{"id":100261,"date":"2026-02-15T20:30:23","date_gmt":"2026-02-15T20:30:23","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100261"},"modified":"2026-07-15T20:47:42","modified_gmt":"2026-07-15T20:47:42","slug":"timing-belt-calculator","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/az\/calculators\/timing-belt-calculator\/","title":{"rendered":"Controlled Synchronous-Belt Geometry Calculator"},"content":{"rendered":"<div id=\"sb-tool\" class=\"sb-shell\">\n<style>\n    #sb-tool{--ink:#172535;--muted:#52657a;--line:#d5e0e8;--soft:#f3f7fa;--accent:#73551a;--accent2:#513b10;--warn:#fff1de;--ok:#136c42;font:16px\/1.55 system-ui,-apple-system,\"Segoe UI\",sans-serif;color:var(--ink);max-width:1180px;margin:0 auto;background:#fff}\n    #sb-tool *{box-sizing:border-box}#sb-tool .sb-hero{text-align:center;padding:52px 24px 42px}#sb-tool .sb-kicker{margin:0 0 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@media(max-width:700px){#sb-tool .sb-hero{padding:38px 18px 32px}#sb-tool .sb-sub{font-size:16px}#sb-tool .sb-card{padding:20px;margin-left:0;margin-right:0}#sb-tool .sb-grid,#sb-tool .sb-results{grid-template-columns:1fr}#sb-tool .sb-wide{grid-column:auto}}@media(max-width:430px){#sb-tool h1{font-size:31px}#sb-tool .sb-actions button{width:100%}}\n  <\/style>\n<header class=\"sb-hero\">\n<p class=\"sb-kicker\">Pitch-line geometry, not belt selection<\/p>\n<h1>Controlled Synchronous-Belt Geometry Calculator<\/h1>\n<p class=\"sb-sub\">Calculate the ideal open-drive pitch path from a documented center distance, or solve center distance for an entered integer belt tooth count. No catalogue size, tooth profile, power capacity or tension is selected.<\/p>\n<div class=\"sb-badges\"><span class=\"sb-badge\">Exact ideal geometry<\/span><span class=\"sb-badge\">No forced even count<\/span><span class=\"sb-badge\">No profile substitution<\/span><span class=\"sb-badge\">No power rating<\/span><\/div>\n<\/header>\n<section class=\"sb-card\" aria-labelledby=\"sb-calc-title\">\n<h2 id=\"sb-calc-title\">Controlled two-pulley calculation<\/h2>\n<div class=\"sb-warning\"><strong>Do not order or rate a drive from this result.<\/strong> Confirm an actual belt and matching pulleys in the current manufacturer catalogue and design method. Width, tooth profile, minimum pulley, teeth in mesh, speed, service factor, transmitted power, tension, tolerances, installation travel, alignment, environment and safety requirements remain outside this geometry model.<\/div>\n<form id=\"sb-form\" novalidate autocomplete=\"off\">\n<div class=\"sb-grid\">\n        <label class=\"sb-wide\" for=\"sb-mode\">Calculation mode<span class=\"sb-help\">The unused input becomes blank and read-only<\/span><select id=\"sb-mode\"><option value=\"\" selected disabled>Select one mode<\/option><option value=\"path\">Pitch path from center distance<\/option><option value=\"center\">Center distance from an entered belt tooth count<\/option><\/select><\/label><br \/>\n        <label for=\"sb-pitch\">Documented tooth pitch p (mm)<span class=\"sb-help\">Positive plain decimal from the controlled belt\/pulley family<\/span><input id=\"sb-pitch\" type=\"text\" inputmode=\"decimal\" maxlength=\"64\"><\/label><br \/>\n        <label for=\"sb-z1\">Pulley 1 tooth count z\u2081<span class=\"sb-help\">Whole number; computational minimum 2 is not a design recommendation<\/span><input id=\"sb-z1\" type=\"text\" inputmode=\"numeric\" maxlength=\"32\"><\/label><br \/>\n        <label for=\"sb-z2\">Pulley 2 tooth count z\u2082<span class=\"sb-help\">Whole number from the documented compatible pulley<\/span><input id=\"sb-z2\" type=\"text\" inputmode=\"numeric\" maxlength=\"32\"><\/label><br \/>\n        <label for=\"sb-center\">Center distance C (mm)<span class=\"sb-help\">Used in pitch-path mode; must keep the ideal pitch circles separate<\/span><input id=\"sb-center\" type=\"text\" inputmode=\"decimal\" maxlength=\"64\"><\/label><br \/>\n        <label for=\"sb-belt-teeth\">Entered belt tooth count N<span class=\"sb-help\">Used in center mode; must be an actual candidate from a controlled catalogue or record<\/span><input id=\"sb-belt-teeth\" type=\"text\" inputmode=\"numeric\" maxlength=\"32\"><\/label><br \/>\n        <label class=\"sb-wide\" for=\"sb-source\">Belt, pulley and source record<span class=\"sb-help\">Record manufacturer, family\/profile, part or catalogue revision, pitch and pulley designations<\/span><textarea id=\"sb-source\" maxlength=\"500\"><\/textarea><\/label><br \/>\n        <label class=\"sb-check sb-wide\" for=\"sb-confirm-family\"><input id=\"sb-confirm-family\" type=\"checkbox\"><span>I confirm that the pitch and both pulley tooth counts belong to one documented, mutually compatible belt\/pulley family; matching pitch alone does not prove profile compatibility.<\/span><\/label><br \/>\n        <label class=\"sb-check sb-wide\" for=\"sb-confirm-boundary\"><input id=\"sb-confirm-boundary\" type=\"checkbox\"><span>I understand that adjacent integer tooth counts are arithmetic only, not stock sizes, and that this result does not verify power capacity, tension, installation or safety.<\/span><\/label>\n      <\/div>\n<div class=\"sb-actions\"><button class=\"sb-primary\" type=\"submit\">Calculate documented geometry<\/button><button class=\"sb-clear\" id=\"sb-clear\" type=\"reset\">Clear<\/button><\/div>\n<div class=\"sb-status\" id=\"sb-status\" role=\"status\" aria-live=\"polite\"><\/div>\n<div class=\"sb-output\" id=\"sb-result\" data-visible=\"false\" aria-live=\"polite\">\n<h3>Ideal pitch-line result<\/h3>\n<div class=\"sb-results\">\n<div class=\"sb-result\">\n<div class=\"sb-rlabel\">Calculation<\/div>\n<div class=\"sb-rvalue\" id=\"sb-r-mode\">\u2014<\/div>\n<\/div>\n<div class=\"sb-result\">\n<div class=\"sb-rlabel\">Pitch and pulley teeth<\/div>\n<div class=\"sb-rvalue\" id=\"sb-r-pitch\">\u2014<\/div>\n<\/div>\n<div class=\"sb-result\">\n<div class=\"sb-rlabel\">Center distance<\/div>\n<div class=\"sb-rvalue\" id=\"sb-r-center\">\u2014<\/div>\n<\/div>\n<div class=\"sb-result\">\n<div class=\"sb-rlabel\">Pitch-path length and count<\/div>\n<div class=\"sb-rvalue\" id=\"sb-r-path\">\u2014<\/div>\n<\/div>\n<div class=\"sb-result\">\n<div class=\"sb-rlabel\">Pitch diameters<\/div>\n<div class=\"sb-rvalue\" id=\"sb-r-diameters\">\u2014<\/div>\n<\/div>\n<div class=\"sb-result\">\n<div class=\"sb-rlabel\">Ideal wrap angles<\/div>\n<div class=\"sb-rvalue\" id=\"sb-r-wrap\">\u2014<\/div>\n<\/div>\n<div class=\"sb-result\">\n<div class=\"sb-rlabel\">Tooth and speed ratios<\/div>\n<div class=\"sb-rvalue\" id=\"sb-r-ratio\">\u2014<\/div>\n<\/div>\n<div class=\"sb-result\">\n<div class=\"sb-rlabel\">Integer-pitch information<\/div>\n<div class=\"sb-rvalue\" id=\"sb-r-integers\">\u2014<\/div>\n<\/div><\/div>\n<div class=\"sb-note\" id=\"sb-r-note\"><\/div>\n<div class=\"sb-record\" id=\"sb-r-record\"><\/div>\n<\/p><\/div>\n<\/p><\/form>\n<\/section>\n<section class=\"sb-card\" aria-labelledby=\"sb-model-title\">\n<h2 id=\"sb-model-title\">Ideal open-drive pitch-line geometry<\/h2>\n<div class=\"sb-formula\">r\u1d62 = z\u1d62 \u00d7 p \/ (2\u03c0)<br \/>\u03b4 = |r\u2082 \u2212 r\u2081| &nbsp;; \u03b1 = asin(\u03b4 \/ C)<br \/>s = \u221a(C\u00b2 \u2212 \u03b4\u00b2)<br \/>L = 2s + r<sub>small<\/sub>(\u03c0 \u2212 2\u03b1) + r<sub>large<\/sub>(\u03c0 + 2\u03b1)<br \/>N<sub>required<\/sub> = L \/ p<\/div>\n<p>This is the exact planar geometry of two circular pitch lines joined by straight external tangents. It is not the common truncated approximation 2C + \u03c0(D\u2081+D\u2082)\/2 + (D\u2082\u2212D\u2081)\u00b2\/(4C). Center mode solves the same exact ideal geometry by bisection until the entered integer pitch length N\u00b7p is met.