{"id":100266,"date":"2026-02-15T20:31:05","date_gmt":"2026-02-15T20:31:05","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100266"},"modified":"2026-07-15T22:04:18","modified_gmt":"2026-07-15T22:04:18","slug":"torque-power-speed","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/ro\/calculators\/torque-power-speed\/","title":{"rendered":"Controlled Shaft Power\u2013Torque\u2013Speed Worksheet"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Controlled Shaft Power\u2013Torque\u2013Speed Worksheet\",\"description\":\"Calculate one positive shaft-power, torque or rotational-speed magnitude from the other two at the same shaft section and operating point, with explicit scope and SI traceability.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/torque-power-speed\/\",\"applicationCategory\":\"EngineeringApplication\",\"operatingSystem\":\"Any web 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.tps-ok{border-left-color:var(--ok);background:#effaf4}#tps-tool .tps-formula{border:1px solid var(--line);border-radius:8px;background:var(--soft);padding:14px;margin:12px 0;font:600 15px\/1.6 ui-monospace,SFMono-Regular,Consolas,monospace;overflow-x:auto}#tps-tool .tps-section{margin-top:20px}#tps-tool .tps-cols{display:grid;grid-template-columns:1fr 1fr;gap:22px}#tps-tool table{width:100%;border-collapse:collapse;margin-top:12px;font-size:14px}#tps-tool th,#tps-tool td{border:1px solid var(--line);padding:9px 10px;text-align:left;vertical-align:top}#tps-tool th{background:var(--soft)}#tps-tool code{font-family:ui-monospace,SFMono-Regular,Consolas,monospace}#tps-tool .tps-small{font-size:13px;color:var(--muted)}#tps-tool .tps-footer{margin:22px 0 8px;text-align:center;color:var(--muted);font-size:13px}\n@media(max-width:760px){#tps-tool{margin:14px auto}#tps-tool .tps-grid,#tps-tool .tps-cols{grid-template-columns:1fr}#tps-tool .tps-card,#tps-tool .tps-section{padding:18px}#tps-tool .tps-result-list{grid-template-columns:1fr}#tps-tool table{display:block;overflow-x:auto}#tps-tool .tps-actions button{width:100%}}\n@media print{#tps-tool .tps-actions{display:none}#tps-tool .tps-card,#tps-tool .tps-section,#tps-tool .tps-hero{box-shadow:none;break-inside:avoid}}\n<\/style>\n<main id=\"tps-tool\">\n  <header class=\"tps-hero\">\n    <p class=\"tps-kicker\">Controlled engineering worksheet<\/p>\n    <h1>Shaft Power\u2013Torque\u2013Speed<\/h1>\n    <p class=\"tps-lead\">Calculate one positive magnitude from two compatible mechanical shaft quantities at the same shaft section and operating point. This worksheet does not convert electrical input power into shaft output.<\/p>\n    <div class=\"tps-badges\"><span class=\"tps-badge\">Mechanical shaft power only<\/span><span class=\"tps-badge\">Explicit operating-point scope<\/span><span class=\"tps-badge\">No ISO compliance verdict<\/span><\/div>\n  <\/header>\n\n  <div class=\"tps-grid\">\n    <section class=\"tps-card\" aria-labelledby=\"tps-input-heading\">\n      <h2 id=\"tps-input-heading\">Inputs<\/h2>\n      <form id=\"tps-form\" novalidate>\n        <div class=\"tps-field\"><label for=\"tps-ref\">Source \/ operating-point record<\/label><input id=\"tps-ref\" type=\"text\" maxlength=\"180\" autocomplete=\"off\" placeholder=\"e.g. dynamometer run 24, shaft A, 2026-07-15\"><span class=\"tps-help\">Required. Identify the data sheet, test, model or measurement record.