{"id":100236,"date":"2026-02-15T20:29:08","date_gmt":"2026-02-15T20:29:08","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100236"},"modified":"2026-07-15T14:38:20","modified_gmt":"2026-07-15T14:38:20","slug":"spline-connection-calculator","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/ro\/calculators\/spline-connection-calculator\/","title":{"rendered":"Nominal Involute-Spline Reference Geometry Worksheet"},"content":{"rendered":"<div class=\"vbm236\">\n<style>\n.vbm236{--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}.vbm236 *{box-sizing:border-box}.vbm236 h1,.vbm236 h2,.vbm236 h3{line-height:1.2}.vbm236 h1{font-size:clamp(27px,4vw,42px);margin:8px 0 12px}.vbm236 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table{display:block;overflow-x:auto}}\n<\/style>\n<header class=\"vbm236-header\">\n<p class=\"vbm236-kicker\">Nominal relations \u00b7 controlled inputs \u00b7 no strength verdict<\/p>\n<h1>Nominal Involute-Spline Reference Geometry Worksheet<\/h1>\n<p class=\"vbm236-lead\">Calculate three preliminary involute reference quantities from a documented metric module, integer tooth count and pressure angle.<\/p>\n<div class=\"vbm236-badges\"><span class=\"vbm236-badge\">d = mz<\/span><span class=\"vbm236-badge\">Point or comma<\/span><span class=\"vbm236-badge\">No design presets<\/span><\/div>\n<\/header>\n<div class=\"vbm236-notice\"><strong>Not a complete ISO 4156 spline calculator.<\/strong> This worksheet does not determine limiting diameters, tooth thickness, effective or actual tolerances, fit, fundamental deviation, inspection dimensions, root\/tip form, load capacity or compliance. Use the current licensed ISO 4156 parts, the controlled drawing and a qualified spline designer for those decisions.<\/div>\n<form id=\"vbm236-form\" class=\"vbm236-card\" autocomplete=\"off\" novalidate>\n<h2>Documented inputs and traceability<\/h2>\n<div class=\"vbm236-grid\">\n<div class=\"vbm236-field\"><label for=\"vbm236-module\">Metric module m (mm) <span class=\"vbm236-hint\">positive controlled nominal value<\/span><\/label><input id=\"vbm236-module\" type=\"text\" inputmode=\"decimal\" placeholder=\"e.g. 2\"><\/div>\n<div class=\"vbm236-field\"><label for=\"vbm236-teeth\">Number of teeth z <span class=\"vbm236-hint\">positive integer from the controlled drawing<\/span><\/label><input id=\"vbm236-teeth\" type=\"text\" inputmode=\"numeric\" placeholder=\"e.g. 20\"><\/div>\n<div class=\"vbm236-field\"><label for=\"vbm236-angle\">Documented pressure angle \u03b1 (degrees) <span class=\"vbm236-hint\">strictly between 0\u00b0 and 90\u00b0; no allowed ISO set is inferred<\/span><\/label><input id=\"vbm236-angle\" type=\"text\" inputmode=\"decimal\" placeholder=\"e.g. 30\"><\/div>\n<div class=\"vbm236-field\"><label for=\"vbm236-record\">Calculation \/ drawing record ID<\/label><input id=\"vbm236-record\" type=\"text\" placeholder=\"required\"><\/div>\n<div class=\"vbm236-field\"><label for=\"vbm236-configuration\">Internal\/external members and spline configuration<\/label><input id=\"vbm236-configuration\" type=\"text\" placeholder=\"required\"><\/div>\n<div class=\"vbm236-field\"><label for=\"vbm236-module-source\">Module source, drawing and revision<\/label><input id=\"vbm236-module-source\" type=\"text\" placeholder=\"required\"><\/div>\n<div class=\"vbm236-field\"><label for=\"vbm236-teeth-source\">Tooth-count source and revision<\/label><input id=\"vbm236-teeth-source\" type=\"text\" placeholder=\"required\"><\/div>\n<div class=\"vbm236-field\"><label for=\"vbm236-angle-source\">Pressure-angle source and revision<\/label><input id=\"vbm236-angle-source\" type=\"text\" placeholder=\"required\"><\/div>\n<div class=\"vbm236-field\"><label for=\"vbm236-standard\">Applicable standard part, edition and licensed clause\/table<\/label><input id=\"vbm236-standard\" type=\"text\" placeholder=\"required\"><\/div>\n<div class=\"vbm236-field\"><label for=\"vbm236-fit\">Fit, fundamental deviation, tolerance class and centring basis<\/label><input id=\"vbm236-fit\" type=\"text\" placeholder=\"required\"><\/div>\n<div class=\"vbm236-field\"><label