{"id":65176,"date":"2026-05-02T11:18:14","date_gmt":"2026-05-02T08:18:14","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=65176"},"modified":"2026-10-26T09:24:35","modified_gmt":"2026-10-26T06:24:35","slug":"centripetal-force-calculator","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/physics\/centripetal-force-calculator\/","title":{"rendered":"Centripetal Force Calculator \u2013 F = mv\u00b2\/r"},"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\">Compute Centripetal Force<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"65176\" data-favorite-title=\"Centripetal Force\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/physics\/centripetal-force-calculator\/\" data-favorite-excerpt=\"Calculate centripetal force, mass, velocity, or radius for an object in circular motion. Enter the known values, choose the variable to solve for, and get an instant result in SI units.\" 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\/centripetal-force-calculator\/\" method=\"POST\" class=\"calculator\" id=\"calculator-65176\" data-post=\"65176\"><fieldset class=\"fieldset-input\"><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=\"f\">Centripetal Force (F)<\/option><option value=\"m\">Mass (m)<\/option><option value=\"v\">Velocity (v)<\/option><option value=\"r\">Radius (r)<\/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\">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\" 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\" id=\"input-4\"><label for=\"field-6\">Radius (r)<\/label><div class=\"field-group\"><input type=\"number\" name=\"radius_r\" id=\"field-6\" step=\"any\" value=\"2\"\/><div class=\"grid grid-cols-1\"><select id=\"field-7\" 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\" id=\"input-5\" hidden><label for=\"field-8\">Centripetal Force (F)<\/label><input type=\"number\" name=\"centripetal_force_f\" id=\"field-8\" aria-describedby=\"calc-unit-8\" step=\"any\" value=\"125\"\/><div class=\"unit\" id=\"calc-unit-8\">N<\/div><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"65176\">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=\"65176\" 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>Centripetal Force 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\\[ F = \\frac{mv^2}{r} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(F\\) \u2014 centripetal force (N)<\/li>\n<li>\\(m\\) \u2014 mass of the object (kg)<\/li>\n<li>\\(v\\) \u2014 tangential velocity of the object (m\/s)<\/li>\n<li>\\(r\\) \u2014 radius of the circular path (m)<\/li>\n<\/ul>\n<p>This formula gives the inward force needed to keep an object of mass \\(m\\) moving at speed \\(v\\) along a circle of radius \\(r\\). The same equation can be rearranged to solve for any of the other variables:<\/p>\n<p>\\[ m = \\frac{Fr}{v^2}, \\quad v = \\sqrt{\\frac{Fr}{m}}, \\quad r = \\frac{mv^2}{F} \\]<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>Centripetal Force \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> a 10 kg object moves in a circle of radius 2 m at a constant speed of 5 m\/s. What centripetal force is required?<\/p>\n<p>\\[ F = \\frac{mv^2}{r} = \\frac{10 \\times 5^2}{2} = \\frac{10 \\times 25}{2} = \\frac{250}{2} = 125 \\text{ N} \\]<\/p>\n<p><strong>Result:<\/strong> the centripetal force is 125 N. This matches the calculator's default values, so you can reproduce it directly.<\/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 variable you need: Centripetal Force (F), Mass (m), Velocity (v), or Radius (r). The calculator hides the field for the selected variable.<\/li>\n<li>Enter the <strong>Mass (m)<\/strong> and choose the unit \u2014 kilograms or grams.<\/li>\n<li>Enter the <strong>Velocity (v)<\/strong> and choose the unit \u2014 m\/s or km\/h.<\/li>\n<li>Enter the <strong>Radius (r)<\/strong> and choose the unit \u2014 meters or centimeters.<\/li>\n<li>If you are solving for mass, velocity, or radius, also enter the known <strong>Centripetal Force (F)<\/strong> in newtons.<\/li>\n<li>The result appears instantly below the inputs. Values entered in grams, km\/h, or centimeters are converted to SI units automatically.<\/li>\n<\/ol>\n<h2>What Is Centripetal Force?