{"id":100012,"date":"2026-02-15T20:05:57","date_gmt":"2026-02-15T20:05:57","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100012"},"modified":"2026-07-02T19:14:29","modified_gmt":"2026-07-02T19:14:29","slug":"ball-screw-calculator","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/fr\/calculators\/ball-screw-calculator\/","title":{"rendered":"Calculateur de vis \u00e0 billes | Outil gratuit #077"},"content":{"rendered":"\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Ball Screw Calculator\",\"description\":\"Ball screw calculator: drive torque, efficiency, critical speed and L10 rated life, based on general ball-screw engineering practice. Terminology per the ISO 3408 ball screw standard series.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/ball-screw-calculator\/\",\"applicationCategory\":\"Engineering Calculator\",\"offers\":{\"@type\":\"Offer\",\"price\":\"0\",\"priceCurrency\":\"EUR\"},\"creator\":{\"@type\":\"Organization\",\"name\":\"Vibromera\"},\"datePublished\":\"2024-01-01\",\"dateModified\":\"2025-02-14\",\"inLanguage\":\"en\",\"isAccessibleForFree\":true}<\/script>\n\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[{\"@type\":\"Question\",\"name\":\"How is ball screw torque calculated?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"T = F*lead\/(2*pi*eta), eta about 0.90 for ball screws.\"}},{\"@type\":\"Question\",\"name\":\"What efficiency for ball screws?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"0.85-0.95, typically 0.90. ACME lead screws: 0.25-0.50.\"}},{\"@type\":\"Question\",\"name\":\"How to avoid critical speed?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Operate below 80% of Ncrit. Use larger dia, shorter length, better end fixity.\"}},{\"@type\":\"Question\",\"name\":\"What affects life?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"L10 = (Ca\/F)^3 x 10^6 rev. Load cubed inverse relationship.\"}},{\"@type\":\"Question\",\"name\":\"End fixity factor?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Fixed-fixed: 4.73. Fixed-supported: 3.93. 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solid var(--vc-border-light);font-size:14px;color:var(--vc-ink-secondary)}.vc-faq-a-inner p{margin:0 0 8px}.vc-faq-a-inner p:last-child{margin-bottom:0}.vc-related{display:flex;flex-wrap:wrap;gap:10px;margin-top:16px}.vc-related-link{display:inline-block;padding:8px 16px;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}.vc-related-link:hover{border-color:var(--vc-accent);color:var(--vc-accent)}.vc-promo{margin-top:24px;padding:20px;background:linear-gradient(135deg,var(--vc-accent-light),var(--vc-surface));border:1px solid var(--vc-border);border-radius:var(--vc-radius-lg);display:flex;align-items:center;gap:16px}.vc-promo-text{flex:1;font-size:14px;color:var(--vc-ink-secondary)}.vc-promo-text strong{color:var(--vc-ink)}.vc-promo-link{padding:8px 20px;font-size:13px;font-weight:700;color:#fff;background:var(--vc-accent);border-radius:var(--vc-radius);text-decoration:none}.vc-footer{text-align:center;padding:32px 16px;font-size:13px;color:var(--vc-ink-muted)}.vc-footer a{color:var(--vc-accent);text-decoration:none}.vc-footer-links{margin-top:8px;font-size:12px}.vc-footer-links a{margin:0 8px}@media