{"id":65433,"date":"2026-09-28T19:17:43","date_gmt":"2026-09-28T16:17:43","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=65433"},"modified":"2026-09-29T15:19:07","modified_gmt":"2026-09-29T12:19:07","slug":"angular-velocity-converter-rpm-to-rad-s","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/converters\/angular-velocity-converter-rpm-to-rad-s\/","title":{"rendered":"Angular Velocity Converter (RPM to rad\/s)"},"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\">Convert Angular Velocity Units<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"65433\" data-favorite-title=\"Angular Velocity\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/converters\/angular-velocity-converter-rpm-to-rad-s\/\" data-favorite-excerpt=\"Convert angular velocity between RPM, rad\/s, deg\/s, rad\/min and more. Enter a value in any unit and instantly get the equivalent in all other common angular speed 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\/converters\/angular-velocity-converter-rpm-to-rad-s\/\" method=\"POST\" class=\"calculator\" id=\"calculator-65433\" data-post=\"65433\"><fieldset class=\"fieldset-input is-1\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field is-single has-term\" id=\"input-1\"><label for=\"field-1\">Angular speed (\u03c9)<\/label><div class=\"term\">\u03c9<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"angular_speed_\" id=\"field-1\" aria-describedby=\"calc-info-1\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 1750\" min=\"0\" value=\"1750\"\/><div class=\"grid grid-cols-1\"><select id=\"field-2\" name=\"unit\" aria-label=\"Unit\"><option value=\"RPM\" selected>RPM (rev\/min)<\/option><option value=\"rad\/s\">rad\/s<\/option><option value=\"deg\/s\">deg\/s<\/option><option value=\"rad\/min\">rad\/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><small id=\"calc-info-1\">Typical motor speed: 1750 RPM.<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"65433\">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> Converted Angular Velocities<\/h3><div class=\"result-box\"><div class=\"field-result is-column\" id=\"output-1\"><span class=\"field-title\"><span>Equivalent angular velocities in all common units<\/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=\"65433\" 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>Angular 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\\[ \\omega_{\\text{rad\/s}} = N_{\\text{RPM}} \\times \\frac{2\\pi}{60} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(\\omega\\) \u2014 angular velocity in radians per second (rad\/s)<\/li>\n<li>\\(N\\) \u2014 rotational speed in revolutions per minute (RPM)<\/li>\n<li>\\(2\\pi\\) \u2014 radians in one full revolution (a circle has \\(360\u00b0 = 2\\pi \\approx 6.2832\\) radians)<\/li>\n<li>\\(60\\) \u2014 seconds in one minute<\/li>\n<\/ul>\n<p>The formula converts RPM to rad\/s by multiplying the number of revolutions per minute by the radians in each revolution and dividing by the seconds in a minute. Rad\/s is the SI unit for angular velocity, which is why all other units in this converter are first changed into rad\/s and then back out into the target unit.<\/p>\n<p>The reverse conversion is just as simple:<\/p>\n<p>\\[ N_{\\text{RPM}} = \\omega_{\\text{rad\/s}} \\times \\frac{60}{2\\pi} \\]<\/p>\n<p>Other useful relationships:<\/p>\n<ul>\n<li>\\(1\\ \\text{RPM} = 0.104720\\ \\text{rad\/s}\\)<\/li>\n<li>\\(1\\ \\text{rad\/s} = 9.549297\\ \\text{RPM}\\)<\/li>\n<li>\\(1\\ \\text{deg\/s} = 0.0174533\\ \\text{rad\/s}\\)<\/li>\n<li>\\(1\\ \\text{RPM} = 6\\ \\text{deg\/s}\\)<\/li>\n<\/ul>\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>Angular Velocity \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> an electric motor runs at 1750 RPM, a typical nameplate speed. What is its angular velocity in rad\/s?<\/p>\n<p>\\[ \\omega = 1750 \\times \\frac{2\\pi}{60} = 1750 \\times 0.10472 \\approx 183.259571\\ \\text{rad\/s} \\]<\/p>\n<p><strong>Result:<\/strong> 1750 RPM \u2248 183.26 rad\/s.<\/p>\n<p>The same speed expressed in the other common units:<\/p>\n<ul>\n<li>29.1667 rev\/s (Hz)<\/li>\n<li>10 995.57 rad\/min<\/li>\n<li>10 500 deg\/s<\/li>\n<li>630 000 deg\/min<\/li>\n<\/ul>\n<p>\n\r\n<\/section>\n<h2>How to use the calculator<\/h2>\n<ol>\n<li>Enter the angular speed \\(\\omega\\) in the <strong>Angular speed (\u03c9)<\/strong> field \u2014 for example the default value of 1750, a typical motor speed.<\/li>\n<li>Choose the unit of that value from the <strong>Unit<\/strong> dropdown: RPM (rev\/min), rad\/s, deg\/s or rad\/min.<\/li>\n<li>Read the result table <strong>Converted Angular Velocities<\/strong>, which shows the same angular velocity in all other common units, including rad\/h, rev\/s (Hz), deg\/s, deg\/min and deg\/h.