{"id":100241,"date":"2026-02-15T20:29:15","date_gmt":"2026-02-15T20:29:15","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100241"},"modified":"2026-07-15T15:11:51","modified_gmt":"2026-07-15T15:11:51","slug":"spur-gear-calculator","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/az\/calculators\/spur-gear-calculator\/","title":{"rendered":"Spur-Gear Reference Geometry and Load Relation Worksheet"},"content":{"rendered":"<div class=\"vbm241\">\n<style>\n.vbm241{--ink:#172235;--muted:#556276;--line:#d8e0e9;--soft:#f4f7fa;--blue:#135ca8;--blue2:#0d447e;--amber:#8a5700;--amber-bg:#fff7df;--red:#a52828;--red-bg:#fff0f0;--green:#17613a;--green-bg:#edf9f1;max-width:1040px;margin:0 auto;padding:18px 14px 44px;color:var(--ink);font:15px\/1.55 system-ui,-apple-system,\"Segoe UI\",sans-serif}.vbm241 *{box-sizing:border-box}.vbm241 h1,.vbm241 h2,.vbm241 h3{line-height:1.2}.vbm241 h1{font-size:clamp(27px,4vw,42px);margin:8px 0 12px}.vbm241 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17px;font:inherit;font-weight:760;cursor:pointer}.vbm241-primary{background:var(--blue);color:#fff}.vbm241-primary:hover{background:var(--blue2)}.vbm241-secondary{background:#e8eef5;color:var(--ink)}.vbm241-error{display:none;margin-top:14px;padding:11px 13px;border:1px solid #edb5b5;border-radius:8px;background:var(--red-bg);color:var(--red);font-weight:650}.vbm241-error.show{display:block}.vbm241-results{display:none}.vbm241-results.show{display:block}.vbm241-result-grid{display:grid;grid-template-columns:repeat(2,minmax(0,1fr));gap:12px}.vbm241-result{border:1px solid var(--line);border-radius:10px;background:var(--soft);padding:13px}.vbm241-result.primary{border-color:#7dacda;background:#eef6ff}.vbm241-result-label{color:var(--muted);font-size:12px;font-weight:700;text-transform:uppercase;letter-spacing:.06em}.vbm241-result-value{font:700 17px\/1.35 ui-monospace,SFMono-Regular,Consolas,monospace;overflow-wrap:anywhere;margin-top:4px}.vbm241-result.primary .vbm241-result-value{font-size:22px;color:var(--blue2)}.vbm241-status{margin-top:14px;border-left:4px solid var(--green);background:var(--green-bg);padding:12px 14px}.vbm241-formula{overflow-x:auto;border:1px solid var(--line);border-radius:9px;background:var(--soft);padding:12px 14px;margin:10px 0;font:600 14px\/1.7 ui-monospace,SFMono-Regular,Consolas,monospace}.vbm241 table{width:100%;border-collapse:collapse;margin:12px 0}.vbm241 th,.vbm241 td{border:1px solid var(--line);padding:9px 10px;text-align:left;vertical-align:top}.vbm241 th{background:#eaf0f6}.vbm241 ul{padding-left:22px}.vbm241 details{border-top:1px solid var(--line);padding:11px 0}.vbm241 summary{cursor:pointer;font-weight:760}.vbm241-small{font-size:13px;color:var(--muted)}.vbm241 .vbm241-result-grid{grid-template-columns:1fr 1fr!important}\n@media(max-width:700px){.vbm241{padding-left:10px;padding-right:10px}.vbm241-card{padding:16px}.vbm241-grid,.vbm241 .vbm241-result-grid{grid-template-columns:1fr!important}.vbm241-field.full{grid-column:auto}.vbm241 table{display:block;overflow-x:auto}}\n<\/style>\n<header class=\"vbm241-header\">\n<div class=\"vbm241-kicker\">external spur pair \u00b7 reference geometry \u00b7 no ISO rating<\/div>\n<h1>Spur-Gear Reference Geometry and Load Relation Worksheet<\/h1>\n<p class=\"vbm241-lead\">Calculate reference diameters, reference centre distance, ratio, angular speed, torque and tangential tooth load for one documented external spur-gear load case.