print{.vc-section-body{max-height:none!important}.vc-results{max-height:none!important;padding:24px!important}.vc-copy-btn,.vc-presets,.vc-promo{display:none!important}}<\/style>\n\n<div class=\"vc-calculator\">\n<header class=\"vc-header\"><p class=\"vc-header-eyebrow\">Free Engineering Tool #077<\/p><h1 class=\"vc-header-title\">Ball Screw Calculator &mdash; Torque, Critical Speed &amp; Life<\/h1><p class=\"vc-header-subtitle\">Enter lead, nominal diameter, axial load, and speed to calculate drive torque, efficiency, critical speed, and rated life. Calculations are based on general ball-screw engineering practice and manufacturer-catalogue methods; ball screw terminology and acceptance tolerances are defined in the ISO 3408 standard series.<\/p><div class=\"vc-badges\"><span class=\"vc-badge\">Drive Torque<\/span><span class=\"vc-badge\">Critical Speed<\/span><span class=\"vc-badge\">Life L10<\/span><\/div><\/header>\n<div class=\"vc-card\">\n<div class=\"vc-unit-bar\"><button type=\"button\" class=\"vc-unit-btn vc-active\" data-system=\"metric\">Metric (mm, N, RPM)<\/button><button type=\"button\" class=\"vc-unit-btn\" data-system=\"imperial\">Imperial (in, lbf, RPM)<\/button><\/div>\n<form class=\"vc-form\" id=\"vc-form\" autocomplete=\"off\"><div class=\"vc-form-grid\">\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-lead\">Lead <span class=\"vc-label-hint\" id=\"vc-leu\">(mm)<\/span><\/label><input class=\"vc-input\" type=\"number\" id=\"vc-lead\" step=\"any\" min=\"1\" value=\"10\"><\/div>\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-bdia\">Nominal Diameter <span class=\"vc-label-hint\" id=\"vc-bdu\">(mm)<\/span><\/label><input class=\"vc-input\" type=\"number\" id=\"vc-bdia\" step=\"any\" min=\"5\" value=\"32\"><\/div>\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-axload\">Axial Load <span class=\"vc-label-hint\" id=\"vc-alu\">(N)<\/span><\/label><input class=\"vc-input\" type=\"number\" id=\"vc-axload\" step=\"any\" min=\"0\" value=\"5000\"><\/div>\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-speed\">Speed <span class=\"vc-label-hint\">(RPM)<\/span><\/label><input class=\"vc-input\" type=\"number\" id=\"vc-speed\" step=\"any\" min=\"1\" value=\"1000\"><\/div>\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-blen\">Unsupported Length <span class=\"vc-label-hint\" id=\"vc-blu\">(mm)<\/span><\/label><input class=\"vc-input\" type=\"number\" id=\"vc-blen\" step=\"any\" min=\"10\" value=\"800\"><\/div>\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-Ca\">Dynamic Load Ca <span class=\"vc-label-hint\">(N)<\/span><\/label><input class=\"vc-input\" type=\"number\" id=\"vc-Ca\" step=\"any\" min=\"1\" value=\"25000\"><\/div>\n<\/div>\n<div class=\"vc-presets\"><div class=\"vc-presets-label\">Quick presets<\/div>\n<button type=\"button\" class=\"vc-preset-btn\" data-d=\"32\" data-l=\"10\" data-f=\"5000\" data-s=\"1000\" data-len=\"800\" data-ca=\"25000\">d32 lead10 5kN<\/button>\n<button type=\"button\" class=\"vc-preset-btn\" data-d=\"25\" data-l=\"5\" data-f=\"2000\" data-s=\"2000\" data-len=\"600\" data-ca=\"15000\">d25 lead5 2kN<\/button>\n<button type=\"button\" class=\"vc-preset-btn\" data-d=\"50\" data-l=\"20\" data-f=\"10000\" data-s=\"500\" data-len=\"1200\" data-ca=\"60000\">d50 