{"id":100213,"date":"2026-02-15T20:27:43","date_gmt":"2026-02-15T20:27:43","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100213"},"modified":"2026-07-14T22:57:18","modified_gmt":"2026-07-14T22:57:18","slug":"rpm-to-rads-converter","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/ro\/calculators\/rpm-to-rads-converter\/","title":{"rendered":"Rotational Speed Unit Converter"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Rotational Speed Unit Converter\",\"description\":\"Convert non-negative rotational speed magnitudes between r\/min, rad\/s, degree\/s, r\/s and one-cycle-per-revolution rotational frequency with explicit quantity 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var(--line);color:var(--muted);font-size:13px}\n@media(max-width:720px){.vbm213-grid,.vbm213-result-grid{grid-template-columns:1fr}.vbm213-result.primary,.vbm213-field.full{grid-column:1}.vbm213-body,.vbm213-section,.vbm213-hero{padding:16px}.vbm213-actions .vbm213-btn{flex:1 1 130px}}\n@media print{.vbm213-actions{display:none}.vbm213-card,.vbm213-section{box-shadow:none;break-inside:avoid}.vbm213-results.show{display:block}}\n<\/style>\n\n<main class=\"vbm213\" id=\"vbm-c100213\">\n  <header class=\"vbm213-hero\">\n    <div class=\"vbm213-kicker\">Reference conversion \u00b7 one rotation axis \u00b7 speed magnitude<\/div>\n    <h1>Rotational Speed Unit Converter<\/h1>\n    <p class=\"vbm213-lead\">Convert a non-negative rotational-speed magnitude between revolutions per minute, radians per second, degrees per second, revolutions per second and a carefully defined rotational frequency.<\/p>\n    <div class=\"vbm213-badges\"><span class=\"vbm213-badge\">r\/min (RPM)<\/span><span class=\"vbm213-badge\">rad\/s<\/span><span class=\"vbm213-badge\">\u00b0\/s<\/span><span class=\"vbm213-badge\">r\/s<\/span><span class=\"vbm213-badge\">Hz only for 1 cycle\/rev<\/span><\/div>\n    <div class=\"vbm213-alert\"><strong>Do not equate every vibration frequency with shaft speed.<\/strong> The hertz result below is the rotational frequency only when one complete revolution is the defined cycle. A 2\u00d7 order, B-blade passage or Z-tooth mesh occurs at 2n, Bn or Zn, respectively.<\/div>\n  <\/header>\n\n  <section class=\"vbm213-card\" aria-labelledby=\"vbm213-input-title\">\n    <div class=\"vbm213-card-h\"><h2 id=\"vbm213-input-title\">Controlled input<\/h2><p>Enter a magnitude. Negative numbers are rejected because direction requires a declared positive axis and a signed angular-velocity model.<\/p><\/div>\n    <div class=\"vbm213-body\">\n      <form id=\"vbm213-form\" novalidate>\n        <div class=\"vbm213-grid\">\n          <div class=\"vbm213-field\"><label for=\"vbm213-value\">Rotational-speed magnitude<\/label><input id=\"vbm213-value\" inputmode=\"decimal\" autocomplete=\"off\" placeholder=\"blank\"><\/div>\n          <div class=\"vbm213-field\"><label for=\"vbm213-unit\">Input quantity and unit<\/label><select id=\"vbm213-unit\"><option value=\"rpm\">Rotational speed \u2014 r\/min (RPM)<\/option><option value=\"rads\">Angular speed \u2014 rad\/s<\/option><option value=\"degs\">Angular speed \u2014 \u00b0\/s<\/option><option value=\"revs\">Rotational frequency \u2014 r\/s<\/option><option value=\"hz\">Rotational frequency \u2014 Hz (1 cycle\/rev)<\/option><\/select><span class=\"vbm213-hint\">Changing the unit clears the numeric field and prior result so a number is never silently reinterpreted.