<\/p>\n<div class=\"vbm241-badges\"><span class=\"vbm241-badge\">d = mz<\/span><span class=\"vbm241-badge\">P = T\u03c9<\/span><span class=\"vbm241-badge\">F\u209c = 2T\/d<\/span><\/div>\n<\/header>\n<div class=\"vbm241-notice\"><strong>Not an ISO 6336 stress or capacity calculator.<\/strong> No contact stress, tooth-root stress, material limit, safety factor, pitting life or acceptance decision is produced. ISO 6336 requires the applicable current parts, validated geometry, load spectrum, materials and many influence factors selected by an experienced gear designer.<\/div>\n<form id=\"vbm241-form\" class=\"vbm241-card\" novalidate>\n<h2>Documented inputs and traceability<\/h2>\n<div class=\"vbm241-grid\">\n<div class=\"vbm241-field\"><label for=\"vbm241-module\">Controlled module m (mm)<span class=\"vbm241-hint\">positive plain decimal; same transverse module for this spur pair<\/span><\/label><input id=\"vbm241-module\" type=\"text\" inputmode=\"decimal\" autocomplete=\"off\"><\/div>\n<div class=\"vbm241-field\"><label for=\"vbm241-z1\">Pinion tooth count z\u2081<span class=\"vbm241-hint\">positive integer; no interference conclusion is inferred<\/span><\/label><input id=\"vbm241-z1\" type=\"text\" inputmode=\"numeric\" autocomplete=\"off\"><\/div>\n<div class=\"vbm241-field\"><label for=\"vbm241-z2\">Gear tooth count z\u2082<span class=\"vbm241-hint\">positive integer; external mating gear<\/span><\/label><input id=\"vbm241-z2\" type=\"text\" inputmode=\"numeric\" autocomplete=\"off\"><\/div>\n<div class=\"vbm241-field\"><label for=\"vbm241-power\">Transmitted mechanical power P (kW)<span class=\"vbm241-hint\">non-negative value at the pinion for the same load case<\/span><\/label><input id=\"vbm241-power\" type=\"text\" inputmode=\"decimal\" autocomplete=\"off\"><\/div>\n<div class=\"vbm241-field\"><label for=\"vbm241-speed\">Pinion rotational speed n\u2081 (r\/min)<span class=\"vbm241-hint\">positive magnitude for the same load case<\/span><\/label><input id=\"vbm241-speed\" type=\"text\" inputmode=\"decimal\" autocomplete=\"off\"><\/div>\n<div class=\"vbm241-field\"><label for=\"vbm241-record\">Calculation \/ model record ID<\/label><input id=\"vbm241-record\" type=\"text\" autocomplete=\"off\"><\/div>\n<div class=\"vbm241-field\"><label for=\"vbm241-pair\">Gear-pair and drawing identifiers<\/label><input id=\"vbm241-pair\" type=\"text\" autocomplete=\"off\"><\/div>\n<div class=\"vbm241-field\"><label for=\"vbm241-module-source\">Module source, method and revision<\/label><input id=\"vbm241-module-source\" type=\"text\" autocomplete=\"off\"><\/div>\n<div class=\"vbm241-field\"><label for=\"vbm241-teeth-source\">Tooth-count source and drawing revision<\/label><input id=\"vbm241-teeth-source\" type=\"text\" autocomplete=\"off\"><\/div>\n<div class=\"vbm241-field\"><label for=\"vbm241-arrangement\">Axis arrangement and external-spur confirmation<\/label><input id=\"vbm241-arrangement\" type=\"text\" autocomplete=\"off\"><\/div>\n<div class=\"vbm241-field\"><label for=\"vbm241-geometry\">Basic rack, pressure angle and profile-shift record<\/label><input id=\"vbm241-geometry\" type=\"text\" autocomplete=\"off\"><\/div>\n<div class=\"vbm241-field\"><label for=\"vbm241-centre\">Operating centre distance, backlash and interference review<\/label><input id=\"vbm241-centre\" type=\"text\" autocomplete=\"off\"><\/div>\n<div class=\"vbm241-field\"><label for=\"vbm241-load\">Power basis, load spectrum, duty and