Spur gear center distance calculator<\/title>\n\n <link rel=\"preconnect\" href=\"https:\/\/fonts.googleapis.com\" \/>\n <link rel=\"preconnect\" href=\"https:\/\/fonts.gstatic.com\" crossorigin \/>\n <link href=\"https:\/\/fonts.googleapis.com\/css2?family=Inter:wght@400;500;600;700&display=swap\" rel=\"stylesheet\" \/>\n\n \n <link rel=\"stylesheet\" href=\"https:\/\/cdn.jsdelivr.net\/npm\/katex@0.16.9\/dist\/katex.min.css\" crossorigin=\"anonymous\" \/>\n <script defer src=\"https:\/\/cdn.jsdelivr.net\/npm\/katex@0.16.9\/dist\/katex.min.js\" crossorigin=\"anonymous\"><\/script>\n\n <style>\n *, *::before, *::after { box-sizing: border-box; margin: 0; padding: 0; }\n\n :root {\n --green: #1a6b3c;\n --green-dark: #0f4a28;\n --green-mid: #2d8a55;\n --green-light: #e8f4ed;\n --green-xlight: #f2faf5;\n --amber: #b45309;\n --amber-light: #fef3c7;\n --red: #b91c1c;\n --bg: #ffffff;\n --bg-soft: #f8f9fa;\n --bg-muted: #f1f3f5;\n --border: #e5e7eb;\n --border-mid: #d1d5db;\n --text-primary: #111827;\n --text-secondary: #4b5563;\n --text-muted: #9ca3af;\n --gray-650: #4b5563;\n --radius-sm: 6px;\n --radius-md: 8px;\n\n font-family: 'Inter', sans-serif;\n font-size: 14px;\n letter-spacing: 0.02em;\n color: var(--text-primary);\n background: var(--bg-soft);\n }\n\n body { background: var(--bg-soft); min-height: 100vh; padding: 40px 28px 64px; }\n\n .article__title {\n font-size: 22px;\n font-weight: 700;\n color: var(--text-primary);\n line-height: 1.3;\n margin-bottom: 8px;\n }\n\n .article__subtitle {\n font-size: 14px;\n color: var(--text-secondary);\n line-height: 1.75;\n margin-bottom: 24px;\n }\n\n \/* \u2500\u2500 Infobox \/ Warnbox \u2500\u2500 *\/\n .infobox {\n display: flex;\n flex-direction: column;\n gap: 4px;\n padding: 12px 14px;\n background: var(--green-xlight);\n border: 1px solid var(--green-light);\n border-radius: var(--radius-sm);\n color: var(--green-dark);\n }\n .infobox__title {\n display: flex;\n align-items: center;\n gap: 6px;\n font-size: 12.5px;\n font-weight: 600;\n }\n .infobox__text { font-size: 12px; line-height: 1.6; }\n\n .warnbox {\n display: flex;\n flex-direction: column;\n gap: 4px;\n padding: 12px 14px;\n background: #fffbeb;\n border: 1px solid #f59e0b;\n border-radius: var(--radius-sm);\n color: #78350f;\n }\n .warnbox__title {\n display: flex;\n align-items: center;\n gap: 6px;\n font-size: 12.5px;\n font-weight: 600;\n }\n .warnbox__text { font-size: 12px; line-height: 1.6; }\n\n \/* \u2500\u2500 Shell \u2500\u2500 *\/\n .ci-host { display: flex; flex-direction: column; gap: 14px; margin-top: 4px; }\n\n .ci-layout {\n display: grid;\n grid-template-columns: repeat(auto-fit, minmax(300px, 1fr));\n gap: 22px;\n align-items: stretch;\n }\n\n .ci-card {\n background: var(--bg);\n border: 1px solid var(--border);\n border-radius: var(--radius-md);\n box-shadow: 0 1px 3px rgba(0,0,0,.05);\n }\n\n \/* \u2500\u2500 Parameters panel \u2500\u2500 *\/\n .ci-params {\n padding: 22px 22px 20px;\n display: flex;\n flex-direction: column;\n gap: 18px;\n }\n\n .ci-params-head { display: flex; align-items: center; justify-content: space-between; }\n\n .ci-params-title {\n font-size: 16px;\n font-weight: 700;\n color: var(--text-primary);\n letter-spacing: -0.01em;\n }\n\n .ci-reset-btn {\n display: inline-flex;\n align-items: center;\n gap: 5px;\n background: none;\n border: none;\n cursor: pointer;\n color: var(--text-secondary);\n font-family: inherit;\n font-size: 