<\/span><\/div>\n        <div class=\"tps-field\"><label for=\"tps-solve\">Quantity to calculate<\/label><select id=\"tps-solve\"><option value=\"torque\">Torque T from shaft power and speed<\/option><option value=\"power\">Shaft power P from torque and speed<\/option><option value=\"speed\">Rotational speed n from shaft power and torque<\/option><\/select><\/div>\n        <div class=\"tps-field\" id=\"tps-field-power\"><label for=\"tps-power\">Mechanical shaft power P (kW)<\/label><input id=\"tps-power\" type=\"text\" inputmode=\"decimal\" autocomplete=\"off\" placeholder=\"e.g. 15\"><span class=\"tps-help\">Positive magnitude. Do not enter electrical, hydraulic, fuel or other upstream input power.<\/span><\/div>\n        <div class=\"tps-field\" id=\"tps-field-torque\" hidden><label for=\"tps-torque\">Shaft torque T (N\u00b7m)<\/label><input id=\"tps-torque\" type=\"text\" inputmode=\"decimal\" autocomplete=\"off\" placeholder=\"e.g. 95.493\"><span class=\"tps-help\">Positive magnitude of the torque component along the rotation axis.<\/span><\/div>\n        <div class=\"tps-field\" id=\"tps-field-speed\"><label for=\"tps-speed\">Rotational speed n (r\/min)<\/label><input id=\"tps-speed\" type=\"text\" inputmode=\"decimal\" autocomplete=\"off\" placeholder=\"e.g. 1500\"><span class=\"tps-help\">Positive rotational-speed magnitude; \u201crpm\u201d is shown as r\/min in the result record.<\/span><\/div>\n        <label class=\"tps-check\" for=\"tps-mechanical\"><input id=\"tps-mechanical\" type=\"checkbox\"><span>I confirm that P is mechanical power transmitted at the shaft, not upstream input power or an efficiency-adjusted estimate.<\/span><\/label>\n        <label class=\"tps-check\" for=\"tps-compatible\"><input id=\"tps-compatible\" type=\"checkbox\"><span>I confirm that the two inputs describe the same shaft section, direction convention and operating point, and are compatible instantaneous or steady values.<\/span><\/label>\n        <div class=\"tps-actions\"><button type=\"submit\">Calculate<\/button><button class=\"tps-secondary\" type=\"button\" id=\"tps-clear\">Clear<\/button><\/div>\n        <div class=\"tps-error\" id=\"tps-error\" role=\"alert\"><\/div>\n      <\/form>\n    <\/section>\n\n    <section class=\"tps-card\" aria-labelledby=\"tps-result-heading\">\n      <h2 id=\"tps-result-heading\">Result record<\/h2>\n      <div class=\"tps-empty\" id=\"tps-empty\">Enter two documented quantities, confirm the scope, and select Calculate. No example values are preloaded.<\/div>\n      <div class=\"tps-results\" id=\"tps-results\" aria-live=\"polite\">\n        <div class=\"tps-result-main\"><span class=\"tps-result-name\" id=\"tps-primary-label\">Calculated value<\/span><span class=\"tps-result-value\" id=\"tps-primary\">\u2014<\/span><\/div>\n        <dl class=\"tps-result-list\">\n          <div class=\"tps-result\"><dt>Mechanical shaft power P<\/dt><dd id=\"tps-out-power\">\u2014<\/dd><\/div>\n          <div class=\"tps-result\"><dt>Shaft torque T<\/dt><dd id=\"tps-out-torque\">\u2014<\/dd><\/div>\n          <div class=\"tps-result\"><dt>Rotational speed n<\/dt><dd id=\"tps-out-speed\">\u2014<\/dd><\/div>\n          <div class=\"tps-result\"><dt>Angular velocity \u03c9<\/dt><dd id=\"tps-out-omega\">\u2014<\/dd><\/div>\n          <div class=\"tps-result\"><dt>Mechanical horsepower<\/dt><dd id=\"tps-out-hp\">\u2014<\/dd><\/div>\n          <div class=\"tps-result\"><dt>Torque in lbf\u00b7ft<\/dt><dd id=\"tps-out-ftlbf\">\u2014<\/dd><\/div>\n        <\/dl>\n        <div class=\"tps-substitution\" id=\"tps-substitution\"><\/div>\n        <p class=\"tps-small\" id=\"tps-result-ref\"><\/p>\n      <\/div>\n    <\/section>\n  <\/div>\n\n  <section class=\"tps-section\" aria-labelledby=\"tps-scope-heading\">\n    <h2 id=\"tps-scope-heading\">Scope and limitations<\/h2>\n    <div class=\"tps-cols\">\n      <div><h3>What is calculated<\/h3><p>For rotation about one axis, mechanical power transfer is the dot product of torque and angular velocity. For aligned positive magnitudes at a compatible operating point:<\/p><div class=\"tps-formula\">P = T\u03c9<br>\u03c9 = 2\u03c0n \/ 60<br>P[kW] = 2\u03c0 \u00b7 n[r\/min] \u00b7 T[N\u00b7m] \/ 60000<\/div><p>Rearranging gives <code>T = 60000P\/(2\u03c0n)<\/code> and <code>n = 60000P\/(2\u03c0T)<\/code>. The familiar factor 9549.296\u2026 is <code>60000\/(2\u03c0)<\/code>; it is a unit-conversion constant, not an ISO tolerance or design rule.<\/p><\/div>\n      <div><h3>What is not calculated<\/h3><ul><li>Electrical input, hydraulic input, fuel power, motor efficiency or transmission losses.<\/li><li>Starting torque, accelerating torque, inertia, duty cycle, thermal rating, service factor or available torque from a machine curve.<\/li><li>Conformity with a motor, gearbox, coupling, shaft or safety standard.<\/li><\/ul><div class=\"tps-callout\"><strong>Variable cycles:<\/strong> in general, average power is the time average of <code>T(t)\u03c9(t)<\/code>. It is not necessarily the product of average torque and average speed. Use synchronized time histories or a justified cycle model.<\/div><\/div>\n    <\/div>\n  <\/section>\n\n  <section class=\"tps-section\" aria-labelledby=\"tps-example-heading\">\n    <h2 id=\"tps-example-heading\">Independent worked example<\/h2>\n    <p>For mechanical shaft power <code>P = 15 kW<\/code> and speed <code>n = 1500 r\/min<\/code> at the same point:<\/p><div class=\"tps-formula\">\u03c9 = 2\u03c0 \u00d7 1500 \/ 60 = 157.0796327 rad\/s<br>T = 15000 \/ 157.0796327 = 95.49296586 N\u00b7m<\/div><p class=\"tps-small\">Displayed digits do not create measurement accuracy. Round the result according to the uncertainty and resolution of the input data.<\/p>\n  <\/section>\n\n  <section class=\"tps-section\" aria-labelledby=\"tps-source-heading\">\n    <h2 id=\"tps-source-heading\">Sources and normative status<\/h2>\n    <table><thead><tr><th>Source<\/th><th>Verified use on this page<\/th><th>Status \/ boundary<\/th><\/tr><\/thead><tbody>\n      <tr><td><a href=\"https:\/\/ocw.mit.edu\/courses\/2-004-dynamics-and-control-ii-spring-2008\/c06ea910fbd7eb70cd197e320d4dffa2_lecture_14.pdf\" rel=\"noopener\" target=\"_blank\">MIT OpenCourseWare, 2.004, Lecture 14<\/a><\/td><td>Derives rotational mechanical power <code>P = T\u03a9<\/code> and explains the sign of power flow.<\/td><td>Open university course note; formula basis, not a conformity standard.<\/td><\/tr>\n      <tr><td><a href=\"https:\/\/www.bipm.org\/en\/publications\/si-brochure\/\" rel=\"noopener\" target=\"_blank\">BIPM SI Brochure, 9th edition, version 4.01 (2026)<\/a><\/td><td>SI units: torque N\u00b7m, angular velocity rad\/s, power W; distinguishes angular velocity from ordinary frequency.<\/td><td>Official SI publication.<\/td><\/tr>\n      <tr><td><a href=\"https:\/\/www.nist.gov\/pml\/special-publication-811\/nist-guide-si-appendix-b-conversion-factors\/nist-guide-si-appendix-b8\" rel=\"noopener\" target=\"_blank\">NIST SP 811, Appendix B.8<\/a><\/td><td>Published factors: 1 hp (550 ft\u00b7lbf\/s) = 745.6999 W; 1 lbf\u00b7ft = 1.355818 N\u00b7m; 1 r\/min = 0.1047198 rad\/s.<\/td><td>Official conversion table; factors are printed to stated precision.<\/td><\/tr>\n      <tr><td><a href=\"https:\/\/www.iso.org\/standard\/64974.html\" rel=\"noopener\" target=\"_blank\">ISO 80000-3:2019 + Amd 1:2025<\/a><\/td><td>Official lifecycle and scope card for space\/time quantities and units.<\/td><td>Published. Clause-level use requires the licensed controlled text.