{"id":65143,"date":"2026-05-02T11:04:23","date_gmt":"2026-05-02T08:04:23","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=65143"},"modified":"2026-10-01T13:53:09","modified_gmt":"2026-10-01T10:53:09","slug":"momentum-calculator","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/physics\/momentum-calculator\/","title":{"rendered":"Momentum 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\">Find Momentum From Mass and Velocity<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"65143\" data-favorite-title=\"Power\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/physics\/momentum-calculator\/\" data-favorite-excerpt=\"Calculate momentum, mass, or velocity with p = mv. Enter any two of the three values, choose your units, and get an instant result in kg\u00b7m\/s.\" 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\/momentum-calculator\/\" method=\"POST\" class=\"calculator\" id=\"calculator-65143\" data-post=\"65143\"><fieldset class=\"fieldset-input is-1\"><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=\"p\">Momentum (p)<\/option><option value=\"m\">Mass (m)<\/option><option value=\"v\">Velocity (v)<\/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\">Mass (m)<\/label><div class=\"field-group\"><input type=\"number\" name=\"mass_m\" id=\"field-2\" step=\"any\" value=\"10\"\/><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\">Velocity (v)<\/label><div class=\"field-group\"><input type=\"number\" name=\"velocity_v\" id=\"field-4\" step=\"any\" value=\"5\"\/><div class=\"grid grid-cols-1\"><select id=\"field-5\" 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-4\" hidden><label for=\"field-6\">Momentum (p)<\/label><input type=\"number\" name=\"momentum_p\" id=\"field-6\" aria-describedby=\"calc-unit-6\" step=\"any\" value=\"50\"\/><div class=\"unit\" id=\"calc-unit-6\">kg\u00b7m\/s<\/div><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"65143\">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=\"65143\" 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 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<\/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>Momentum 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\\[ p = m \\cdot v \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(p\\) \u2014 momentum (kg\u00b7m\/s)<\/li>\n<li>\\(m\\) \u2014 mass of the object (kg)<\/li>\n<li>\\(v\\) \u2014 velocity of the object (m\/s)<\/li>\n<\/ul>\n<p>Momentum is the product of an object's mass and its velocity. The two equations below let you rearrange the same relationship to solve for mass or velocity when momentum is known:<\/p>\n<p>\\[ m = \\frac{p}{v} \\qquad v = \\frac{p}{m} \\]<br \/>\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>Momentum \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> a cart with a mass of 10 kg rolls along a track at 5 m\/s. Find its momentum.<\/p>\n<p>\\[ p = m \\cdot v = 10 \\times 5 = 50 \\ \\text{kg\u00b7m\/s} \\]<\/p>\n<p><strong>Result:<\/strong> the momentum of the cart is 50 kg\u00b7m\/s.<\/p>\n<p>The same calculation works in reverse: if a 10 kg object has a momentum of 50 kg\u00b7m\/s, its velocity is \\( 50 \/ 10 = 5 \\) m\/s, and if it moves at 5 m\/s with a momentum of 50 kg\u00b7m\/s, its mass is \\( 50 \/ 5 = 10 \\) kg.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to Use the Calculator<\/h2>\n<ol>\n<li>Open the <strong>\u201cI want to calculate\u201d<\/strong> dropdown and choose whether you need <em>Momentum (p)<\/em>, <em>Mass (m)<\/em>, or <em>Velocity (v)<\/em>. The calculator hides the field for the value you are solving for.<\/li>\n<li>Enter the <strong>Mass (m)<\/strong> and select <strong>kg<\/strong> or <strong>g<\/strong> as the unit in the dropdown next to the input.<\/li>\n<li>Enter the <strong>Velocity (v)<\/strong> and select <strong>m\/s<\/strong> or <strong>km\/h<\/strong> as the unit.<\/li>\n<li>If you are solving for mass or velocity, enter the known <strong>Momentum (p)<\/strong> in kg\u00b7m\/s instead of the missing field.<\/li>\n<li>Read the result under <strong>Result<\/strong>. Momentum is given in kg\u00b7m\/s, mass in kg, and velocity in m\/s.<\/li>\n<\/ol>\n<h2>What Is Momentum?<\/h2>\n<p>Momentum (also called linear momentum) is a measure of the quantity of motion an object has. It combines two things that matter in a collision: how much stuff is moving (mass) and how fast it is moving (velocity). A loaded truck creeping at 5 km\/h and a rifle bullet at 900 m\/s can carry comparable momentum, even though their masses and speeds differ enormously.