{"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":"2026-02-15T20:05:57","modified_gmt":"2026-02-15T20:05:57","slug":"ball-screw-calculator","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/bn\/calculators\/ball-screw-calculator\/","title":{"rendered":"\u09ac\u09b2 \u09b8\u09cd\u0995\u09cd\u09b0\u09c1 \u0995\u09cd\u09af\u09be\u09b2\u0995\u09c1\u09b2\u09c7\u099f\u09b0 ISO 3408 | \u09ac\u09bf\u09a8\u09be\u09ae\u09c2\u09b2\u09cd\u09af\u09c7 \u09b8\u09b0\u099e\u09cd\u099c\u09be\u09ae #077"},"content":{"rendered":"\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Ball Screw Calculator\",\"description\":\"ISO 3408 ball screw calculator.\",\"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; ISO 3408<\/h1><p class=\"vc-header-subtitle\">ISO 3408 ball screw design. Enter lead, nominal diameter, axial load, and speed to calculate drive torque, efficiency, critical speed, and rated life.<\/p><div class=\"vc-badges\"><span class=\"vc-badge\">ISO 3408<\/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>ISO 3408 \u09ac\u09b2 \u09b8\u09cd\u0995\u09cd\u09b0\u09c1 \u0995\u09cd\u09af\u09be\u09b2\u0995\u09c1\u09b2\u09c7\u099f\u09b0\u0964 \u09b2\u09bf\u09a1, \u09ac\u09cd\u09af\u09be\u09b8, \u09b2\u09cb\u09a1, \u0997\u09a4\u09bf \u09aa\u09cd\u09b0\u09ac\u09c7\u09b6 \u0995\u09b0\u09c1\u09a8\u0964 \u09a1\u09cd\u09b0\u09be\u0987\u09ad \u099f\u09b0\u09cd\u0995, \u09a6\u0995\u09cd\u09b7\u09a4\u09be, \u09b8\u09ae\u09be\u09b2\u09cb\u099a\u09a8\u09be\u09ae\u09c2\u09b2\u0995 \u0997\u09a4\u09bf \u098f\u09ac\u0982 \u099c\u09c0\u09ac\u09a8 \u0997\u09a3\u09a8\u09be \u0995\u09b0\u09c1\u09a8\u0964<\/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\/bn\/wp-json\/wp\/v2\/calculator\/100012","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/calculator"}],"about":[{"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/types\/calculator"}],"version-history":[{"count":1,"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/calculator\/100012\/revisions"}],"predecessor-version":[{"id":100325,"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/calculator\/100012\/revisions\/100325"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/media?parent=100012"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/categories?post=100012"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/tags?post=100012"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}