<\/td><\/tr>\n      <tr><td><a href=\"https:\/\/www.iso.org\/standard\/64975.html\" rel=\"noopener\" target=\"_blank\">ISO 80000-4:2019 + Amd 1:2025<\/a><\/td><td>Official lifecycle and scope card for mechanics quantities and units.<\/td><td>Published; edition 3 is under development as ISO\/AWI 80000-4. No ISO compliance claim is made here.<\/td><\/tr>\n    <\/tbody><\/table>\n    <div class=\"tps-callout tps-ok\"><strong>Classification:<\/strong> this is a general mechanics identity with documented unit conversions. It is not presented as a formula prescribed by ISO 80000, and it does not determine compliance or equipment suitability.<\/div>\n  <\/section>\n\n  <section class=\"tps-section\" aria-labelledby=\"tps-faq-heading\"><h2 id=\"tps-faq-heading\">Practical questions<\/h2><h3>Can motor electrical input power be entered?<\/h3><p>No. Obtain mechanical shaft output at the same operating point, or apply a separately justified efficiency\/loss model before using this worksheet.<\/p><h3>Why are zero values rejected?<\/h3><p>Each solve mode divides by speed or torque, and the worksheet is deliberately limited to positive operating magnitudes. At standstill, the relationship can report zero instantaneous shaft power even when nonzero torque exists; it cannot infer speed or torque by division.<\/p><h3>Can average torque and average speed be multiplied?<\/h3><p>Only when a justified steady or cycle model makes them compatible. Otherwise calculate or measure the time average of the instantaneous product.<\/p><\/section>\n  <p class=\"tps-footer\">Technical revision: 15 July 2026 \u00b7 English source page \u00b7 Worksheet result does not replace equipment data, uncertainty analysis or engineering review.<\/p>\n<\/main>\n<script>\n(function(){\n  'use strict';\n  const byId=id=>document.getElementById(id),form=byId('tps-form'),solve=byId('tps-solve'),error=byId('tps-error'),results=byId('tps-results'),empty=byId('tps-empty');\n  const fields={power:byId('tps-field-power'),torque:byId('tps-field-torque'),speed:byId('tps-field-speed')};\n  const inputs={power:byId('tps-power'),torque:byId('tps-torque'),speed:byId('tps-speed')};\n  function parseDecimal(raw,label){const s=String(raw).trim();if(!s)throw new Error(label+' is required.');if(s.length>40||!\/^\\+?(?:\\d+(?:[.,]\\d*)?|[.,]\\d+)$\/.test(s))throw new Error(label+' must be one positive decimal number; exponent notation and unit text are not accepted.');const value=Number(s.replace(',','.'));if(!Number.isFinite(value)||value<=0||value>1e12)throw new Error(label+' must be greater than 0 and no greater than 1\u00d710\u00b9\u00b2.');return value;}\n  function format(value,digits=10){if(!Number.isFinite(value))return '\u2014';const abs=Math.abs(value);if(abs!==0&&(abs>=1e12||abs<1e-6))return value.toExponential(8);return Number(value.toPrecision(digits)).toString();}\n  function setMode(){const mode=solve.value;fields.power.hidden=mode==='power';fields.torque.hidden=mode==='torque';fields.speed.hidden=mode==='speed';clearResult();}\n  function clearResult(){results.classList.remove('tps-show');empty.hidden=false;error.classList.remove('tps-show');error.textContent='';}\n  function showError(message){clearResult();error.textContent=message;error.classList.add('tps-show');}\n  function calculate(event){event.preventDefault();try{\n    const ref=byId('tps-ref').value.trim();if(!ref)throw new Error('Source \/ operating-point record is required.');if(!byId('tps-mechanical').checked)throw new Error('Confirm that the power quantity is mechanical shaft power.');if(!byId('tps-compatible').checked)throw new Error('Confirm