{"id":65151,"date":"2026-05-02T11:08:26","date_gmt":"2026-05-02T08:08:26","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=65151"},"modified":"2026-10-01T13:48:47","modified_gmt":"2026-10-01T10:48:47","slug":"displacement-calculator","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/physics\/displacement-calculator\/","title":{"rendered":"Displacement 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\">Displacement Calculator Physics Kinematics<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"65151\" data-favorite-title=\"Displacement\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/physics\/displacement-calculator\/\" data-favorite-excerpt=\"Calculate displacement, initial velocity, acceleration, or time using the kinematic equation s = ut + \u00bdat\u00b2. Select what you want to find, enter the known values, and get an instant answer.\" 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\/displacement-calculator\/\" method=\"POST\" class=\"calculator\" id=\"calculator-65151\" data-post=\"65151\"><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=\"s\">Displacement (s)<\/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\">Displacement (s)<\/label><div class=\"field-group\"><input type=\"number\" name=\"displacement_s\" id=\"field-7\" step=\"any\" value=\"122.5\"\/><div class=\"grid grid-cols-1\"><select id=\"field-8\" name=\"unit\" aria-label=\"Unit\"><option value=\"m\">m<\/option><option value=\"km\">km<\/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=\"65151\">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 is-grid\" 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=\"65151\" 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>Displacement 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\\[ s = ut + \\frac{1}{2}at^2 \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(s\\) \u2014 displacement of the object (m)<\/li>\n<li>\\(u\\) \u2014 initial velocity (m\/s)<\/li>\n<li>\\(a\\) \u2014 constant acceleration (m\/s\u00b2)<\/li>\n<li>\\(t\\) \u2014 time elapsed (s)<\/li>\n<\/ul>\n<p>This is one of the fundamental kinematic equations of physics. It gives the position change of an object that moves with constant acceleration \\(a\\), starting with velocity \\(u\\), over a time interval \\(t\\). The equation rearranges to solve for any of the other variables:<\/p>\n<p>\\[ u = \\frac{s - \\frac{1}{2}at^2}{t}, \\quad a = \\frac{2(s - ut)}{t^2}, \\quad t = \\frac{-u + \\sqrt{u^2 + 2as}}{a} \\]<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>Displacement \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> a stone is dropped from rest (\\(u = 0\\) m\/s) and falls with an acceleration of \\(9.8\\) m\/s\u00b2 for \\(5\\) seconds. How far does it fall?<\/p>\n<p>\\[ s = ut + \\frac{1}{2}at^2 = 0 \\times 5 + \\frac{1}{2} \\times 9.8 \\times 5^2 \\]<\/p>\n<p>\\[ s = 0 + 4.9 \\times 25 = 122.5 \\text{ m} \\]<\/p>\n<p><strong>Result:<\/strong> the stone travels \\(122.5\\) m in 5 seconds \u2014 the same answer the calculator returns with its default values.<\/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 the unknown quantity: Displacement (s), Initial Velocity (u), Acceleration (a), or Time (t).<\/li>\n<li>Enter the <strong>Initial Velocity (u)<\/strong> and pick its unit \u2014 m\/s or km\/h.<\/li>\n<li>Enter the <strong>Acceleration (a)<\/strong> in m\/s\u00b2.<\/li>\n<li>Enter the <strong>Time (t)<\/strong> and choose seconds or minutes.<\/li>\n<li>If you are solving for u, a, or t, also enter the known <strong>Displacement (s)<\/strong> in meters or kilometers.<\/li>\n<li>Click <strong>Calculate<\/strong>. The result appears instantly, and the field you are solving for is hidden since its value is not needed as input.<\/li>\n<\/ol>\n<h2>What Is Displacement?<\/h2>\n<p>Displacement is the change in position of an object: the straight-line distance from its starting point to its ending point, together with the direction. It differs from <em>distance travelled<\/em>, which counts the total path length. If you walk 3 m east and then 3 m west, you covered a distance of 6 m, but your displacement is zero because you ended where you started.<\/p>\n<p>The formula \\(s = ut + \\frac{1}{2}at^2\\) comes from the kinematics of uniformly accelerated motion. The first term, \\(ut\\), is the distance the object would cover at its initial velocity alone. The second term, \\(\\frac{1}{2}at^2\\), is the extra distance gained (or lost) because the velocity keeps changing at rate \\(a\\). This equation is one of the standard set of kinematic equations, alongside \\(v = u + at\\) and \\(v^2 = u^2 + 2as\\).<\/p>\n<p>Interpreting the result is straightforward: a positive displacement means the object moved in the direction you treat as positive; a negative value means it moved the other way. Note that the calculator always assumes motion along a straight line. For motion in two dimensions, such as a ball thrown at an angle, use the <a href=\"https:\/\/wpcalc.com\/en\/physics\/projectile-motion-calculator\/\">Projectile Motion Calculator<\/a> instead.<\/p>\n<h2>Assumptions and Limitations<\/h2>\n<ul>\n<li><strong>Constant acceleration only.<\/strong> The formula is exact only when acceleration is uniform. If acceleration changes over time (e.g. air drag becoming significant), the result is an approximation.<\/li>\n<li><strong>Straight-line motion.<\/strong> Only the component of motion along one axis is handled; horizontal and vertical motion must be computed separately.<\/li>\n<li><strong>Solving for time.<\/strong> When you solve for \\(t\\), the calculator uses \\(t = \\frac{-u + \\sqrt{u^2 + 2as}}{a}\\) and returns the earliest positive solution. If \\(u^2 + 2as &lt; 0\\) or \\(a = 0\\) with nonzero displacement and zero velocity, no valid solution exists and an error is shown.<\/li>\n<li><strong>Units are converted automatically.<\/strong> Velocity entered in km\/h is converted to m\/s, time in minutes to seconds, and displacement in km to meters before computing, so you can mix units freely.<\/li>\n<\/ul>\n<h2>Practical Tips<\/h2>\n<p>A common source of confusion is the sign of acceleration. Gravity near Earth's surface gives \\(a \\approx 9.8\\) m\/s\u00b2 downward. If you define upward as positive, use \\(a = -9.8\\) m\/s\u00b2 for a falling object; if downward is positive, use \\(+9.8\\) m\/s\u00b2. The default values in this calculator (\\(u = 0\\), \\(a = 9.8\\), \\(t = 5\\)) describe an object in <a href=\"https:\/\/wpcalc.com\/en\/physics\/free-fall-calculator\/\">free fall<\/a> from rest.<\/p>\n<p>This equation also applies to braking problems: enter a negative acceleration for a decelerating vehicle and the displacement becomes its <a href=\"https:\/\/wpcalc.com\/en\/physics\/stopping-distance-calculator\/\">stopping distance<\/a>. To average results over a whole trip rather than analyzing a single acceleration phase, see the <a href=\"https:\/\/wpcalc.com\/en\/physics\/average-speed-calculator\/\">Average Speed Calculator<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Calculate displacement, initial velocity, acceleration, or time using the kinematic equation s = ut + \u00bdat\u00b2. Select what you want to find, enter the known values, and get an instant answer.<\/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-65151","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\/65151","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=65151"}],"version-history":[{"count":3,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/65151\/revisions"}],"predecessor-version":[{"id":66356,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/65151\/revisions\/66356"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=65151"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=65151"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=65151"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}