{"id":65148,"date":"2026-05-02T11:07:14","date_gmt":"2026-05-02T08:07:14","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=65148"},"modified":"2026-10-01T13:49:59","modified_gmt":"2026-10-01T10:49:59","slug":"final-velocity-calculator","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/physics\/final-velocity-calculator\/","title":{"rendered":"Final Velocity 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 Final Velocity<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"65148\" data-favorite-title=\"Final Velocity\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/physics\/final-velocity-calculator\/\" data-favorite-excerpt=\"Calculate final velocity, initial velocity, acceleration or time using the kinematic equation v = u + at. Enter any three values and the calculator solves the fourth, with m\/s, km\/h, s and min units supported.\" 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\/final-velocity-calculator\/\" method=\"POST\" class=\"calculator\" id=\"calculator-65148\" data-post=\"65148\"><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=\"v\">Final Velocity (v)<\/option><option value=\"u\">Initial Velocity (u)<\/option><option value=\"a\">Acceleration (a)<\/option><option value=\"t\">Time (t)<\/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\" id=\"input-2\"><label for=\"field-2\">Initial Velocity (u)<\/label><div class=\"field-group\"><input type=\"number\" name=\"initial_velocity_u\" id=\"field-2\" step=\"any\" value=\"0\"\/><div class=\"grid grid-cols-1\"><select id=\"field-3\" 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\" id=\"input-3\"><label for=\"field-4\">Acceleration (a)<\/label><input type=\"number\" name=\"acceleration_a\" id=\"field-4\" aria-describedby=\"calc-unit-4\" step=\"any\" value=\"9.8\"\/><div class=\"unit\" id=\"calc-unit-4\">m\/s\u00b2<\/div><\/div><div class=\"field\" id=\"input-4\"><label for=\"field-5\">Time (t)<\/label><div class=\"field-group\"><input type=\"number\" name=\"time_t\" id=\"field-5\" step=\"any\" value=\"5\"\/><div class=\"grid grid-cols-1\"><select id=\"field-6\" name=\"unit\" aria-label=\"Unit\"><option value=\"s\">s<\/option><option value=\"min\">min<\/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-5\" hidden><label for=\"field-7\">Final Velocity (v)<\/label><div class=\"field-group\"><input type=\"number\" name=\"final_velocity_v\" id=\"field-7\" step=\"any\" value=\"49\"\/><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=\"65148\">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=\"65148\" 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>Final Velocity 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\\[ v = u + a \\cdot t \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(v\\) \u2014 final velocity of the object (m\/s)<\/li>\n<li>\\(u\\) \u2014 initial velocity of the object (m\/s)<\/li>\n<li>\\(a\\) \u2014 constant acceleration (m\/s\u00b2)<\/li>\n<li>\\(t\\) \u2014 time interval during which the acceleration acts (s)<\/li>\n<\/ul>\n<p>This is the first of the standard kinematic equations of motion. It states that under constant acceleration, velocity changes linearly with time: every second, the speed changes by exactly \\(a\\) meters per second. The same equation can be rearranged to find \\(u\\), \\(a\\), or \\(t\\) when the other three quantities are known.<\/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>Final Velocity \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> an object is dropped from rest and falls freely under gravity for 5 seconds. Taking the downward direction as positive, the initial velocity is 0 m\/s and the acceleration is 9.8 m\/s\u00b2.<\/p>\n<p>\\[ v = u + a \\cdot t = 0 + 9.8 \\times 5 = 49 \\text{ m\/s} \\]<\/p>\n<p><strong>Result:<\/strong> the final velocity is 49 m\/s, which is about 176.4 km\/h.<\/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, select the quantity you want to solve for: Final Velocity (v), Initial Velocity (u), Acceleration (a), or Time (t).<\/li>\n<li>Enter the <strong>Initial Velocity (u)<\/strong> and choose its unit \u2014 m\/s or km\/h.<\/li>\n<li>Enter the <strong>Acceleration (a)<\/strong> in m\/s\u00b2. Use 9.8 for objects falling freely near Earth's surface.<\/li>\n<li>Enter the <strong>Time (t)<\/strong> and pick seconds or minutes as the unit.<\/li>\n<li>If you are solving for u, a, or t, also fill in the <strong>Final Velocity (v)<\/strong> field with its unit.<\/li>\n<li>The result appears instantly in the Result box below the inputs.<\/li>\n<\/ol>\n<p>The calculator automatically hides the input field you are solving for, so you only ever see the values you need to provide. All unit conversions (km\/h to m\/s, minutes to seconds) are handled internally, and the result is displayed in the unit you selected.<\/p>\n<h2>What Is Final Velocity?<\/h2>\n<p>Final velocity is the speed and direction of motion an object has at the end of a given time interval. In kinematics \u2014 the branch of physics that describes motion \u2014 the relationship \\(v = u + at\\) is one of the most frequently used equations because it connects the four fundamental quantities of uniformly accelerated motion: starting speed, acceleration, elapsed time, and ending speed.