service-factor record<\/label><input id=\"vbm241-load\" type=\"text\" autocomplete=\"off\"><\/div>\n<div class=\"vbm241-field\"><label for=\"vbm241-speed-source\">Speed source, direction and transient record<\/label><input id=\"vbm241-speed-source\" type=\"text\" autocomplete=\"off\"><\/div>\n<div class=\"vbm241-field\"><label for=\"vbm241-manufacturing\">Materials, heat treatment, quality and manufacturing record<\/label><input id=\"vbm241-manufacturing\" type=\"text\" autocomplete=\"off\"><\/div>\n<div class=\"vbm241-field\"><label for=\"vbm241-lubrication\">Lubrication, temperature, roughness and contact-pattern record<\/label><input id=\"vbm241-lubrication\" type=\"text\" autocomplete=\"off\"><\/div>\n<div class=\"vbm241-field\"><label for=\"vbm241-rating\">Licensed ISO 6336 parts, factors and rating record<\/label><input id=\"vbm241-rating\" type=\"text\" autocomplete=\"off\"><\/div>\n<div class=\"vbm241-field\"><label for=\"vbm241-person\">Responsible gear engineer \/ reviewer<\/label><input id=\"vbm241-person\" type=\"text\" autocomplete=\"off\"><\/div>\n<div class=\"vbm241-field\"><label for=\"vbm241-date\">Review date<\/label><input id=\"vbm241-date\" type=\"text\" inputmode=\"numeric\" placeholder=\"YYYY-MM-DD\" autocomplete=\"off\"><\/div>\n<div class=\"vbm241-field full\"><label for=\"vbm241-notes\">Notes and exclusions<span class=\"vbm241-hint\">Optional: losses, measurement uncertainty, profile modifications, overloads and omitted failure modes.<\/span><\/label><textarea id=\"vbm241-notes\"><\/textarea><\/div>\n<\/div>\n<div class=\"vbm241-checks\">\n <label class=\"vbm241-check\"><input id=\"vbm241-c1\" type=\"checkbox\"><span>The pair is documented as parallel-axis external spur gears using the same controlled module; the entered tooth counts and module come from the cited drawings.<\/span><\/label><br \/>\n <label class=\"vbm241-check\"><input id=\"vbm241-c2\" type=\"checkbox\"><span>P and n\u2081 describe the same pinion load case; P is transmitted mechanical power at that shaft and no efficiency, overload, application or dynamic factor is added automatically.<\/span><\/label><br \/>\n <label class=\"vbm241-check\"><input id=\"vbm241-c3\" type=\"checkbox\"><span>a\u2080 is only the zero-shift reference-centre relation. Operating centre distance, profile shift, pressure angle, backlash, contact ratio, interference and contact pattern were reviewed separately.<\/span><\/label><br \/>\n <label class=\"vbm241-check\"><input id=\"vbm241-c4\" type=\"checkbox\"><span>No ISO 6336 stress, capacity, life, safety factor or acceptance verdict will be inferred from these reference and load relations.<\/span><\/label>\n<\/div>\n<div class=\"vbm241-actions\"><button class=\"vbm241-primary\" type=\"submit\">Calculate documented relations<\/button><button class=\"vbm241-secondary\" id=\"vbm241-clear\" type=\"button\">Clear<\/button><\/div>\n<div id=\"vbm241-error\" class=\"vbm241-error\" role=\"alert\"><\/div>\n<\/form>\n<section id=\"vbm241-results\" class=\"vbm241-card vbm241-results\" aria-live=\"polite\">\n<h2>Reference and load quantities<\/h2>\n<div class=\"vbm241-result-grid\">\n<div class=\"vbm241-result primary\">\n<div class=\"vbm241-result-label\">Reference diameters d\u2081 \/ d\u2082<\/div>\n<div class=\"vbm241-result-value\" id=\"vbm241-r-diameters\">\u2014<\/div>\n<\/div>\n<div class=\"vbm241-result\">\n<div class=\"vbm241-result-label\">Reference centre distance a\u2080<\/div>\n<div