{"id":100053,"date":"2026-02-15T20:09:29","date_gmt":"2026-02-15T20:09:29","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100053"},"modified":"2026-07-11T22:53:49","modified_gmt":"2026-07-11T22:53:49","slug":"centrifugal-force-unbalance","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/nl\/calculators\/centrifugal-force-unbalance\/","title":{"rendered":"Rotating-Unbalance Force Amplitude | F = U\u03c9\u00b2"},"content":{"rendered":"\r\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Rotating-Unbalance Force-Amplitude Arithmetic\",\"description\":\"Convert a specified unbalance magnitude and constant rotational speed into ideal synchronous force amplitude without estimating bearing reactions or vibration response.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/centrifugal-force-unbalance\/\",\"applicationCategory\":\"Engineering Calculator\",\"operatingSystem\":\"Any\",\"offers\":{\"@type\":\"Offer\",\"price\":\"0\",\"priceCurrency\":\"EUR\"},\"creator\":{\"@type\":\"Organization\",\"name\":\"Vibromera\",\"url\":\"https:\/\/vibromera.eu\/\"},\"dateModified\":\"2026-07-11\",\"inLanguage\":\"en\",\"isAccessibleForFree\":true}<\/script>\r\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[{\"@type\":\"Question\",\"name\":\"What does U times angular speed squared calculate?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"It is the ideal force amplitude associated with a specified mass-eccentricity product U at constant angular speed.\"}},{\"@type\":\"Question\",\"name\":\"Is this the load on each bearing?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"No. Bearing reactions depend on axial unbalance location, couples, rotor and support dynamics, geometry and operating condition.\"}},{\"@type\":\"Question\",\"name\":\"Does the result prove ISO balancing compliance?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"No. ISO 21940-11 covers procedures, tolerances, correction planes, allocation and balancing errors for rigid-behaviour rotors; 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}\r\n.vc-faq-a-inner { padding:14px 16px; border-top:1px solid var(--vc-border-light); font-size:14px; color:var(--vc-ink-secondary); }\r\n.vc-faq-a-inner p { margin:0 0 8px; }\r\n.vc-faq-a-inner p:last-child { margin-bottom:0; }\r\n.vc-faq-a-inner ul { margin:4px 0 8px 16px; padding:0; }\r\n.vc-faq-a-inner li { margin-bottom:3px; }\r\n\r\n\/* \u2500\u2500 RELATED \u2500\u2500 *\/\r\n.vc-related { display:flex; flex-wrap:wrap; gap:10px; margin-top:16px; }\r\n.vc-related-link { display:inline-block; padding:8px 16px; font-family:var(--vc-font); font-size:13px; font-weight:600; background:var(--vc-surface-alt); color:var(--vc-ink-secondary); border:1px solid var(--vc-border); border-radius:var(--vc-radius); text-decoration:none; transition:all 0.15s; }\r\n.vc-related-link:hover { border-color:var(--vc-accent); color:var(--vc-accent); background:var(--vc-accent-light); }\r\n\r\n\/* \u2500\u2500 PROMO \u2500\u2500 *\/\r\n.vc-promo { margin-top:24px; padding:20px; background:linear-gradient(135deg, var(--vc-accent-light), var(--vc-surface)); 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}\r\n    .vc-faq-a { max-height:none!important; }\r\n    .vc-results { max-height:none!important; padding:24px!important; }\r\n    .vc-copy-btn, .vc-section-chevron, .vc-faq-chevron, .vc-presets, .vc-promo { display:none!important; }\r\n}\r\n<\/style>\r\n<div class=\"vc-calculator\" id=\"vc-unbalance-force\"><header class=\"vc-header\"><p class=\"vc-header-eyebrow\">Ideal synchronous excitation arithmetic<\/p><h1 class=\"vc-header-title\">Rotating-Unbalance Force Amplitude<\/h1><p class=\"vc-header-subtitle\">Evaluate F\u0302 = U\u03c9\u00b2 from a specified unbalance magnitude and constant speed. The result is an ideal rotating excitation magnitude\u2014not a bearing reaction, vibration response or acceptance verdict.