<\/p>\n<p>The equation only holds when acceleration is <em>constant<\/em>. This covers a wide range of practical situations: a car pulling away from a stoplight, an object in free fall (ignoring air resistance), a ball rolling down an incline, or a braking vehicle with steady deceleration. In such cases the velocity does not jump around \u2014 it grows (or shrinks) by the same amount every second, which is exactly what the term \\(a \\cdot t\\) represents.<\/p>\n<p>Interpreting the result is straightforward. If \\(a\\) is positive and in the same direction as \\(u\\), the object speeds up. If \\(a\\) is negative (enter it as a negative number), the object slows down, and a negative final velocity means the object has reversed direction during the interval. For example, a ball thrown straight up at 20 m\/s under gravity \\(a = -9.8\\ \\text{m\/s}^2\\) reaches \\(v = 0\\) after about 2.04 s \u2014 the turning point of its flight.<\/p>\n<p>This calculator is useful for physics homework, engineering estimates, vehicle performance analysis, and sports science. Since it can also rearrange the equation to find \\(u\\), \\(a\\), or \\(t\\), it effectively doubles as a four-in-one kinematics solver. For problems involving distance rather than time, you will need the other kinematic equations, such as \\(v^2 = u^2 + 2as\\).<\/p>\n<h2>Assumptions and Limitations<\/h2>\n<ul>\n<li><strong>Constant acceleration only.<\/strong> The formula is invalid when acceleration changes over time, as with drag-dominated motion or non-uniform engine thrust. For falling objects where air resistance matters, the <a href=\"https:\/\/wpcalc.com\/en\/physics\/terminal-velocity-calculator\/\">Terminal Velocity Calculator<\/a> is more appropriate.<\/li>\n<li><strong>One-dimensional motion.<\/strong> The calculation assumes motion along a straight line. For objects launched at an angle, split the motion into horizontal and vertical components, or use the <a href=\"https:\/\/wpcalc.com\/en\/physics\/projectile-motion-calculator\/\">Projectile Motion Calculator<\/a>.<\/li>\n<li><strong>Signs matter.<\/strong> Velocities and accelerations in opposite directions must have opposite signs. Decide on a positive direction before entering values and stay consistent.<\/li>\n<li><strong>Gravity on Earth is 9.8 m\/s\u00b2.<\/strong> For free-fall problems without air resistance this default value works directly; see also the <a href=\"https:\/\/wpcalc.com\/en\/physics\/free-fall-calculator\/\">Free Fall Calculator<\/a> for distance-based calculations.<\/li>\n<li><strong>Division-by-zero cases.<\/strong> Solving for \\(a\\) requires a nonzero time, and solving for \\(t\\) requires a nonzero acceleration; the calculator reports an error for these inputs instead of a number.<\/li>\n<li><strong>Relativistic speeds.<\/strong> Classical kinematics breaks down near the speed of light (about \\(3 \\times 10^8\\) m\/s), but for any everyday situation \u2014 cars, balls, aircraft \u2014 the equation is exact to any practical precision.<\/li>\n<\/ul>\n<h2>Quick Reference: Rearranged Forms of the Equation<\/h2>\n<table>\n<thead>\n<tr>\n<th>Unknown<\/th>\n<th>Rearranged formula<\/th>\n<th>Required inputs<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Final velocity \\(v\\)<\/td>\n<td>\\(v = u + at\\)<\/td>\n<td>\\(u\\), \\(a\\), \\(t\\)<\/td>\n<\/tr>\n<tr>\n<td>Initial velocity \\(u\\)<\/td>\n<td>\\(u = v - at\\)<\/td>\n<td>\\(v\\), \\(a\\), \\(t\\)<\/td>\n<\/tr>\n<tr>\n<td>Acceleration \\(a\\)<\/td>\n<td>\\(a = \\dfrac{v - u}{t}\\)<\/td>\n<td>\\(v\\), \\(u\\), \\(t\\)<\/td>\n<\/tr>\n<tr>\n<td>Time \\(t\\)<\/td>\n<td>\\(t = \\dfrac{v - u}{a}\\)<\/td>\n<td>\\(v\\), \\(u\\), \\(a\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Each of these four forms corresponds to one mode of the calculator. If your problem also involves distance, stopping distances, or average speeds over a trip, consider the <a href=\"https:\/\/wpcalc.com\/en\/physics\/stopping-distance-calculator\/\">Stopping Distance Calculator<\/a> or the <a href=\"https:\/\/wpcalc.com\/en\/physics\/average-speed-calculator\/\">Average Speed Calculator<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Calculate final velocity, initial velocity, acceleration or time using the kinematic equation v = u + at. Enter any three values and the calculator solves the fourth, with m\/s, km\/h, s and min units supported.<\/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-65148","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\/65148","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=65148"}],"version-history":[{"count":4,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/65148\/revisions"}],"predecessor-version":[{"id":66360,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/65148\/revisions\/66360"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=65148"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=65148"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=65148"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}