class=\"vbm241-result-value\" id=\"vbm241-r-centre\">\u2014<\/div>\n<\/div>\n<div class=\"vbm241-result\">\n<div class=\"vbm241-result-label\">Tooth-count ratio u = z\u2082\/z\u2081<\/div>\n<div class=\"vbm241-result-value\" id=\"vbm241-r-ratio\">\u2014<\/div>\n<\/div>\n<div class=\"vbm241-result\">\n<div class=\"vbm241-result-label\">Pinion angular speed \u03c9\u2081<\/div>\n<div class=\"vbm241-result-value\" id=\"vbm241-r-omega\">\u2014<\/div>\n<\/div>\n<div class=\"vbm241-result\">\n<div class=\"vbm241-result-label\">Transmitted pinion torque T\u2081<\/div>\n<div class=\"vbm241-result-value\" id=\"vbm241-r-torque\">\u2014<\/div>\n<\/div>\n<div class=\"vbm241-result\">\n<div class=\"vbm241-result-label\">Nominal tangential tooth load F\u209c<\/div>\n<div class=\"vbm241-result-value\" id=\"vbm241-r-force\">\u2014<\/div>\n<\/div>\n<\/div>\n<div class=\"vbm241-status\" id=\"vbm241-r-status\"><\/div>\n<\/section>\n<section class=\"vbm241-card\">\n<h2>Formula, units and classification<\/h2>\n<div class=\"vbm241-formula\">d\u2081 = m z\u2081; d\u2082 = m z\u2082 &nbsp; [mm]<br \/>a\u2080 = (d\u2081 + d\u2082)\/2 &nbsp; [mm], reference-centre relation only<br \/>u = z\u2082\/z\u2081 &nbsp; [1]<br \/>\u03c9\u2081 = 2\u03c0n\u2081\/60 &nbsp; [rad\/s]<br \/>T\u2081 = 1000P\/\u03c9\u2081 &nbsp; [N\u00b7m], P in kW<br \/>F\u209c = 2000T\u2081\/d\u2081 &nbsp; [N], d\u2081 in mm<\/div>\n<table>\n<thead>\n<tr>\n<th>Symbol<\/th>\n<th>Quantity and unit<\/th>\n<th>Boundary<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>m,z\u2081,z\u2082<\/td>\n<td>controlled module in mm and integer tooth counts<\/td>\n<td>not proof of standard module, compatibility, undercut or manufacturability<\/td>\n<\/tr>\n<tr>\n<td>d\u2081,d\u2082<\/td>\n<td>reference diameters, mm<\/td>\n<td>not necessarily operating pitch or tip\/root diameters<\/td>\n<\/tr>\n<tr>\n<td>a\u2080<\/td>\n<td>half-sum reference-centre relation, mm<\/td>\n<td>not the approved operating centre distance when modifications apply<\/td>\n<\/tr>\n<tr>\n<td>P,n\u2081<\/td>\n<td>transmitted mechanical power, kW; pinion speed, r\/min<\/td>\n<td>same documented load case; no efficiency or service factor added<\/td>\n<\/tr>\n<tr>\n<td>T\u2081,F\u209c<\/td>\n<td>torque, N\u00b7m; nominal tangential load, N<\/td>\n<td>not design tooth load, stress, capacity, bearing reaction or acceptance result<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p class=\"vbm241-small\">These are general geometry and mechanics relations, not ISO 6336 rating formulae. Exact ISO geometry, preferred module values, stress factors, permissible stresses and rating procedures require the applicable licensed current documents.<\/p>\n<\/section>\n<section class=\"vbm241-card\">\n<h2>Removed unsafe rating claims<\/h2>\n<ul>\n<li><strong>No invented ISO contact stress.<\/strong> The former code fixed Z<sub>E<\/sub>=190 and Z<sub>H<\/sub>=2.5, omitted the required geometry, material, load-distribution, dynamic and application factors, then called the result simplified ISO 6336.<\/li>\n<li><strong>No invented ISO tooth-root stress.<\/strong> A universal Y<sub>F<\/sub>=2.5 cannot represent tooth form, stress correction, contact ratio, helix\/load-distribution and other required terms.<\/li>\n<li><strong>No generic material limits or colour verdict.<\/strong> Hardness labels alone do not establish permissible pitting or bending stress; heat treatment, material quality, size, life, reliability and stress-cycle factors matter.