lead20 10kN<\/button>\n<\/div><\/form>\n<div class=\"vc-results\" id=\"vc-results\"><div class=\"vc-results-head\"><h2 class=\"vc-results-title\">Results<\/h2><button type=\"button\" class=\"vc-copy-btn\" id=\"vc-copy-btn\">Copy<\/button><\/div>\n<div class=\"vc-result-grid\">\n<div class=\"vc-rcard vc-rcard-primary\"><div class=\"vc-rcard-label\">Drive Torque<\/div><div class=\"vc-rcard-value\" id=\"vc-r-torque\">&mdash;<\/div><\/div>\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Efficiency<\/div><div class=\"vc-rcard-value\" id=\"vc-r-eff\">&mdash;<\/div><\/div>\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Critical Speed<\/div><div class=\"vc-rcard-value\" id=\"vc-r-ncrit\">&mdash;<\/div><\/div>\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Rated Life L10<\/div><div class=\"vc-rcard-value\" id=\"vc-r-life\">&mdash;<\/div><\/div>\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Linear Speed<\/div><div class=\"vc-rcard-value\" id=\"vc-r-vlin\">&mdash;<\/div><\/div>\n<\/div><\/div><\/div>\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\">&#x1F4D8;<\/span><span class=\"vc-section-title\">Theory<\/span><\/span><svg class=\"vc-section-chevron\" viewbox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg><\/button>\n<div class=\"vc-section-body\"><div class=\"vc-section-inner vc-theory\">\n<h3>Drive Torque<\/h3><div class=\"vc-formula-box\" id=\"vc-katex-1\"><\/div>\n<h3>Critical Speed<\/h3><div class=\"vc-formula-box\" id=\"vc-katex-2\"><\/div>\n<h3>Life<\/h3><div class=\"vc-formula-box\" id=\"vc-katex-3\"><\/div>\n<div class=\"vc-warning-box\"><p style=\"margin:0;font-size:14px;color:var(--vc-ink-secondary)\">Apply 0.8 safety factor to critical speed. Use fixed-fixed supports where possible.<\/p><\/div>\n<\/div><\/div><\/div>\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\">&#x1F517;<\/span><span class=\"vc-section-title\">Related<\/span><\/span><svg class=\"vc-section-chevron\" viewbox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg><\/button><div class=\"vc-section-body\"><div class=\"vc-section-inner\"><div class=\"vc-related\"><a class=\"vc-related-link\" href=\"\/calculators\/shaft-diameter-torsion\/\">Shaft Diameter<\/a><a class=\"vc-related-link\" href=\"\/calculators\/rotor-acceleration-time\/\">Acceleration Time<\/a><a class=\"vc-related-link\" href=\"\/calculators\/shaft-deflection-calculator\/\">Shaft Deflection<\/a><\/div><\/div><\/div><\/div>\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\">&#x2753;<\/span><span class=\"vc-section-title\">FAQ<\/span><\/span><svg class=\"vc-section-chevron\" viewbox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg><\/button><div class=\"vc-section-body\"><div class=\"vc-section-inner\"><div class=\"vc-faq-list\" id=\"vc-faq-list\"><\/div><\/div><\/div><\/div>\n<div class=\"vc-promo\"><div class=\"vc-promo-text\"><strong>Vibromera<\/strong> &mdash; Portable Balancing &amp; Vibration Analysis.