for=\"vbm236-inspection\">Inspection dimensions, gauges and acceptance plan<\/label><input id=\"vbm236-inspection\" type=\"text\" placeholder=\"required\"><\/div>\n<div class=\"vbm236-field\"><label for=\"vbm236-uncertainty\">Source uncertainty and reporting precision<\/label><input id=\"vbm236-uncertainty\" type=\"text\" placeholder=\"required\"><\/div>\n<div class=\"vbm236-field\"><label for=\"vbm236-person\">Responsible designer \/ reviewer<\/label><input id=\"vbm236-person\" type=\"text\" placeholder=\"required\"><\/div>\n<div class=\"vbm236-field\"><label for=\"vbm236-date\">Review date<\/label><input id=\"vbm236-date\" type=\"text\" placeholder=\"YYYY-MM-DD\"><\/div>\n<div class=\"vbm236-field full\"><label for=\"vbm236-notes\">Notes and exclusions <span class=\"vbm236-hint\">Optional: profile shift, manufacturing process, root form, material, lubrication, load spectrum and mating-member controls<\/span><\/label><textarea id=\"vbm236-notes\"><\/textarea><\/div>\n<\/p><\/div>\n<div class=\"vbm236-checks\">\n  <label class=\"vbm236-check\"><input type=\"checkbox\" id=\"vbm236-c1\"><span>The module, tooth count and pressure angle were copied from one controlled, mutually compatible spline definition; the worksheet must not choose them.<\/span><\/label><br \/>\n  <label class=\"vbm236-check\"><input type=\"checkbox\" id=\"vbm236-c2\"><span>The application is a straight cylindrical involute spline, and the applicable ISO 4156 part\/edition, member type, fit and tolerance data are controlled outside this arithmetic.<\/span><\/label><br \/>\n  <label class=\"vbm236-check\"><input type=\"checkbox\" id=\"vbm236-c3\"><span>No root\/tip diameter, tooth thickness, backlash, tolerance, gauge dimension, contact stress, torque capacity or safety factor will be inferred from these three relations.<\/span><\/label><br \/>\n  <label class=\"vbm236-check\"><input type=\"checkbox\" id=\"vbm236-c4\"><span>Manufacturing and acceptance will follow the controlled drawing, licensed standard, inspection plan and qualified design review\u2014not the displayed nominal quantities alone.<\/span><\/label>\n <\/div>\n<div class=\"vbm236-actions\"><button type=\"submit\" class=\"vbm236-primary\">Calculate nominal relations<\/button><button type=\"button\" class=\"vbm236-secondary\" id=\"vbm236-clear\">Clear<\/button><\/div>\n<div id=\"vbm236-error\" class=\"vbm236-error\" role=\"alert\"><\/div>\n<\/form>\n<section id=\"vbm236-results\" class=\"vbm236-card vbm236-results\" aria-live=\"polite\">\n<h2>Preliminary reference quantities<\/h2>\n<div class=\"vbm236-result-grid\">\n<div class=\"vbm236-result primary\">\n<div class=\"vbm236-result-label\">Nominal reference diameter d<\/div>\n<div class=\"vbm236-result-value\" id=\"vbm236-r-d\">\u2014<\/div>\n<\/div>\n<div class=\"vbm236-result\">\n<div class=\"vbm236-result-label\">Base-circle diameter d\u1d66<\/div>\n<div class=\"vbm236-result-value\" id=\"vbm236-r-db\">\u2014<\/div>\n<\/div>\n<div class=\"vbm236-result\">\n<div class=\"vbm236-result-label\">Circular pitch p<\/div>\n<div class=\"vbm236-result-value\" id=\"vbm236-r-p\">\u2014<\/div>\n<\/div><\/div>\n<div class=\"vbm236-status\" id=\"vbm236-r-status\"><\/div>\n<\/section>\n<section class=\"vbm236-card\">\n<h2>Formula, units and classification<\/h2>\n<div class=\"vbm236-formula\">d = m \u00b7 z &nbsp; [mm]<br \/>d<sub>b<\/sub> = d \u00b7 cos(\u03b1) &nbsp; [mm], with \u03b1 converted from degrees to radians for cos()<br \/>p = \u03c0 \u00b7 m &nbsp; [mm per tooth]<\/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<\/td>\n<td>documented metric module, mm<\/td>\n<td>controlled nominal input; no series or preferred value selected<\/td>\n<\/tr>\n<tr>\n<td>z<\/td>\n<td>documented number of teeth, integer<\/td>\n<td>no ISO range, undercut or mating compatibility inferred<\/td>\n<\/tr>\n<tr>\n<td>\u03b1<\/td>\n<td>documented pressure angle, degrees<\/td>\n<td>no allowed ISO angle set or tolerance inferred<\/td>\n<\/tr>\n<tr>\n<td>d<\/td>\n<td>nominal reference diameter, mm<\/td>\n<td>not a limiting tip, root, form, effective or inspection diameter<\/td>\n<\/tr>\n<tr>\n<td>d<sub>b<\/sub><\/td>\n<td>base-circle diameter, mm<\/td>\n<td>generic involute reference relation, not an inspection result<\/td>\n<\/tr>\n<tr>\n<td>p<\/td>\n<td>circular pitch, mm per tooth<\/td>\n<td>nominal reference relation only<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>These are general involute-geometry relations, not a verbatim ISO 4156 tolerance table and not a load-capacity method. All calculated lengths scale linearly with module; only the base-circle result depends on the supplied pressure angle.