<\/p>\n<p class=\"sb-small\">Real pulley outside diameters, tooth geometry, belt neutral axis, manufacturing tolerances and installation tension are product-specific. The computational non-overlap condition C &gt; r\u2081+r\u2082 is conservative pitch-circle geometry, not a manufacturer clearance requirement.<\/p>\n<\/section>\n<section class=\"sb-card\" aria-labelledby=\"sb-boundary-title\">\n<h2 id=\"sb-boundary-title\">Standards and catalogue boundary<\/h2>\n<ul class=\"sb-list\">\n<li>ISO 13050:2022, Edition 3 covers specified metric curvilinear profile systems and includes pitch spacing, length, pulley geometry and tolerances. A common numerical pitch does not make proprietary or ISO profiles interchangeable.<\/li>\n<li>ISO 5295:2023, Edition 4 establishes power-rating and centre-distance formulae for <strong>trapezoidal belts only<\/strong> and explicitly does not apply to curvilinear synchronous belts. This page does not use it to rate HTD or GT products.<\/li>\n<li>The official Gates PowerGrip GT3 manual says exact center distance is found by convergence between center-distance and belt-length equations, and that synchronous-belt pitch length increments are multiples of pitch. It requires catalogue and power-rating steps beyond geometry.<\/li>\n<li>There is no universal even-tooth rule. An official Gates GT3 product record lists a 105 mm, 3 mm-pitch belt with 35 teeth; current catalogue availability must be checked by exact family and part.<\/li>\n<\/ul>\n<\/section>\n<section class=\"sb-card\" aria-labelledby=\"sb-evidence-title\">\n<h2 id=\"sb-evidence-title\">Official evidence<\/h2>\n<div class=\"sb-source\"><a href=\"https:\/\/www.gates.com\/content\/dam\/documents-library\/catalogs\/powergrip-gt3-drive-design-manual-en.pdf\" target=\"_blank\" rel=\"noopener\">Gates PowerGrip GT3 Drive Design Manual<\/a><\/p>\n<p>Official design procedure, stock tables, exact center-distance iteration, pitch-length increments, profile distinctions, tolerances and installation considerations.<\/p>\n<\/div>\n<div class=\"sb-source\"><a href=\"https:\/\/www.gates.com\/es\/es\/power-transmission\/synchronous-belts\/rubber-synchronous-belts.p.9356-000000-000000.v.9400-43175.html\" target=\"_blank\" rel=\"noopener\">Gates GT3 105-3MGT product record<\/a><\/p>\n<p>Official example with 105 mm pitch length, 3 mm pitch and 35 teeth, directly disproving automatic even-tooth rounding.<\/p>\n<\/div>\n<div class=\"sb-source\"><a href=\"https:\/\/www.iso.org\/standard\/82453.html\" target=\"_blank\" rel=\"noopener\">ISO 13050:2022, Edition 3<\/a><\/p>\n<p>Official current-status and scope page for specified metric curvilinear synchronous belt and pulley systems.<\/p>\n<\/div>\n<div class=\"sb-source\"><a href=\"https:\/\/www.iso.org\/standard\/86235.html\" target=\"_blank\" rel=\"noopener\">ISO 5295:2023, Edition 4<\/a><\/p>\n<p>Official scope page: power rating and centre distance for trapezoidal belts only, not curvilinear belts.<\/p>\n<\/div>\n<\/section>\n<footer class=\"sb-footer\">Vibromera controlled pitch-line geometry \u00b7 No catalogue, rating or safety decision<\/footer>\n<p>  <script>\n  (function(){'use strict';\n    var form=document.getElementById('sb-form'),result=document.getElementById('sb-result'),status=document.getElementById('sb-status');\n    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value=Number(s);if(!Number.isSafeInteger(value)||value<2||value>1000000)throw new Error(label.charAt(0).toUpperCase()+label.slice(1)+' must be a whole number from 2 to 1,000,000.');return value}\n    function record(raw){var s=String(raw).trim();if(s.length<3||s.length>500||\/[\\u0000-\\u0008\\u000B\\u000C\\u000E-\\u001F\\u007F]\/.test(s))throw new Error('Describe the belt, pulleys and source record in 3\u2013500 printable characters.');return s}\n    function fmt(value){if(Math.abs(value)<1e-14)return'0';return Number(value.toPrecision(12)).toString()}\n    function geometry(r1,r2,C){var small=Math.min(r1,r2),large=Math.max(r1,r2),delta=large-small;if(!Number.isFinite(C)||C<=delta)throw