12.5px;\n font-weight: 500;\n padding: 4px 8px;\n border-radius: var(--radius-sm);\n transition: color 0.15s, background 0.15s;\n }\n .ci-reset-btn:hover { color: var(--text-primary); 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}\n\n .ci-readout-unit {\n font-size: 13px;\n color: var(--gray-650);\n font-weight: 500;\n }\n .ci-readout--big .ci-readout-unit { font-size: 15px; }\n\n \/* \u2500\u2500 Diameters table card \u2500\u2500 *\/\n .ci-diam-card { overflow: hidden; }\n\n .ci-diam-head {\n display: flex;\n align-items: center;\n justify-content: space-between;\n padding: 13px 18px 10px;\n }\n\n .ci-diam-title {\n font-size: 14px;\n font-weight: 700;\n color: var(--text-primary);\n }\n\n .ci-diam-unit {\n font-size: 11px;\n color: var(--gray-650);\n }\n\n \/* \u2500\u2500 Table \u2500\u2500 *\/\n .ci-table {\n width: 100%;\n border-collapse: collapse;\n font-size: 13px;\n font-variant-numeric: tabular-nums;\n }\n .ci-th {\n padding: 8px 14px;\n background: var(--green);\n color: #fff;\n font-size: 11px;\n font-weight: 600;\n letter-spacing: 0.04em;\n white-space: nowrap;\n }\n .ci-th--label { text-align: left; }\n .ci-th--val { text-align: right; }\n .ci-tr { border-top: 1px solid var(--border); }\n .ci-tr--alt { background: var(--bg-soft); }\n .ci-td--label {\n padding: 8px 14px;\n font-weight: 500;\n color: var(--text-secondary);\n font-size: 12.5px;\n }\n .ci-td--val {\n padding: 8px 14px;\n text-align: right;\n color: var(--text-primary);\n font-family: ui-monospace, 'SF Mono', Menlo, Consolas, monospace;\n font-size: 13px;\n }\n\n \/* \u2500\u2500 Formula bar \u2500\u2500 *\/\n .ci-formula-bar {\n display: flex;\n align-items: center;\n gap: 16px;\n flex-wrap: wrap;\n padding: 14px 20px;\n background: var(--bg-soft);\n border: 1px solid var(--border);\n border-radius: var(--radius-md);\n }\n\n .ci-formula-tag {\n font-size: 10px;\n font-weight: 700;\n letter-spacing: 0.1em;\n text-transform: uppercase;\n color: var(--gray-650);\n flex-shrink: 0;\n }\n\n .ci-formula-text {\n font-family: ui-monospace, 'SF Mono', Menlo, Consolas, monospace;\n font-size: 15px;\n color: var(--text-primary);\n font-weight: 500;\n }\n\n .ci-formula-spacer { flex: 1; min-width: 0; }\n\n .ci-formula-toggle {\n display: inline-flex;\n align-items: center;\n gap: 5px;\n background: none;\n border: 1px solid var(--green-light);\n border-radius: var(--radius-sm);\n cursor: pointer;\n color: var(--green);\n font-family: inherit;\n font-size: 12.5px;\n font-weight: 600;\n padding: 5px 10px;\n transition: background 0.15s, border-color 0.15s;\n flex-shrink: 0;\n }\n .ci-formula-toggle:hover { background: var(--green-xlight); border-color: var(--green-mid); }\n .ci-formula-toggle svg { transition: transform 0.2s; }\n .ci-formula-toggle--open svg { transform: rotate(180deg); }\n\n \/* \u2500\u2500 Formula reference panel \u2500\u2500 *\/\n .ci-formula-panel {\n border: 1px solid var(--border);\n border-radius: var(--radius-md);\n overflow: hidden;\n }\n\n .ci-ftable { width: 100%; border-collapse: collapse; font-size: 12.5px; }\n\n .ci-fth {\n padding: 9px 16px;\n background: var(--green);\n color: #fff;\n font-weight: 600;\n font-size: 11px;\n letter-spacing: 0.04em;\n text-align: left;\n }\n .ci-fth--right { text-align: right; }\n\n .ci-ftd {\n padding: 9px 16px;\n border-top: 1px solid var(--border);\n color: var(--text-secondary);\n vertical-align: middle;\n }\n .ci-ftd--val {\n text-align: right;\n font-family: ui-monospace, 'SF Mono', Menlo, Consolas, monospace;\n font-weight: 600;\n color: var(--green);\n }\n\n .hidden { display: none; }\n\n @media (max-width: 900px) {\n body { padding: 28px 16px 48px; }\n .ci-layout { grid-template-columns: 1fr; }\n }\n @media (max-width: 540px) {\n .ci-field-grid { grid-template-columns: 1fr; }\n .ci-readout--big .ci-readout-val { font-size: 30px; }\n }\n <\/style>\n<\/head>\n<body>\n\n <script type=\"application\/ld+json\">\n{\n \"@context\": \"https:\/\/schema.org\",\n \"@type\": \"WebApplication\",\n \"@id\": \"#calc-center-distance\",\n \"name\": \"Spur gear center distance calculator\",\n \"description\": \"Calculate the nominal zero-backlash center distance of a pair of spur gears, along with the module, reference, tip, root and base diameters, gear ratio and speeds.\",\n \"applicationCategory\": \"UtilitiesApplication\",\n \"operatingSystem\": \"Web\",\n \"browserRequirements\": \"Requires JavaScript\",\n \"inLanguage\": \"en\",\n \"isAccessibleForFree\": true,\n \"offers\": {\n \"@type\": \"Offer\",\n \"price\": \"0\",\n \"priceCurrency\": \"EUR\"\n },\n \"featureList\": [\n \"Nominal zero-backlash center distance\",\n \"Module\",\n \"Reference, tip, root and base diameters\",\n \"Gear ratio\",\n \"Output speed and pitch line velocity\"\n ],\n \"about\": [\n {\n \"@type\": \"Thing\",\n \"name\": \"Center distance\"\n },\n {\n \"@type\": \"Thing\",\n \"name\": \"Module\"\n },\n {\n \"@type\": \"Thing\",\n \"name\": \"Gear ratio\"\n }\n ]\n}\n <\/script>\n\n <h1 class=\"article__title\">Spur gear center distance calculator<\/h1>\n <p class=\"article__subtitle\">\n Calculate the nominal zero-backlash center distance for a pair of straight-tooth spur gears\n \u2014 module, reference, tip, root and base diameters, gear ratio and speeds.\n <\/p>\n\n <div class=\"ci-host\">\n\n \n <div class=\"infobox\">\n <div class=\"infobox__title\">\n <svg width=\"13\" height=\"13\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><circle cx=\"12\" cy=\"12\" r=\"10\"><\/circle><line x1=\"12\" y1=\"16\" x2=\"12\" y2=\"12\"><\/line><line x1=\"12\" y1=\"8\" x2=\"12.01\" y2=\"8\"><\/line><\/svg>\n Nominal zero-backlash center distance\n <\/div>\n <p class=\"infobox__text\">\n This calculator returns the nominal center distance for standard full-depth gears without\n profile shift, corresponding to theoretical zero backlash. In practice it is good practice to\n allow a small amount of backlash to compensate for machining tolerances and thermal expansion,\n and to ensure adequate lubrication.\n <\/p>\n <\/div>\n\n \n <div id=\"warn-z1\" class=\"warnbox hidden\">\n <div class=\"warnbox__title\">\n <svg width=\"13\" height=\"13\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><path d=\"M10.29 3.86L1.82 18a2 2 0 0 0 1.71 3h16.94a2 2 0 0 0 1.71-3L13.71 3.86a2 2 0 0 0-3.42 0z\"><\/path><line x1=\"12\" y1=\"9\" x2=\"12\" y2=\"13\"><\/line><line x1=\"12\" y1=\"17\" x2=\"12.01\" y2=\"17\"><\/line><\/svg>\n Warning\n <\/div>\n <p class=\"warnbox__text\" id=\"warn-z1-text\"><\/p>\n <\/div>\n <div id=\"warn-z2\" class=\"warnbox hidden\">\n <div class=\"warnbox__title\">\n <svg width=\"13\" height=\"13\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><path d=\"M10.29 3.86L1.82 18a2 2 0 0 0 1.71 3h16.94a2 2 0 0 0 1.71-3L13.71 3.86a2 2 0 0 0-3.42 0z\"><\/path><line x1=\"12\" y1=\"9\" x2=\"12\" y2=\"13\"><\/line><line x1=\"12\" y1=\"17\" x2=\"12.01\" y2=\"17\"><\/line><\/svg>\n