<\/p><div class=\"vc-badges\"><span class=\"vc-badge\">F\u0302 = U\u03c9\u00b2<\/span><span class=\"vc-badge\">Exact unit conversion<\/span><span class=\"vc-badge\">No bearing-load claim<\/span><\/div><\/header>\r\n<div class=\"vc-card\"><form class=\"vc-form\" id=\"vc-form\" autocomplete=\"off\"><div class=\"vc-form-grid\"><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-unbalance\">Specified unbalance magnitude U<\/label><input class=\"vc-input\" type=\"text\" id=\"vc-unbalance\" inputmode=\"decimal\" placeholder=\"e.g. 1000\"><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-unit\">Unbalance unit<\/label><select class=\"vc-select\" id=\"vc-unit\"><option value=\"gmm\">g\u00b7mm<\/option><option value=\"kgm\">kg\u00b7m<\/option><option value=\"ozin\">oz\u00b7in (avoirdupois)<\/option><\/select><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-speed\">Constant rotational speed n <span class=\"vc-label-hint\">(rpm)<\/span><\/label><input class=\"vc-input\" type=\"text\" id=\"vc-speed\" inputmode=\"decimal\" placeholder=\"e.g. 3000\"><\/div><\/div><p id=\"vc-error\" role=\"alert\" style=\"margin:.75rem 0 0;color:#b42318\"><\/p><div class=\"vc-warning-box\"><p style=\"margin:0\"><strong>Input responsibility:<\/strong> U must represent the particular unbalance vector or equivalent mass-eccentricity product being evaluated. Do not add scalar magnitudes from different angular positions or planes.<\/p><\/div><\/form>\r\n<div class=\"vc-results\" id=\"vc-results\"><div class=\"vc-results-head\"><h2 class=\"vc-results-title\">Ideal force amplitude<\/h2><button type=\"button\" class=\"vc-copy-btn\" id=\"vc-copy-btn\">Copy<\/button><\/div><div class=\"vc-result-grid\"><div class=\"vc-rcard vc-rcard-primary\"><div class=\"vc-rcard-label\">Force amplitude F\u0302<\/div><div class=\"vc-rcard-value\" id=\"vc-r-force\">\u2014<\/div><\/div><div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Force amplitude<\/div><div class=\"vc-rcard-value\" id=\"vc-r-kn\">\u2014<\/div><\/div><div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Force amplitude<\/div><div class=\"vc-rcard-value\" id=\"vc-r-lbf\">\u2014<\/div><\/div><div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Angular speed \u03c9<\/div><div class=\"vc-rcard-value\" id=\"vc-r-omega\">\u2014<\/div><\/div><div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Rotational frequency<\/div><div class=\"vc-rcard-value\" id=\"vc-r-freq\">\u2014<\/div><\/div><div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Converted U<\/div><div class=\"vc-rcard-value\" id=\"vc-r-u\">\u2014<\/div><\/div><\/div><p style=\"margin:0;color:var(--vc-ink-secondary)\">Amplitude only. Direction rotates at 1\u00d7 speed for this ideal single-vector representation.<\/p><\/div><\/div>\r\n<div class=\"vc-section vc-open\"><button type=\"button\" class=\"vc-section-toggle\" aria-expanded=\"true\"><span class=\"vc-section-toggle-text\"><span class=\"vc-section-icon\">\ud83d\udcd8<\/span><span class=\"vc-section-title\">Equation and applicability<\/span><\/span><\/button><div class=\"vc-section-body\"><div class=\"vc-section-inner vc-theory\"><h3>Mass-eccentricity arithmetic<\/h3><div class=\"vc-formula-box\">U = m\u00b7e; &nbsp; \u03c9 = 2\u03c0n\/60; &nbsp; F\u0302 = U\u00b7\u03c9\u00b2<\/div><p>For uniform circular motion, the <a href=\"https:\/\/www.nasa.gov\/pdf\/563410main_FTNL_Instructor_Manual.pdf\" target=\"_blank\" rel=\"noopener\">NASA circular-motion derivation<\/a> gives the required force magnitude as m\u03c9\u00b2r. Substituting the mass-eccentricity product U = m\u00b7e gives F\u0302 = U\u03c9\u00b2. In an inertial frame the supporting reaction is centripetal; \u201ccentrifugal force\u201d is the corresponding rotating-frame description.