<\/span><\/div>\n        <\/div>\n        <div class=\"vbm213-actions\"><button class=\"vbm213-btn\" type=\"submit\">Convert documented value<\/button><button class=\"vbm213-btn secondary\" type=\"button\" id=\"vbm213-reset\">Clear<\/button><\/div>\n        <div class=\"vbm213-error\" id=\"vbm213-error\" role=\"alert\" aria-live=\"assertive\" tabindex=\"-1\"><\/div>\n      <\/form>\n    <\/div>\n  <\/section>\n\n  <section class=\"vbm213-card vbm213-results\" id=\"vbm213-results\" aria-live=\"polite\">\n    <div class=\"vbm213-card-h\"><h2>Reference result<\/h2><p id=\"vbm213-result-context\"><\/p><\/div>\n    <div class=\"vbm213-body\">\n      <div class=\"vbm213-result-grid\">\n        <div class=\"vbm213-result primary\"><div class=\"vbm213-result-label\">Angular speed \u03c9<\/div><div class=\"vbm213-result-value\" id=\"vbm213-r-rads\">\u2014<\/div><div class=\"vbm213-result-note\">SI coherent unit for angular velocity\/angular frequency<\/div><\/div>\n        <div class=\"vbm213-result\"><div class=\"vbm213-result-label\">Rotational speed<\/div><div class=\"vbm213-result-value\" id=\"vbm213-r-rpm\">\u2014<\/div><\/div>\n        <div class=\"vbm213-result\"><div class=\"vbm213-result-label\">Angular speed<\/div><div class=\"vbm213-result-value\" id=\"vbm213-r-degs\">\u2014<\/div><\/div>\n        <div class=\"vbm213-result\"><div class=\"vbm213-result-label\">Rotational frequency n<\/div><div class=\"vbm213-result-value\" id=\"vbm213-r-revs\">\u2014<\/div><div class=\"vbm213-result-note\">Revolutions divided by time<\/div><\/div>\n        <div class=\"vbm213-result\"><div class=\"vbm213-result-label\">One-cycle-per-revolution frequency<\/div><div class=\"vbm213-result-value\" id=\"vbm213-r-hz\">\u2014<\/div><div class=\"vbm213-result-note\">Not automatically a vibration, blade-pass or gear-mesh frequency<\/div><\/div>\n        <div class=\"vbm213-result\"><div class=\"vbm213-result-label\">Period per revolution<\/div><div class=\"vbm213-result-value\" id=\"vbm213-r-period\">\u2014<\/div><div class=\"vbm213-result-note\">Defined as 1\/n only for n &gt; 0<\/div><\/div>\n      <\/div>\n      <div class=\"vbm213-pass\">No resonance, critical-speed, motor-slip, balancing, vibration-severity or safe-operating-speed conclusion is produced.<\/div>\n    <\/div>\n  <\/section>\n\n  <section class=\"vbm213-section\">\n    <h2>Equations, quantities and boundary<\/h2>\n    <p>Let <strong>n<\/strong> be the magnitude of rotational frequency in revolutions per second and <strong>\u03c9<\/strong> the corresponding angular-speed magnitude in radians per second.<\/p>\n    <div class=\"vbm213-equation\">\u03c9 = 2\u03c0n \u00b7 n = N\/60 for N in r\/min \u00b7 T = 1\/n for n &gt; 0<\/div>\n    <p>One revolution is exactly 2\u03c0 radians and one minute is exactly 60 seconds, so the worksheet uses the mathematical factor \u03c0\/30 rather than a rounded lookup factor.<\/p>\n    <div class=\"vbm213-table-wrap\"><table>\n      <thead><tr><th>Input of 1 unit<\/th><th>Angular speed<\/th><th>Rotational frequency<\/th><th>r\/min<\/th><\/tr><\/thead>\n      <tbody>\n        <tr><td>1 r\/min<\/td><td>\u03c0\/30 rad\/s<\/td><td>1\/60 r\/s<\/td><td>1<\/td><\/tr>\n        <tr><td>1 rad\/s<\/td><td>1 rad\/s<\/td><td>1\/(2\u03c0) r\/s<\/td><td>30\/\u03c0<\/td><\/tr>\n        <tr><td>1 \u00b0\/s<\/td><td>\u03c0\/180 rad\/s<\/td><td>1\/360 r\/s<\/td><td>1\/6<\/td><\/tr>\n        <tr><td>1 r\/s<\/td><td>2\u03c0 rad\/s<\/td><td>1 r\/s<\/td><td>60<\/td><\/tr>\n        <tr><td>1 Hz rotational frequency<\/td><td>2\u03c0 rad\/s<\/td><td>1 r\/s only for 1 cycle\/rev<\/td><td>60<\/td><\/tr>\n      <\/tbody>\n    <\/table><\/div>\n\n    <h3>Why Hz needs a quantity name<\/h3>\n    <p>Hertz is the SI unit of frequency; radian per second is the SI unit of angular velocity and angular frequency. The BIPM warns that frequency and angular frequency differ numerically by 2\u03c0. This page therefore never labels rad\/s as Hz. Its Hz result means <em>rotational frequency with exactly one counted cycle per revolution<\/em>.<\/p>\n    <p>If a shaft rotates at n, a once-per-revolution feature is n Hz, second order is 2n Hz, blade-pass for B equally spaced blades is Bn Hz, and tooth mesh for Z teeth is Zn Hz. Those are different physical quantities even though every result has dimension s\u207b\u00b9.<\/p>\n\n    <h3>Signed angular velocity is outside this scalar converter<\/h3>\n    <p>Angular velocity is a vector. A negative scalar is meaningful only after defining an axis and positive direction. This worksheet converts speed magnitudes and therefore accepts zero or positive values only.