<\/li>\n<li><strong>No tip diameter without a controlled tooth system.<\/strong> d<sub>a<\/sub>=d+2m applies to a stated standard unshifted geometry, not every spur gear.<\/li>\n<li><strong>No truncated torque constant.<\/strong> The worksheet uses P=T\u03c9 and \u03c9=2\u03c0n\/60 directly rather than the rounded shortcut 9549P\/n.<\/li>\n<li><strong>No hidden state.<\/strong> Defaults, presets, auto-calculation, clipboard output, generated FAQ HTML and external KaTeX were removed.<\/li>\n<\/ul>\n<\/section>\n<section class=\"vbm241-card\">\n<h2>Source traceability<\/h2>\n<table>\n<thead>\n<tr>\n<th>Claim<\/th>\n<th>Classification<\/th>\n<th>Evidence<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>ISO 6336-1:2019 Edition 3 is current and confirmed in 2025; its public scope says the method is for experienced gear designers and does not assure an assembled drive.<\/td>\n<td>Official ISO status and scope<\/td>\n<td><a href=\"https:\/\/www.iso.org\/standard\/63819.html\" target=\"_blank\" rel=\"noopener\">ISO 6336-1:2019<\/a><\/td>\n<\/tr>\n<tr>\n<td>ISO 6336-2:2019 Edition 3, corrected 2020-11, addresses surface durability and includes the influences that can be assessed quantitatively.<\/td>\n<td>Official ISO status and scope<\/td>\n<td><a href=\"https:\/\/www.iso.org\/standard\/63821.html\" target=\"_blank\" rel=\"noopener\">ISO 6336-2:2019<\/a><\/td>\n<\/tr>\n<tr>\n<td>ISO 6336-3:2019 Edition 3, corrected 2020-11, specifies tooth-bending-strength calculation.<\/td>\n<td>Official ISO status and scope<\/td>\n<td><a href=\"https:\/\/www.iso.org\/standard\/63822.html\" target=\"_blank\" rel=\"noopener\">ISO 6336-3:2019<\/a><\/td>\n<\/tr>\n<tr>\n<td>ISO 21771-1:2024 covers cylindrical involute-gear concepts and geometry; it is published but marked to be revised and has a replacement draft in development.<\/td>\n<td>Official ISO status and scope<\/td>\n<td><a href=\"https:\/\/www.iso.org\/standard\/84949.html\" target=\"_blank\" rel=\"noopener\">ISO 21771-1:2024<\/a><\/td>\n<\/tr>\n<tr>\n<td>ISO 54:1996 Edition 2 specifies normal-module values and remains current after confirmation in 2022; this worksheet does not certify an entered value as a preferred ISO module.<\/td>\n<td>Official ISO status and boundary<\/td>\n<td><a href=\"https:\/\/www.iso.org\/standard\/22644.html\" target=\"_blank\" rel=\"noopener\">ISO 54:1996<\/a><\/td>\n<\/tr>\n<tr>\n<td>For a documented standard external spur pair, KHK Table 4.1 gives d=zm and distinguishes standard from profile-shifted geometry.<\/td>\n<td>Manufacturer technical reference<\/td>\n<td><a href=\"https:\/\/khkgears.net\/gear-knowledge\/gear-technical-reference\/calculation-gear-dimensions\/\" target=\"_blank\" rel=\"noopener\">KHK gear dimensions<\/a><\/td>\n<\/tr>\n<tr>\n<td>Rotational mechanical power is P=T\u03c9.<\/td>\n<td>MIT engineering tutorial<\/td>\n<td><a href=\"http:\/\/lancet.mit.edu\/motor\/motors3.html\" target=\"_blank\" rel=\"noopener\">MIT motor torque\/speed tutorial<\/a><\/td>\n<\/tr>\n<tr>\n<td>Tangential tooth load is F\u209c=T\/r=2T\/D at the pitch\/reference radius.<\/td>\n<td>University mechanical-engineering material; page visually inspected<\/td>\n<td><a href=\"https:\/\/www.faculty.fairfield.edu\/wdornfeld\/ME312\/ToothLoads04.pdf\" target=\"_blank\" rel=\"noopener\">Fairfield ME312 Tooth Loads, p. 2<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p class=\"vbm241-small\">Accessed: 15 July 2026. No ISO clause\/table-level stress implementation is claimed. Exact geometry and rating details remain <strong>NEEDS_LICENSED_SOURCE<\/strong>.