<\/p><h3>Units<\/h3><p>g\u00b7mm is converted by 10\u207b\u2076 kg\u00b7m. For avoirdupois oz\u00b7in, this page uses 1 oz = 0.028349523125 kg and 1 in = 0.0254 m, hence 1 oz\u00b7in = 720.077887375 g\u00b7mm. The exact base conversions are documented by <a href=\"https:\/\/www.nist.gov\/pml\/special-publication-811\/nist-guide-si-appendix-b-conversion-factors\/nist-guide-si-appendix-b8\" target=\"_blank\" rel=\"noopener\">NIST SP 811 conversion factors<\/a>.<\/p><h3>ISO and system boundary<\/h3><p><a href=\"https:\/\/www.iso.org\/standard\/68131.html\" target=\"_blank\" rel=\"noopener\">ISO 21940-2:2017<\/a>, confirmed in 2022, is the current balancing vocabulary standard. <a href=\"https:\/\/www.iso.org\/standard\/54074.html\" target=\"_blank\" rel=\"noopener\">ISO 21940-11:2016 with Amendment 1:2022<\/a> covers rigid-behaviour rotor balancing procedures, tolerances, correction planes, allocation and errors. This arithmetic neither reproduces those procedures nor establishes compliance.<\/p><div class=\"vc-warning-box\"><p style=\"margin:0\"><strong>Not a bearing or vibration model:<\/strong> bearing reactions and transmitted forces depend on the axial\/vector distribution of unbalance, rotor geometry, support stiffness and damping, modes, speed and other loads. Vibration displacement, velocity, acceleration, stress and bearing life require a validated dynamic model or measurements. Flexible behaviour and unbalance couples cannot be reduced to one scalar output here.<\/p><\/div><h3>Checked example<\/h3><div class=\"vc-example-box\"><p style=\"margin:0\">For U = 1000 g\u00b7mm and n = 3000 rpm: U = 0.001 kg\u00b7m, \u03c9 = 314.159265 rad\/s, and F\u0302 = 98.696044 N.<\/p><\/div><\/div><\/div><\/div>\r\n<div class=\"vc-section\"><button type=\"button\" class=\"vc-section-toggle\" aria-expanded=\"false\"><span class=\"vc-section-toggle-text\"><span class=\"vc-section-icon\">\u2753<\/span><span class=\"vc-section-title\">Frequently Asked Questions<\/span><\/span><\/button><div class=\"vc-section-body\"><div class=\"vc-section-inner\"><div class=\"vc-faq-list\" id=\"vc-faq-list\"><\/div><\/div><\/div><\/div><footer class=\"vc-footer\"><p>\u00a9 2024\u20132026 <a href=\"https:\/\/vibromera.eu\/\">Vibromera<\/a><\/p><p>Ideal input arithmetic only; not bearing load, response, balance tolerance or ISO compliance. Scientific review: July 2026.<\/p><\/footer><\/div>\r\n<script>(function(){'use strict';var OZIN_GMM=720.077887375,N_LBF=0.2248089430997105;function $(i){return document.getElementById(i)}function num(raw){var s=String(raw).trim().replace(\/\\s+\/g,'');if(!\/^[+]?(?:\\d+(?:[.,]\\d*)?|[.,]\\d+)$\/.test(s))return NaN;var n=Number(s.replace(',','.'));return Number.isFinite(n)&&n>=0?n:NaN}function f(n){if(Math.abs(n)<5e-13)n=0;if(Math.abs(n)>=1e12)return n.toExponential(9);return n.toFixed(9).replace(\/(\\.\\d*?)0+$\/,'$1').replace(\/\\.$\/,'')}function calc(){var Uv=num($('vc-unbalance').value),n=num($('vc-speed').value),unit=$('vc-unit').value;if(!Number.isFinite(Uv)||!Number.isFinite(n)){$('vc-error').textContent=$('vc-unbalance').value.trim()||$('vc-speed').value.trim()?'Enter finite non-negative numbers only.':'';$('vc-results').classList.remove('vc-visible');return}$('vc-error').textContent='';var U=unit==='kgm'?Uv:unit==='ozin'?Uv*OZIN_GMM*1e-6:Uv*1e-6,w=2*Math.PI*n\/60,F=U*w*w;if(![U,w,F].every(Number.isFinite)){$('vc-error').textContent='The values exceed the finite calculation range.';$('vc-results').classList.remove('vc-visible');return}$('vc-r-force').innerHTML=f(F)+' <span