$PE$$ is potential energy.<\/li>\n<\/ul>\n<p>This formula expresses that the total mechanical energy remains constant in a closed system with no energy losses.<br \/>\r\n<\/section>\n<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>Conservation of Energy \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> A 5 kg object at a height of 10 m with zero initial velocity falls to ground level (h\u2082 = 0).<\/p>\n<p>$$m = 5\\text{ kg},\\quad h_1 = 10\\text{ m},\\quad v_1 = 0\\text{ m\/s},\\quad h_2 = 0\\text{ m},\\quad g = 9.81\\text{ m\/s}^2$$<\/p>\n<p>$$KE_1 = 0.5 \\times 5 \\times 0^2 = 0\\text{ J}$$<\/p>\n<p>$$PE_1 = 5 \\times 9.81 \\times 10 = 490.5\\text{ J}$$<\/p>\n<p>$$E_1 = 0 + 490.5 = 490.5\\text{ J}$$<\/p>\n<p>$$v_2 = \\sqrt{\\frac{2 \\times (490.5 &#8211; 0)}{5}} = \\sqrt{196.2} = 14.007\\text{ m\/s}$$<\/p>\n<p><strong>Result:<\/strong> Total energy = 490.5 J, $$v_2 = 14.007\\text{ m\/s}$$<\/p>\n<p>\n\r\n<\/section>\n<p>This tool is ideal for physics students, engineers, and educators studying energy transformations. It quickly calculates velocities and energy values at different states, demonstrating the conservation of mechanical energy principle.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This calculator computes the total mechanical energy at two different states using the principle of conservation of energy. Enter the mass, height, and velocity at state 1, along with the height at state 2, to find the velocity at state 2 and verify that total energy is conserved.<\/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":[73],"class_list":["post-65179","post","type-post","status-publish","format-standard","hentry","category-physics","tag-mechanics"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/65179","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=65179"}],"version-history":[{"count":2,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/65179\/revisions"}],"predecessor-version":[{"id":65181,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/65179\/revisions\/65181"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=65179"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=65179"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=65179"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}