<\/h2>\n<p>Centripetal force is the net inward force that keeps an object moving along a circular path. Without it, the object would fly off in a straight line, as described by Newton's first law. Importantly, \"centripetal\" describes the direction of the force \u2014 toward the center of the circle \u2014 not a new type of force. In real situations it is supplied by something concrete: tension in a string, friction between car tires and the road, gravity for orbiting satellites, or the normal force from a loop-the-loop track.<\/p>\n<p>The formula \\( F = mv^2\/r \\) reveals two key relationships. First, the force grows with the square of the speed: doubling the speed requires four times the inward force. Second, a smaller radius demands more force \u2014 taking a tight turn is harder than a wide one at the same speed. This is why cars slow down for sharp curves and why high-speed turns on banked tracks are designed so carefully.<\/p>\n<p>The result is expressed in newtons (N), the SI unit of force. To interpret it, compare it with the object's weight \\(mg\\): a centripetal force of 125 N on a 10 kg object (weight \u2248 98 N) means the circular motion pushes the object harder than gravity does \u2014 a passenger would feel noticeably heavier at the bottom of the loop. To express the same idea as a multiple of gravity, use the <a href=\"https:\/\/wpcalc.com\/en\/physics\/g-force-calculator\/\">G-Force Calculator<\/a>.<\/p>\n<h2>Assumptions and Limitations<\/h2>\n<ul>\n<li><strong>Uniform circular motion:<\/strong> the formula assumes the object moves at constant speed. If the speed changes (non-uniform circular motion), there is also a tangential acceleration component, and the analysis becomes more complex.<\/li>\n<li><strong>Point mass:<\/strong> the object is treated as a point mass. For extended rotating bodies, use tools like the <a href=\"https:\/\/wpcalc.com\/en\/physics\/rotational-kinetic-energy-calculator\/\">Rotational Kinetic Energy Calculator<\/a> or the <a href=\"https:\/\/wpcalc.com\/en\/physics\/angular-momentum-calculator\/\">Angular Momentum Calculator<\/a>.<\/li>\n<li><strong>Net force:<\/strong> the calculated value is the net inward force. Real-world sources of that force (friction, tension, gravity) must be able to supply it \u2014 if friction on a road is insufficient, the vehicle skids outward.<\/li>\n<li><strong>Speed, not angular velocity:<\/strong> the input is the linear (tangential) speed. If you know the angular velocity \\(\\omega\\), convert first with \\(v = \\omega r\\).<\/li>\n<li><strong>Unit conversions:<\/strong> grams, km\/h, and centimeters are converted automatically, but the force must always be entered in newtons.<\/li>\n<\/ul>\n<h2>Practical Tips<\/h2>\n<ul>\n<li>For orbital problems around Earth or other planets, gravity acts as the centripetal force; pair this calculator with the <a href=\"https:\/\/wpcalc.com\/en\/physics\/gravitational-force-calculator\/\">Gravitational Force Calculator<\/a> to check that the two are equal.<\/li>\n<li>A quick sanity check: the centripetal force always points toward the center, and the centripetal acceleration is \\(a = v^2\/r\\), independent of mass. Mass only scales the force, not the acceleration.<\/li>\n<li>When analyzing banked curves or vehicle dynamics, keep in mind that friction limits are often the deciding factor rather than the theoretical force value.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Calculate centripetal force, mass, velocity, or radius for an object in circular motion. Enter the known values, choose the variable to solve for, and get an instant result in SI units.<\/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":[86],"class_list":["post-65176","post","type-post","status-publish","format-standard","hentry","category-physics","tag-rotational-motion"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/65176","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=65176"}],"version-history":[{"count":5,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/65176\/revisions"}],"predecessor-version":[{"id":67530,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/65176\/revisions\/67530"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=65176"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=65176"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=65176"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}