<\/p>\n<\/section>\n<section class=\"vbm236-card\">\n<h2>Model boundary and removed unsupported outputs<\/h2>\n<ul>\n<li><strong>No false complete ISO geometry.<\/strong> The former page accepted a pressure angle but ignored it in every result while advertising \u201cISO 4156 geometry.\u201d It now affects the base-circle relation, and the page explicitly excludes the standard\u2019s controlled limiting\/tolerance\/fit data.<\/li>\n<li><strong>No universal root diameter.<\/strong> The former d \u2212 2.5m shortcut was presented as a spline root diameter. Actual internal\/external spline form and limits depend on the specified system, coefficients, deviations, tolerances and manufacturing\/inspection requirements.<\/li>\n<li><strong>No invented capacity model.<\/strong> The former bearing-pressure and torque-capacity outputs assumed effective height h = 0.9m, load factor K = 0.75 and uniform sharing by every tooth without a controlled source.<\/li>\n<li><strong>No \u201cOK\u201d safety verdict.<\/strong> Strength needs material properties, member geometry, root stress, wear\/contact criteria, load spectrum, misalignment, lubrication, manufacturing deviations and an approved method.<\/li>\n<li><strong>No generic design advice.<\/strong> Universal K values, engagement-length ratios, hardness, \u201cstronger angle\u201d and spline-versus-key claims were removed because their validity depends on the application and source.<\/li>\n<li><strong>No hidden state.<\/strong> Defaults, presets, auto-calculation, local history, clipboard output, dynamic FAQ HTML and external KaTeX were removed.<\/li>\n<\/ul>\n<\/section>\n<section class=\"vbm236-card\">\n<h2>Current ISO 4156 series status<\/h2>\n<table>\n<thead>\n<tr>\n<th>Part<\/th>\n<th>Publicly verified scope\/status<\/th>\n<th>Evidence<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>ISO 4156-1:2021, Edition 2<\/td>\n<td>Generalities for design\/manufacture of straight, non-helical, side-fitting cylindrical involute splines; limiting dimensions, tolerances and deviations are defined by formulas\/tables. Published; confirmed in 2026.<\/td>\n<td><a href=\"https:\/\/www.iso.org\/standard\/77819.html\" target=\"_blank\" rel=\"noopener\">Official ISO card<\/a><\/td>\n<\/tr>\n<tr>\n<td>ISO 4156-2:2021, Edition 2<\/td>\n<td>Geometry and inspection dimensions; tables for external fundamental deviation h have a stated scope, while other deviations require formulas from Parts 1 and 3. Published and under review.<\/td>\n<td><a href=\"https:\/\/www.iso.org\/standard\/77821.html\" target=\"_blank\" rel=\"noopener\">Official ISO card<\/a><\/td>\n<\/tr>\n<tr>\n<td>ISO 4156-3:2021, Edition 2<\/td>\n<td>Inspection data, guidance and requirements. Published and under review; corrected English and French versions issued December 2025.<\/td>\n<td><a href=\"https:\/\/www.iso.org\/standard\/77822.html\" target=\"_blank\" rel=\"noopener\">Official ISO card<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p class=\"vbm236-small\"><strong>Accessed:<\/strong> 15 July 2026. The former undated \u201cISO 4156\u201d reference omitted the three current parts and their 2021 editions. Exact formulas, tables, limits, permitted parameter sets, deviations, tolerances, fits and inspection requirements remain <strong>NEEDS_LICENSED_SOURCE<\/strong>.<\/p>\n<\/section>\n<section class=\"vbm236-card\">\n<h2>Open formula evidence<\/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>Metric module m = d\/z, base-circle diameter d<sub>b<\/sub> = d cos \u03b1 and circular pitch p = \u03c0m.