{"id":65169,"date":"2026-05-02T11:16:11","date_gmt":"2026-05-02T08:16:11","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=65169"},"modified":"2026-05-02T11:20:06","modified_gmt":"2026-05-02T08:20:06","slug":"elastic-collision-1d-calculator","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/physics\/elastic-collision-1d-calculator\/","title":{"rendered":"Elastic Collision (1D) Calculator"},"content":{"rendered":"<p>This calculator determines the final velocities of two objects after a one-dimensional elastic collision. Enter the masses and initial velocities of both objects to find their velocities after impact, using the conservation of momentum and kinetic energy principles.<\/p>\n<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\">Elastic Collision 1D Calculator<\/h2><\/div><div class=\"relative group inline-block\">\n  <button class=\"favorite\" id=\"favorite\" data-favorite-id=\"65169\" data-favorite-title=\"Elastic Collision (1D)\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/physics\/elastic-collision-1d-calculator\/\" data-favorite-excerpt=\"This calculator determines the final velocities of two objects after a one-dimensional elastic collision. Enter the masses and initial velocities of both objects to find their velocities after impact, using the conservation of momentum and kinetic energy principles.\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\/elastic-collision-1d-calculator\/\" method=\"POST\" class=\"calculator\" id=\"calculator-65169\" data-post=\"65169\"><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\">Mass 1 (m\u2081)<\/label><div class=\"field-group\"><input type=\"number\" name=\"mass_1_m\" id=\"field-1\" step=\"any\" value=\"2\"\/><div class=\"grid grid-cols-1\"><select id=\"field-2\" 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-2\"><label for=\"field-3\">Initial Velocity 1 (u\u2081)<\/label><div class=\"field-group\"><input type=\"number\" name=\"initial_velocity_1_u\" id=\"field-3\" step=\"any\" value=\"5\"\/><div class=\"grid grid-cols-1\"><select id=\"field-4\" 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-3\"><label for=\"field-5\">Mass 2 (m\u2082)<\/label><div class=\"field-group\"><input type=\"number\" name=\"mass_2_m\" id=\"field-5\" step=\"any\" value=\"1\"\/><div class=\"grid grid-cols-1\"><select id=\"field-6\" 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-4\"><label for=\"field-7\">Initial Velocity 2 (u\u2082)<\/label><div class=\"field-group\"><input type=\"number\" name=\"initial_velocity_2_u\" id=\"field-7\" step=\"any\" value=\"0\"\/><div class=\"grid grid-cols-1\"><select id=\"field-8\" 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><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"65169\">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>Final Velocity of Object 1 (v\u2081)<\/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>Final Velocity of Object 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><\/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=\"65169\" 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>Elastic Collision Formulas<\/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$$\nv_1 = \\frac{m_1 &#8211; m_2}{m_1 + m_2} u_1 + \\frac{2m_2}{m_1 + m_2} u_2 \\\\[1em]\nv_2 = \\frac{2m_1}{m_1 + m_2} u_1 + \\frac{m_2 &#8211; m_1}{m_1 + m_2} u_2\n$$\n<\/div>\r\n\t<\/figure>\r\n\t<br \/>\n<strong>Where:<\/strong><\/p>\n<ul>\n<li>$$m_1$$ and $$m_2$$ are the masses of the two objects.<\/li>\n<li>$$u_1$$ and $$u_2$$ are the initial velocities.<\/li>\n<li>$$v_1$$ and $$v_2$$ are the final velocities after the collision.<\/li>\n<\/ul>\n<p>These formulas are derived from the conservation of momentum and conservation of kinetic energy, which both hold true in a perfectly elastic collision.<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>Elastic Collision \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> A 2 kg object moving at 5 m\/s collides with a 1 kg object at rest.<\/p>\n<p>$$m_1 = 2\\text{ kg},\\quad u_1 = 5\\text{ m\/s},\\quad m_2 = 1\\text{ kg},\\quad u_2 = 0\\text{ m\/s}$$<\/p>\n<p>$$v_1 = \\frac{2 &#8211; 1}{2 + 1} \\cdot 5 + \\frac{2 \\cdot 1}{2 + 1} \\cdot 0 = \\frac{1}{3} \\cdot 5 + 0 = 1.667\\text{ m\/s}$$<\/p>\n<p>$$v_2 = \\frac{2 \\cdot 2}{2 + 1} \\cdot 5 + \\frac{1 &#8211; 2}{2 + 1} \\cdot 0 = \\frac{4}{3} \\cdot 5 + 0 = 6.667\\text{ m\/s}$$<\/p>\n<p><strong>Result:<\/strong> $$v_1 = 1.667\\text{ m\/s}$$, $$v_2 = 6.667\\text{ m\/s}$$<\/p>\n\r\n<\/section>\n<p>This tool is useful for physics students, engineers, and educators studying collision dynamics. It instantly computes the outcome of 1D elastic collisions without manual algebra, saving time and reducing calculation errors.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This calculator determines the final velocities of two objects after a one-dimensional elastic collision. Enter the masses and initial velocities of both objects to find their velocities after impact, using the conservation of momentum and kinetic energy principles.<\/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-65169","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\/65169","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=65169"}],"version-history":[{"count":3,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/65169\/revisions"}],"predecessor-version":[{"id":65172,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/65169\/revisions\/65172"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=65169"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=65169"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=65169"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}