<\/p>\n<\/section>\n<section class=\"vbm241-card\">\n<h2>Reference check<\/h2>\n<p>For m=3 mm, z\u2081=20, z\u2082=80, P=15 kW and n\u2081=1500 r\/min: d\u2081=60 mm, d\u2082=240 mm, a\u2080=150 mm, u=4, \u03c9\u2081=157.079632679 rad\/s, T\u2081=95.4929658551 N\u00b7m and F\u209c=3183.09886184 N.<\/p>\n<\/section>\n<section class=\"vbm241-card\">\n<h2>Questions<\/h2>\n<details>\n<summary>Does this prove ISO 6336 capacity?<\/summary>\n<p>No. The worksheet deliberately produces no contact\/root stress, permissible stress, safety factor, life or acceptance result.<\/p>\n<\/details>\n<details>\n<summary>Is a\u2080 the mounting centre distance?<\/summary>\n<p>Only for the documented zero-shift reference case when the relevant geometry conditions are satisfied. Use the controlled drawing and full geometry calculation for the operating distance.<\/p>\n<\/details>\n<details>\n<summary>Why is face width absent?<\/summary>\n<p>Face width is needed for stress rating, which this worksheet does not perform. Including it would suggest a capacity conclusion that the available inputs cannot support.<\/p>\n<\/details>\n<\/section>\n<p><script>\n(function(){'use strict';var form=document.getElementById('vbm241-form'),error=document.getElementById('vbm241-error'),results=document.getElementById('vbm241-results');\nfunction text(id){return document.getElementById(id).value.trim()}function requiredText(id,label){var v=text(id);if(!v)throw new Error(label+' is required.');return v}function decimal(id,label,allowZero){var raw=text(id);if(!\/^(?:\\d+(?:[.,]\\d*)?|[.,]\\d+)$\/.test(raw))throw new Error(label+' must be one '+(allowZero?'non-negative':'positive')+' plain decimal using a point or comma.');var v=Number(raw.replace(',','.'));if(!Number.isFinite(v)||(allowZero?v<0:v<=0))throw new Error(label+' must be finite and '+(allowZero?'non-negative.':'greater than zero.'));return v}function integer(id,label){var raw=text(id);if(!\/^\\d+$\/.test(raw))throw new Error(label+' must be one positive integer.');var v=Number(raw);if(!Number.isSafeInteger(v)||v<=0)throw new Error(label+' must be a positive safe integer.');return v}function fmt(v){if(!Number.isFinite(v))throw new Error('The calculated result is outside the finite numeric range.');return Number(v.toPrecision(12)).toString()}function setText(id,value){document.getElementById(id).textContent=value}\nfunction compute(m,z1,z2,power,speed){var d1=m*z1,d2=m*z2,a0=(d1+d2)\/2,ratio=z2\/z1,omega=2*Math.PI*speed\/60,torque=power*1000\/omega,force=2000*torque\/d1;[d1,d2,a0,ratio,omega,torque,force].forEach(function(v){if(!Number.isFinite(v))throw new Error('The calculated result is outside the finite numeric range.')});return{d1:d1,d2:d2,a0:a0,ratio:ratio,omega:omega,torque:torque,force:force}}\nfunction render(r){setText('vbm241-r-diameters',fmt(r.d1)+' \/ '+fmt(r.d2)+' mm');setText('vbm241-r-centre',fmt(r.a0)+' mm');setText('vbm241-r-ratio',fmt(r.ratio));setText('vbm241-r-omega',fmt(r.omega)+' rad\/s');setText('vbm241-r-torque',fmt(r.torque)+' N\u00b7m');setText('vbm241-r-force',fmt(r.force)+' N');setText('vbm241-r-status','Reference geometry and nominal load relations only. No contact stress, tooth-root stress, material limit, ISO 6336 rating, safety factor, life or acceptance verdict has been generated. 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