<\/div><a class=\"vc-promo-link\" href=\"https:\/\/vibromera.eu\/\" target=\"_blank\" rel=\"noopener\">Learn More<\/a><\/div>\n<footer class=\"vc-footer\"><p>&copy; 2024&ndash;2025 <a href=\"https:\/\/vibromera.eu\/\">Vibromera<\/a><\/p><div class=\"vc-footer-links\"><a href=\"\/calculators\/engineering-calculators\/\">All Calculators<\/a><a href=\"https:\/\/vibromera.eu\/contacts\/\">Contact<\/a><\/div><\/footer>\n<\/div>\n<script src=\"https:\/\/cdn.jsdelivr.net\/npm\/katex@0.16.11\/dist\/katex.min.js\"><\/script>\n<script>\n(function(){\n'use strict';var SLUG='ball-screw-calculator',uS='metric';\nfunction $(id){return document.getElementById(id)}\nfunction fmt(n,d){if(isNaN(n)||!isFinite(n))return'\\u2014';return n.toFixed(d==null?2:d).replace(\/(\\.\\d*?)0+$\/,'$1').replace(\/\\.$\/,'')}\nfunction calc(){\n  var lead=parseFloat($('vc-lead').value),d=parseFloat($('vc-bdia').value),F=parseFloat($('vc-axload').value),n=parseFloat($('vc-speed').value),Luns=parseFloat($('vc-blen').value),Ca=parseFloat($('vc-Ca').value);\n  if(!lead||!d||!F||F<=0||!n||n<=0||!Luns||!Ca){$('vc-results').classList.remove('vc-visible');return}\n  var lMm=uS==='imperial'?lead*25.4:lead,dMm=uS==='imperial'?d*25.4:d,FN=uS==='imperial'?F*4.44822:F,LMm=uS==='imperial'?Luns*25.4:Luns,CaN=uS==='imperial'?Ca*4.44822:Ca;\n  var eta=0.90,T=FN*lMm\/(2*Math.PI*eta);\n  var lam=3.93,Ncrit=2.71e7*dMm\/(LMm*LMm)*lam\/3.93;\n  var L10rev=Math.pow(CaN\/FN,3)*1e6,L10hr=L10rev\/(n*60),vLin=lMm*n\/60;\n  if(uS==='imperial'){$('vc-r-torque').innerHTML=fmt(T*0.000738,3)+' <span class=\"vc-rcard-unit\">lbf\\u00B7ft<\/span>';$('vc-r-vlin').innerHTML=fmt(vLin\/25.4,2)+' <span class=\"vc-rcard-unit\">in\/s<\/span>'}\n  else{$('vc-r-torque').innerHTML=fmt(T\/1000,2)+' <span class=\"vc-rcard-unit\">N\\u00B7m<\/span>';$('vc-r-vlin').innerHTML=fmt(vLin,1)+' <span class=\"vc-rcard-unit\">mm\/s<\/span>'}\n  $('vc-r-eff').innerHTML=fmt(eta*100,0)+' <span class=\"vc-rcard-unit\">%<\/span>';\n  $('vc-r-ncrit').innerHTML=fmt(Ncrit,0)+' <span class=\"vc-rcard-unit\">RPM (80%='+fmt(Ncrit*0.8,0)+')<\/span>';\n  $('vc-r-life').innerHTML=fmt(L10hr,0)+' <span class=\"vc-rcard-unit\">hours ('+fmt(L10rev\/1e6,1)+'M rev)<\/span>';\n  $('vc-results').classList.add('vc-visible');\n  sH({lead:lead,d:d,F:F,n:n,_summary:'d='+d+' lead='+lead+' F='+F});\n}\nvar uB=document.querySelectorAll('.vc-unit-btn');uB.forEach(function(b){b.addEventListener('click',function(){uB.forEach(function(x){x.classList.remove('vc-active')});this.classList.add('vc-active');uS=this.getAttribute('data-system');$('vc-leu').textContent=uS==='imperial'?'(in)':'(mm)';$('vc-bdu').textContent=uS==='imperial'?'(in)':'(mm)';$('vc-alu').textContent=uS==='imperial'?'(lbf)':'(N)';$('vc-blu').textContent=uS==='imperial'?'(in)':'(mm)';calc()})});\ndocument.querySelectorAll('.vc-preset-btn').forEach(function(b){b.addEventListener('click',function(e){e.preventDefault();$('vc-bdia').value=this.getAttribute('data-d');$('vc-lead').value=this.getAttribute('data-l');$('vc-axload').value=this.getAttribute('data-f');$('vc-speed').value=this.getAttribute('data-s');$('vc-blen').value=this.getAttribute('data-len');$('vc-Ca').value=this.getAttribute('data-ca');calc()})});\n$('vc-form').addEventListener('input',calc);$('vc-form').addEventListener('change',calc);\n$('vc-copy-btn').addEventListener('click',function(){var t='Ball Screw\\nTorque: '+$('vc-r-torque').textContent+'\\nNcrit: '+$('vc-r-ncrit').textContent+'\\nLife: '+$('vc-r-life').textContent;if(navigator.clipboard){navigator.clipboard.writeText(t).then(function(){var b=$('vc-copy-btn');b.classList.add('vc-copied');b.textContent='Copied!';setTimeout(function(){b.classList.remove('vc-copied');b.textContent='Copy'},2000)})}});\ndocument.