class=\"vc-rcard-unit\">N<\/span>';$('vc-r-kn').innerHTML=f(F\/1000)+' <span class=\"vc-rcard-unit\">kN<\/span>';$('vc-r-lbf').innerHTML=f(F*N_LBF)+' <span class=\"vc-rcard-unit\">lbf<\/span>';$('vc-r-omega').innerHTML=f(w)+' <span class=\"vc-rcard-unit\">rad\/s<\/span>';$('vc-r-freq').innerHTML=f(n\/60)+' <span class=\"vc-rcard-unit\">Hz<\/span>';$('vc-r-u').innerHTML=f(U)+' <span class=\"vc-rcard-unit\">kg\u00b7m<\/span>';$('vc-results').classList.add('vc-visible');var q=new URL(location);q.searchParams.set('unbalance_magnitude',Uv);q.searchParams.set('unbalance_unit',unit);q.searchParams.set('rotational_speed_rpm',n);history.replaceState(null,'',q.toString())}$('vc-form').addEventListener('input',calc);$('vc-form').addEventListener('change',calc);$('vc-copy-btn').addEventListener('click',function(){if(navigator.clipboard)navigator.clipboard.writeText($('vc-results').innerText)});document.querySelectorAll('.vc-section-toggle').forEach(function(b){b.addEventListener('click',function(){var s=this.closest('.vc-section');s.classList.toggle('vc-open');this.setAttribute('aria-expanded',s.classList.contains('vc-open'))})});var q=[['Is this the load on each bearing?','No. It is only an ideal excitation magnitude. Bearing reactions require vector\/plane locations and rotor-support dynamics.'],['Can I add unbalance magnitudes from two planes?','Not as scalars. Angular phase and axial location matter; separated vectors can also form an unbalance couple.'],['Does this establish ISO 21940 compliance?','No. The applicable rotor classification, tolerance, planes, allocation, procedure and error assessment remain outside this arithmetic.']];var l=$('vc-faq-list');q.forEach(function(v){l.innerHTML+='<div class=\"vc-faq-item\"><button type=\"button\" class=\"vc-faq-q\">'+v[0]+'<\/button><div class=\"vc-faq-a\"><div class=\"vc-faq-a-inner\"><p>'+v[1]+'<\/p><\/div><\/div><\/div>'});l.addEventListener('click',function(e){var b=e.target.closest('.vc-faq-q');if(b)b.closest('.vc-faq-item').classList.toggle('vc-open')});var z=new URLSearchParams(location.search);if(z.has('unbalance_magnitude'))$('vc-unbalance').value=z.get('unbalance_magnitude');if(z.has('unbalance_unit')&&['gmm','kgm','ozin'].indexOf(z.get('unbalance_unit'))>=0)$('vc-unit').value=z.get('unbalance_unit');if(z.has('rotational_speed_rpm'))$('vc-speed').value=z.get('rotational_speed_rpm');calc()})();<\/script>\r\n","protected":false},"excerpt":{"rendered":"<p>Convert a specified unbalance magnitude and constant rotational speed into ideal synchronous force amplitude; not a bearing reaction, vibration response or ISO verdict.<\/p>","protected":false},"featured_media":0,"template":"","meta":{"ai_generated_summary":"","footnotes":""},"categories":[],"tags":[],"class_list":["post-100053","calculator","type-calculator","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/vibromera.eu\/nl\/wp-json\/wp\/v2\/calculator\/100053","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vibromera.eu\/nl\/wp-json\/wp\/v2\/calculator"}],"about":[{"href":"https:\/\/vibromera.eu\/nl\/wp-json\/wp\/v2\/types\/calculator"}],"version-history":[{"count":2,"href":"https:\/\/vibromera.eu\/nl\/wp-json\/wp\/v2\/calculator\/100053\/revisions"}],"predecessor-version":[{"id":102343,"href":"https:\/\/vibromera.eu\/nl\/wp-json\/wp\/v2\/calculator\/100053\/revisions\/102343"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/nl\/wp-json\/wp\/v2\/media?parent=100053"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/nl\/wp-json\/wp\/v2\/categories?post=100053"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/nl\/wp-json\/wp\/v2\/tags?post=100053"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}