that the two inputs describe the same shaft section and compatible operating point.');\n    const mode=solve.value,C=60000\/(2*Math.PI),HP_W=745.6999,NM_PER_LBFFT=1.355818;let P,T,n,substitution,label,primary;\n    if(mode==='torque'){P=parseDecimal(inputs.power.value,'Mechanical shaft power');n=parseDecimal(inputs.speed.value,'Rotational speed');T=C*P\/n;label='Calculated shaft torque';primary=format(T)+' N\u00b7m';substitution='T = 60000 \u00d7 '+format(P)+' \/ (2\u03c0 \u00d7 '+format(n)+') = '+format(T)+' N\u00b7m';}\n    else if(mode==='power'){T=parseDecimal(inputs.torque.value,'Shaft torque');n=parseDecimal(inputs.speed.value,'Rotational speed');P=2*Math.PI*n*T\/60000;label='Calculated mechanical shaft power';primary=format(P)+' kW';substitution='P = 2\u03c0 \u00d7 '+format(n)+' \u00d7 '+format(T)+' \/ 60000 = '+format(P)+' kW';}\n    else{P=parseDecimal(inputs.power.value,'Mechanical shaft power');T=parseDecimal(inputs.torque.value,'Shaft torque');n=C*P\/T;label='Calculated rotational speed';primary=format(n)+' r\/min';substitution='n = 60000 \u00d7 '+format(P)+' \/ (2\u03c0 \u00d7 '+format(T)+') = '+format(n)+' r\/min';}\n    const omega=2*Math.PI*n\/60,hp=P*1000\/HP_W,ftlbf=T\/NM_PER_LBFFT;if(![P,T,n,omega,hp,ftlbf].every(Number.isFinite)||[P,T,n].some(v=>v<=0))throw new Error('The calculated value is outside the finite positive range. Check the input scale.');\n    byId('tps-primary-label').textContent=label;byId('tps-primary').textContent=primary;byId('tps-out-power').textContent=format(P)+' kW';byId('tps-out-torque').textContent=format(T)+' N\u00b7m';byId('tps-out-speed').textContent=format(n)+' r\/min';byId('tps-out-omega').textContent=format(omega)+' rad\/s';byId('tps-out-hp').textContent=format(hp)+' hp (550 ft\u00b7lbf\/s)';byId('tps-out-ftlbf').textContent=format(ftlbf)+' lbf\u00b7ft';byId('tps-substitution').textContent=substitution;byId('tps-result-ref').textContent='Source \/ operating point: '+ref;\n    error.classList.remove('tps-show');error.textContent='';empty.hidden=true;results.classList.add('tps-show');\n  }catch(e){showError(e instanceof Error?e.message:'Calculation failed.');}}\n  solve.addEventListener('change',setMode);form.addEventListener('submit',calculate);byId('tps-clear').addEventListener('click',function(){form.reset();setMode();inputs.power.focus();});setMode();\n})();\n<\/script>\n\n","protected":false},"excerpt":{"rendered":"<p>Calculate one positive mechanical shaft power, torque or speed magnitude from two compatible values at the same shaft section and operating point.<\/p>","protected":false},"featured_media":0,"template":"","meta":{"ai_generated_summary":"","footnotes":""},"categories":[],"tags":[],"class_list":["post-100266","calculator","type-calculator","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/vibromera.eu\/ro\/wp-json\/wp\/v2\/calculator\/100266","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vibromera.eu\/ro\/wp-json\/wp\/v2\/calculator"}],"about":[{"href":"https:\/\/vibromera.eu\/ro\/wp-json\/wp\/v2\/types\/calculator"}],"version-history":[{"count":2,"href":"https:\/\/vibromera.eu\/ro\/wp-json\/wp\/v2\/calculator\/100266\/revisions"}],"predecessor-version":[{"id":102609,"href":"https:\/\/vibromera.eu\/ro\/wp-json\/wp\/v2\/calculator\/100266\/revisions\/102609"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/ro\/wp-json\/wp\/v2\/media?parent=100266"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/ro\/wp-json\/wp\/v2\/categories?post=100266"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/ro\/wp-json\/wp\/v2\/tags?post=100266"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}