<\/p>\n<p>Momentum is a <strong>vector quantity<\/strong>: it has both a magnitude and a direction, and the direction is the same as the object's velocity. In one-dimensional problems the sign of the result tells you the direction \u2014 a negative momentum means the object moves in the negative direction of your chosen axis. This calculator works with the magnitude, so enter speeds as positive numbers unless your problem defines a direction.<\/p>\n<p>Momentum matters because it is <em>conserved<\/em>. In an isolated system \u2014 one with no external forces acting \u2014 the total momentum before an event equals the total momentum after it. This conservation law is what makes collision analysis possible: you can predict how objects rebound after a crash, how rockets gain speed by expelling exhaust, or how a recoil works, all by tracking momentum. It follows directly from Newton's second law, since force equals the rate of change of momentum, \\( F = \\Delta p \/ \\Delta t \\).<\/p>\n<p>When interpreting your result, remember that momentum alone doesn't tell the whole story of a collision. Two objects with the same momentum can deliver very different forces on impact, because the force depends on how quickly the momentum changes \u2014 a principle you can explore with our <a href=\"https:\/\/wpcalc.com\/en\/physics\/stopping-distance-calculator\/\">Stopping Distance Calculator<\/a>. For rotating objects, the analogous quantity is angular momentum; see our <a href=\"https:\/\/wpcalc.com\/en\/physics\/angular-momentum-calculator\/\">Angular Momentum Calculator<\/a>.<\/p>\n<h2>Units and Conversions<\/h2>\n<p>The SI unit of momentum is the kilogram-meter per second (kg\u00b7m\/s), which is what this calculator returns. If you enter mass in grams, the calculator converts it to kilograms (1 kg = 1000 g), and if you enter velocity in km\/h, it converts it to m\/s (divide by 3.6) before applying the formula. For example, 1 kg at 36 km\/h has a momentum of \\( 1 \\times (36\/3.6) = 10 \\) kg\u00b7m\/s, not 36.<\/p>\n<h2>Assumptions and Limitations<\/h2>\n<ul>\n<li><strong>Classical speeds only.<\/strong> The formula \\( p = mv \\) is valid at everyday speeds. Near the speed of light, relativistic effects increase momentum, and this calculator does not account for them.<\/li>\n<li><strong>Constant mass.<\/strong> The object's mass is assumed not to change during the motion. Systems like rockets, which lose mass as they burn fuel, need a variable-mass treatment.<\/li>\n<li><strong>Point-mass, straight-line motion.<\/strong> The calculator treats the object as a single mass moving along a line. Rotating bodies have additional <a href=\"https:\/\/wpcalc.com\/en\/physics\/rotational-kinetic-energy-calculator\/\">rotational motion<\/a> described by angular momentum.<\/li>\n<li><strong>Direction is not tracked.<\/strong> Enter the speed (magnitude of velocity). If your problem involves opposite directions, assign signs manually \u2014 for example, head-on collisions where one object's momentum is negative.<\/li>\n<li><strong>Zero values.<\/strong> Solving for mass requires a non-zero velocity, and solving for velocity requires a non-zero mass; the calculator warns you if the divisor is zero. An object at rest (\\( v = 0 \\)) simply has zero momentum.<\/li>\n<\/ul>\n<h2>Practical Tips<\/h2>\n<ul>\n<li>Keep units consistent before doing math by hand: convert grams to kilograms and km\/h to m\/s first, exactly as the calculator does automatically.<\/li>\n<li>In collision problems, calculate the momentum of each object separately, assign signs by direction, then add them to get the total momentum of the system.<\/li>\n<li>Momentum pairs naturally with kinetic energy: momentum depends on \\( v \\), while kinetic energy depends on \\( v^2 \\). Doubling the speed doubles momentum but quadruples kinetic energy.<\/li>\n<li>For motion problems involving gravity, combine this tool with the <a href=\"https:\/\/wpcalc.com\/en\/physics\/free-fall-calculator\/\">Free Fall Calculator<\/a> to find velocities before computing momentum.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Calculate momentum, mass, or velocity with p = mv. Enter any two of the three values, choose your units, and get an instant result in kg\u00b7m\/s.<\/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-65143","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\/65143","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=65143"}],"version-history":[{"count":3,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/65143\/revisions"}],"predecessor-version":[{"id":66368,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/65143\/revisions\/66368"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=65143"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=65143"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=65143"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}