<\/li>\n<\/ol>\n<h2>What is angular velocity?<\/h2>\n<p>Angular velocity describes how fast an object rotates or revolves around an axis. While linear velocity is measured in distance per unit of time (m\/s, mph), angular velocity is measured in angle per unit of time \u2014 most often radians per second (rad\/s), the SI unit, or revolutions per minute (RPM), the unit commonly printed on motor nameplates, lathe spec sheets and fan curves.<\/p>\n<p>One full revolution equals \\(2\\pi\\) radians, and a minute contains 60 seconds. That is the entire idea behind the conversion: 1 RPM means the object sweeps \\(2\\pi\\) radians every 60 seconds, or about 0.10472 rad\/s. Going the other way, 1 rad\/s corresponds to roughly 9.55 RPM \u2014 a number worth remembering when you move between engineering documents that mix the two conventions.<\/p>\n<p>Angular velocity appears everywhere something spins: shafts, wheels, turbines, hard drives, centrifuges and orbiting satellites. It links directly to linear speed at the rim through \\(v = \\omega r\\), where \\(r\\) is the radius, and to frequency through \\(f = \\omega \/ 2\\pi\\) (so rad\/s divided by \\(2\\pi\\) gives revolutions per second, i.e. hertz). If you also work with rotational power, combining angular velocity with torque via \\(P = \\tau\\omega\\) gives mechanical power in watts \u2014 see our <a href=\"https:\/\/wpcalc.com\/en\/converters\/torque\/\">Torque Converter<\/a> for the other half of that calculation.<\/p>\n<h2>Interpreting the result<\/h2>\n<p>The calculator first converts your input into rad\/s, then expresses it in every other unit so you can compare conventions at a glance. Note that rev\/s (Hz) and RPM differ only by a factor of 60 \u2014 they measure the same thing on different time scales. Similarly, deg\/s and rad\/s differ by \\(180\/\\pi \\approx 57.2958\\), because one radian is about 57.3 degrees.<\/p>\n<p>Large values in deg\/min or deg\/h can look surprising: the same 1750 RPM motor turns through 630 000 degrees per minute. That is not an error \u2014 degrees are simply a much smaller unit than revolutions. For most physics and engineering formulas, stay in rad\/s; radians are the \"natural\" unit in which formulas like \\(v = \\omega r\\) work without extra correction factors.<\/p>\n<h2>Tips, assumptions and limitations<\/h2>\n<ul>\n<li>The calculator accepts only non-negative values. If you need to indicate rotation direction, keep the magnitude here and note the direction (clockwise or counterclockwise) separately; angular velocity as a vector carries a sign, but unit conversion only concerns the magnitude.<\/li>\n<li>Results are rounded to 6 decimal places. For very large inputs (tens of thousands of RPM or more), the trailing digits in deg\/h may lose visible precision \u2014 keep more significant figures in your own work if that matters.<\/li>\n<li>The conversion assumes a constant angular speed. Real motors under varying load speed up and slow down; if you need average angular velocity, convert the average RPM, not instantaneous peaks.<\/li>\n<li>Watch out for the similar-looking unit rad\/min: it is 60 times smaller than rad\/s, and it is not the same as RPM (1 RPM \u2248 6.2832 rad\/min).<\/li>\n<li>If your rotational data eventually turns into a surface or cutting speed, pair this tool with our <a href=\"https:\/\/wpcalc.com\/en\/converters\/speed-units-converter\/\">Speed Converter<\/a> for the linear side, or the <a href=\"https:\/\/wpcalc.com\/en\/converters\/frequency\/\">Frequency Converter<\/a> when working with cycles per second.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Convert angular velocity between RPM, rad\/s, deg\/s, rad\/min and more. Enter a value in any unit and instantly get the equivalent in all other common angular speed 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":[3],"tags":[34],"class_list":["post-65433","post","type-post","status-publish","format-standard","hentry","category-converters","tag-physics-units"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/65433","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=65433"}],"version-history":[{"count":6,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/65433\/revisions"}],"predecessor-version":[{"id":65668,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/65433\/revisions\/65668"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=65433"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=65433"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=65433"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}