<\/td>\n<td>University mechanical-engineering teaching material; page 3 visually inspected<\/td>\n<td><a href=\"https:\/\/www.faculty.fairfield.edu\/wdornfeld\/ME312\/Gears.pdf\" target=\"_blank\" rel=\"noopener\">Fairfield University ME 312, Gears, p. 3<\/a><\/td>\n<\/tr>\n<tr>\n<td>Reference diameter d = zm and base diameter d<sub>b<\/sub> = d cos \u03b1 for standard involute gear geometry.<\/td>\n<td>Gear manufacturer technical reference; corroborating public source<\/td>\n<td><a href=\"https:\/\/khkgears.net\/gear-knowledge\/gear-technical-reference\/calculation-gear-dimensions\/\" target=\"_blank\" rel=\"noopener\">KHK Gear Technical Reference<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>These public sources support only the displayed generic involute relations. They do not substitute for licensed ISO 4156 spline dimensions, tolerances, fits or inspection rules.<\/p>\n<\/section>\n<section class=\"vbm236-card\">\n<h2>Reference checks<\/h2>\n<p>For m = 2 mm, z = 20 and \u03b1 = 30\u00b0, d = 40 mm, d<sub>b<\/sub> = 34.641016151\u2026 mm and p = 6.283185307\u2026 mm. For m = 1.5 mm, z = 30 and \u03b1 = 45\u00b0, d = 45 mm, d<sub>b<\/sub> = 31.819805153\u2026 mm and p = 4.712388980\u2026 mm.<\/p>\n<\/section>\n<section class=\"vbm236-card\">\n<h2>Questions<\/h2>\n<details>\n<summary>Can I manufacture a spline from these three outputs?<\/summary>\n<p>No. A manufacturing definition needs the applicable ISO 4156 part\/edition, member types, fit, deviations, tolerance class, tooth\/root form, inspection dimensions and drawing controls.<\/p>\n<\/details>\n<details>\n<summary>Why is torque capacity absent?<\/summary>\n<p>ISO 4156\u2019s public scope concerns geometry, tolerances, fits and inspection. A defensible strength calculation needs a separately validated load-capacity method and many more controlled inputs.<\/p>\n<\/details>\n<details>\n<summary>Why is root diameter absent?<\/summary>\n<p>A single d \u2212 2.5m rule is not a universal ISO 4156 spline root-diameter calculation. Use the applicable licensed tables\/formulas for the exact internal\/external member and specification.<\/p>\n<\/details>\n<\/section>\n<p><script>\n(function(){'use strict';var form=document.getElementById('vbm236-form'),error=document.getElementById('vbm236-error'),results=document.getElementById('vbm236-results');\nfunction parsePositive(value,label){var s=String(value==null?'':value).trim();if(!\/^[+]?(?:\\d+(?:[.,]\\d*)?|[.,]\\d+)$\/.test(s))throw new Error(label+' must be one positive plain decimal using a point or comma.');var n=Number(s.replace(',','.'));if(!Number.isFinite(n)||n<=0)throw new Error(label+' must be finite and greater than zero.');return n}\nfunction parseTeeth(value){var s=String(value==null?'':value).trim();if(!\/^[+]?\\d+$\/.test(s))throw new Error('Number of teeth must be one positive integer.');var n=Number(s);if(!Number.isSafeInteger(n)||n<=0)throw new Error('Number of teeth must be a safe positive integer.');return n}\nfunction requiredText(id,label){var value=document.getElementById(id).value.trim();if(!value)throw new Error(label+' is required.');return value}\nfunction calculate(moduleValue,teethValue,angleValue){var m=parsePositive(moduleValue,'Metric module'),z=parseTeeth(teethValue),alpha=parsePositive(angleValue,'Pressure angle');if(!(alpha<90))throw new Error('Pressure angle must be strictly less than 90 degrees.');var rad=alpha*Math.PI\/180,d=m*z,db=d*Math.cos(rad),p=Math.PI*m;if(![rad,d,db,p].every(function(x){return Number.isFinite(x)&&x>0}))throw new Error('The derived geometry is outside the finite numeric range.');return{module:m,teeth:z,angle:alpha,rad:rad,d:d,db:db,p:p}}\nfunction fmt(n){if(!Number.isFinite(n))return'\u2014';return(n>=1e12||n<1e-9?n.toExponential(11):n.toPrecision(12)).replace(\/(\\.\\d*?[1-9])0+(e|$)\/,'$1$2').replace(\/\\.0+(e|$)\/,'$1')}\nfunction setText(id,text){document.getElementById(id).textContent=text}function render(r){setText('vbm236-r-d',fmt(r.d)+' mm');setText('vbm236-r-db',fmt(r.db)+' mm');setText('vbm236-r-p',fmt(r.p)+' mm\/tooth');setText('vbm236-r-status','Nominal involute relations only. 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