new Error('Center distance does not support two external tangent spans.');var alpha=Math.asin(delta\/C),span=Math.sqrt((C-delta)*(C+delta)),length=2*span+small*(Math.PI-2*alpha)+large*(Math.PI+2*alpha),wSmall=Math.PI-2*alpha,wLarge=Math.PI+2*alpha;return{length:length,alpha:alpha,span:span,w1:r1<=r2?wSmall:wLarge,w2:r1<=r2?wLarge:wSmall}}\n    function solveCenter(r1,r2,target){var lo=(r1+r2)*(1+1e-12),min=geometry(r1,r2,lo).length;if(target<=min*(1+1e-13))throw new Error('The entered belt pitch length is too short for the supported non-overlapping pitch-circle geometry.');var hi=Math.max(lo*2,target\/2+r1+r2),n=0;while(geometry(r1,r2,hi).length<target&&n<200){hi*=2;n++}if(n>=200||!Number.isFinite(hi)||hi>1000000000)throw new Error('No finite center-distance solution was found in the supported range.');for(n=0;n<200;n++){var mid=(lo+hi)\/2;if(geometry(r1,r2,mid).length<target)lo=mid;else hi=mid}return(lo+hi)\/2}\n    function applyMode(){var mode=byId('sb-mode').value,center=byId('sb-center'),teeth=byId('sb-belt-teeth');center.readOnly=mode==='center';teeth.readOnly=mode==='path';if(center.readOnly)center.value='';if(teeth.readOnly)teeth.value='';status.textContent='';delete status.dataset.kind;clearResult()}\n    byId('sb-mode').addEventListener('change',applyMode);\n    form.addEventListener('submit',function(event){event.preventDefault();try{var mode=byId('sb-mode').value;if(mode!=='path'&&mode!=='center')throw new Error('Select the calculation mode.');var pitch=plain(byId('sb-pitch').value,'documented tooth pitch'),z1=whole(byId('sb-z1').value,'pulley 1 tooth count'),z2=whole(byId('sb-z2').value,'pulley 2 tooth count'),source=record(byId('sb-source').value);if(pitch>1000)throw new Error('Documented tooth pitch is outside this calculator\u2019s supported finite range.');if(!byId('sb-confirm-family').checked)throw new Error('Confirm the documented compatible belt and pulley family.');if(!byId('sb-confirm-boundary').checked)throw new Error('Confirm the catalogue, rating and installation boundary.');var r1=z1*pitch\/(2*Math.PI),r2=z2*pitch\/(2*Math.PI),center,N,path,integerText;if(mode==='path'){center=plain(byId('sb-center').value,'center distance');if(center>1000000000)throw new Error('Center distance is outside this calculator\u2019s supported finite range.');if(center<=r1+r2)throw new Error('Center distance must exceed the sum of the two pitch radii in this supported geometry.');path=geometry(r1,r2,center);N=path.length\/pitch;var low=Math.floor(N),high=Math.ceil(N);integerText=low===high?low+' teeth ('+fmt(low*pitch)+' mm) \u2014 integral geometry only, catalogue unchecked':low+' \/ '+high+' teeth ('+fmt(low*pitch)+' \/ '+fmt(high*pitch)+' mm) \u2014 adjacent integers, catalogue unchecked'}else{N=whole(byId('sb-belt-teeth').value,'entered belt tooth count');center=solveCenter(r1,r2,N*pitch);path=geometry(r1,r2,center);integerText=N+' entered teeth = '+fmt(N*pitch)+' mm pitch length; catalogue identity still required'}if(!Number.isFinite(center)||!Number.isFinite(path.length)||!Number.isFinite(N)||center<=0||path.length<=0)throw new Error('The calculated geometry is not finite.');byId('sb-r-mode').textContent=mode==='path'?'Required ideal pitch path from documented center':'Ideal center from entered integer belt count';byId('sb-r-pitch').textContent='p = '+fmt(pitch)+' mm \u00b7 z\u2081\/z\u2082 = '+z1+'\/'+z2;byId('sb-r-center').textContent=fmt(center)+' mm';byId('sb-r-path').textContent=fmt(path.length)+' mm \u00b7 '+fmt(path.length\/pitch)+' pitches';byId('sb-r-diameters').textContent='d\u2081 = '+fmt(2*r1)+' mm \u00b7 d\u2082 = '+fmt(2*r2)+' mm';byId('sb-r-wrap').textContent='pulley 1 = '+fmt(path.w1*180\/Math.PI)+'\u00b0 \u00b7 pulley 2 = '+fmt(path.w2*180\/Math.PI)+'\u00b0';byId('sb-r-ratio').textContent='z\u2082\/z\u2081 = '+fmt(z2\/z1)+' \u00b7 n\u2082\/n\u2081 = 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