<\/p>\n\n    <h3>Exact reference checks<\/h3>\n    <div class=\"vbm213-table-wrap\"><table>\n      <thead><tr><th>Input<\/th><th>Exact result<\/th><th>Decimal check<\/th><th>Period<\/th><\/tr><\/thead>\n      <tbody>\n        <tr><td>60 r\/min<\/td><td>2\u03c0 rad\/s; 1 r\/s<\/td><td>6.283185307179586 rad\/s<\/td><td>1 s\/rev<\/td><\/tr>\n        <tr><td>1500 r\/min<\/td><td>50\u03c0 rad\/s; 25 r\/s<\/td><td>157.07963267948966 rad\/s<\/td><td>0.04 s\/rev<\/td><\/tr>\n        <tr><td>3600 r\/min<\/td><td>120\u03c0 rad\/s; 60 r\/s<\/td><td>376.99111843077515 rad\/s<\/td><td>1\/60 s\/rev<\/td><\/tr>\n      <\/tbody>\n    <\/table><\/div>\n  <\/section>\n\n  <section class=\"vbm213-section\">\n    <h2>Source classification<\/h2>\n    <div class=\"vbm213-table-wrap\"><table>\n      <thead><tr><th>Claim<\/th><th>Classification<\/th><th>Inspected source<\/th><\/tr><\/thead>\n      <tbody>\n        <tr><td>Angular velocity\/angular frequency use rad\/s; frequency uses Hz; their numerical values differ by 2\u03c0<\/td><td>Current SI unit guidance<\/td><td>BIPM SI Brochure, 9th edition, version 4.01, June 2026, printed pages 135\u2013136<\/td><\/tr>\n        <tr><td>Rotational frequency is revolutions divided by time; r\/s and r\/min are widely used for rotating machinery<\/td><td>NIST SI guidance<\/td><td>NIST SP 811, Chapter 8.1<\/td><\/tr>\n        <tr><td>r\/min to rad\/s tabulated factor 1.047198\u00d710\u207b\u00b9<\/td><td>NIST conversion table; rounded display<\/td><td>NIST SP 811, Appendix B.9<\/td><\/tr>\n        <tr><td>360\u00b0 = 2\u03c0 rad<\/td><td>Plane-angle relation<\/td><td>NIST SP 330, section 5.4.8<\/td><\/tr>\n      <\/tbody>\n    <\/table><\/div>\n    <p class=\"vbm213-source\"><a href=\"https:\/\/www.bipm.org\/en\/publications\/si-brochure\/\" target=\"_blank\" rel=\"noopener\">BIPM SI Brochure page<\/a> \u2014 current edition\/status and official version 4.01 PDF.<\/p>\n    <p class=\"vbm213-source\"><a href=\"https:\/\/www.nist.gov\/pml\/special-publication-811\/nist-guide-si-chapter-8\" target=\"_blank\" rel=\"noopener\">NIST SP 811 Chapter 8.1<\/a> \u2014 rotational-frequency definition and r\/s\/r\/min usage.<\/p>\n    <p class=\"vbm213-source\"><a href=\"https:\/\/www.nist.gov\/pml\/special-publication-811\/nist-guide-si-appendix-b-conversion-factors\/nist-guide-si-appendix-b9\" target=\"_blank\" rel=\"noopener\">NIST SP 811 Appendix B.9<\/a> \u2014 r\/min to rad\/s conversion table.<\/p>\n    <p class=\"vbm213-source\"><a href=\"https:\/\/www.nist.gov\/pml\/special-publication-330\/sp-330-section-5\" target=\"_blank\" rel=\"noopener\">NIST SP 330 section 5.4.8<\/a> \u2014 radian\/degree relation and unit-symbol rules.<\/p>\n    <p><strong>Accessed:<\/strong> 14 July 2026. The official BIPM PDF was downloaded, rendered and visually inspected. The BIPM text cites ISO 80000-3 for further quantity details; no ISO clause or conformity claim is made here because licensed ISO text was not used.<\/p>\n    <div class=\"vbm213-limit\"><strong>Reference calculation only.<\/strong> This unit conversion does not determine an allowable machine speed, synchronous\/asynchronous motor slip, critical speed, resonance margin or a vibration acceptance zone.<\/div>\n  <\/section>\n\n  <footer class=\"vbm213-footer\">Revision: scientific audit 2026-07-14 \u00b7 English source page \u00b7 Exact \u03c0-based conversion \u00b7 Preserve the quantity definition with any copied value.<\/footer>\n<\/main>\n\n<script id=\"vbm-c100213-logic\">\n(function(){\n  'use strict';\n  function el(id){return document.getElementById(id)}\n  function value(id){return el(id).value}\n  function setText(id,text){el(id).textContent=text}\n  function clearError(){var box=el('vbm213-error');box.textContent='';box.classList.remove('show')}\n  function 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