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'))})});\nvar fD=[{q:'How is torque calculated?',a:'<p>T=F\\u00B7l\/(2\\u03C0\\u03B7), \\u03B7\\u22480.90 for ball screws.<\/p>'},{q:'Efficiency?',a:'<p>Ball: 0.85\\u20130.95. ACME: 0.25\\u20130.50.<\/p>'},{q:'Avoid critical speed?',a:'<p>Below 80% Ncrit. Larger dia, shorter length.<\/p>'},{q:'Life factors?',a:'<p>L10=(Ca\/F)\\u00B3\\u00D710\\u2076 rev. Cubed inverse.<\/p>'},{q:'End fixity?',a:'<p>Fixed-fixed: 4.73. Fixed-supported: 3.93.<\/p>'}];\nvar fL=$('vc-faq-list');fD.forEach(function(f){fL.innerHTML+='<div class=\"vc-faq-item\"><button type=\"button\" class=\"vc-faq-q\"><span>'+f.q+'<\/span><svg class=\"vc-faq-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg><\/button><div class=\"vc-faq-a\"><div class=\"vc-faq-a-inner\">'+f.a+'<\/div><\/div><\/div>'});\nfL.addEventListener('click',function(e){var b=e.target.closest('.vc-faq-q');if(b)b.closest('.vc-faq-item').classList.toggle('vc-open')});\nfunction sH(e){var k='vc_history_'+SLUG,a=[];try{a=JSON.parse(localStorage.getItem(k))||[]}catch(x){}e._ts=new Date().toISOString();a.unshift(e);if(a.length>10)a=a.slice(0,10);try{localStorage.setItem(k,JSON.stringify(a))}catch(x){}}\nfunction rF(){try{katex.render('T=\\\\frac{F\\\\cdot l}{2\\\\pi\\\\eta}',$('vc-katex-1'),{displayMode:true,throwOnError:false});katex.render('N_{crit}=\\\\frac{\\\\lambda\\\\cdot d}{L^2}\\\\times 2.71\\\\times10^7',$('vc-katex-2'),{displayMode:true,throwOnError:false});katex.render('L_{10}=\\\\left(\\\\frac{C_a}{F}\\\\right)^3\\\\times 10^6\\\\;[\\\\text{rev}]',$('vc-katex-3'),{displayMode:true,throwOnError:false})}catch(e){}}\nrF();calc();\n})();\n<\/script>\n","protected":false},"excerpt":{"rendered":"<p>Calculateur de vis \u00e0 billes ISO 3408. Saisissez le pas, le diam\u00e8tre, la charge et la vitesse. Calculez le couple moteur, le rendement, la vitesse critique et la dur\u00e9e de vie.<\/p>","protected":false},"featured_media":0,"template":"","meta":{"ai_generated_summary":"","footnotes":""},"categories":[],"tags":[],"class_list":["post-100012","calculator","type-calculator","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/vibromera.eu\/fr\/wp-json\/wp\/v2\/calculator\/100012","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vibromera.eu\/fr\/wp-json\/wp\/v2\/calculator"}],"about":[{"href":"https:\/\/vibromera.eu\/fr\/wp-json\/wp\/v2\/types\/calculator"}],"version-history":[{"count":3,"href":"https:\/\/vibromera.eu\/fr\/wp-json\/wp\/v2\/calculator\/100012\/revisions"}],"predecessor-version":[{"id":102107,"href":"https:\/\/vibromera.eu\/fr\/wp-json\/wp\/v2\/calculator\/100012\/revisions\/102107"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/fr\/wp-json\/wp\/v2\/media?parent=100012"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/fr\/wp-json\/wp\/v2\/categories?post=100012"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/fr\/wp-json\/wp\/v2\/tags?post=100012"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}