Warning\n <\/div>\n <p class=\"warnbox__text\" id=\"warn-z2-text\"><\/p>\n <\/div>\n <div id=\"warn-df\" class=\"warnbox hidden\">\n <div class=\"warnbox__title\">\n <svg width=\"13\" height=\"13\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><path d=\"M10.29 3.86L1.82 18a2 2 0 0 0 1.71 3h16.94a2 2 0 0 0 1.71-3L13.71 3.86a2 2 0 0 0-3.42 0z\"><\/path><line x1=\"12\" y1=\"9\" x2=\"12\" y2=\"13\"><\/line><line x1=\"12\" y1=\"17\" x2=\"12.01\" y2=\"17\"><\/line><\/svg>\n Warning\n <\/div>\n <p class=\"warnbox__text\">Root diameter \u2264 0: module too large for the selected number of teeth<\/p>\n <\/div>\n\n <div class=\"ci-layout\">\n\n \n <section class=\"ci-card ci-params\">\n <div class=\"ci-params-head\">\n <h2 class=\"ci-params-title\">Parameters<\/h2>\n <button class=\"ci-reset-btn\" id=\"btn-reset\" type=\"button\">\n <svg width=\"13\" height=\"13\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\">\n <polyline points=\"1 4 1 10 7 10\"><\/polyline>\n <path d=\"M3.51 15a9 9 0 1 0 .49-5.66\"><\/path>\n <\/svg>\n Reset\n <\/button>\n <\/div>\n\n \n <div class=\"ci-seg-wrap\">\n <span class=\"ci-field-label\">Calculate<\/span>\n <div class=\"ci-seg\">\n <button class=\"ci-seg-btn ci-seg-btn--active\" id=\"seg-modulo\" type=\"button\">Center distance<\/button>\n <button class=\"ci-seg-btn\" id=\"seg-interasse\" type=\"button\">Module<\/button>\n <\/div>\n <\/div>\n\n \n <div class=\"ci-field-grid\">\n <label class=\"ci-field\" id=\"field-m\">\n <div class=\"ci-field-head\">\n <span class=\"ci-field-label\">Module<\/span>\n <span class=\"ci-field-hint\">m<\/span>\n <\/div>\n <div class=\"ci-field-input-wrap\">\n <input class=\"ci-field-input\" id=\"input-m\" type=\"number\"\n placeholder=\"\u2014\" step=\"0.25\" min=\"0.25\" max=\"20\"\n style=\"padding-right:13px\" \/>\n <\/div>\n <\/label>\n <label class=\"ci-field hidden\" id=\"field-a\">\n <div class=\"ci-field-head\">\n <span class=\"ci-field-label\">Center distance<\/span>\n <span class=\"ci-field-hint\">a \u2014 target<\/span>\n <\/div>\n <div class=\"ci-field-input-wrap\">\n <input class=\"ci-field-input\" id=\"input-a\" type=\"number\"\n placeholder=\"\u2014\" step=\"1\" min=\"1\" \/>\n <span class=\"ci-field-suffix\">mm<\/span>\n <\/div>\n <\/label>\n\n <label class=\"ci-field\">\n <div class=\"ci-field-head\">\n <span class=\"ci-field-label\">Pressure angle<\/span>\n <span class=\"ci-field-hint\">\u03b1<\/span>\n <\/div>\n <div class=\"ci-field-input-wrap\">\n <input class=\"ci-field-input\" id=\"input-alpha\" type=\"number\"\n placeholder=\"\u2014\" step=\"0.5\" min=\"0\" max=\"45\" \/>\n <span class=\"ci-field-suffix\">\u00b0<\/span>\n <\/div>\n <\/label>\n <\/div>\n\n <div class=\"ci-divider\"><\/div>\n\n <div class=\"ci-field-grid\">\n <label class=\"ci-field\">\n <div class=\"ci-field-head\">\n <span class=\"ci-field-label\">Pinion teeth<\/span>\n <span class=\"ci-field-hint\">z\u2081<\/span>\n <\/div>\n <div class=\"ci-field-input-wrap\">\n <input class=\"ci-field-input\" id=\"input-z1\" type=\"number\"\n placeholder=\"\u2014\" step=\"1\" min=\"6\" max=\"300\"\n style=\"padding-right:13px\" \/>\n <\/div>\n <\/label>\n <label class=\"ci-field\">\n <div class=\"ci-field-head\">\n <span class=\"ci-field-label\">Gear teeth<\/span>\n <span class=\"ci-field-hint\">z\u2082<\/span>\n <\/div>\n <div class=\"ci-field-input-wrap\">\n <input class=\"ci-field-input\" id=\"input-z2\" type=\"number\"\n placeholder=\"\u2014\" step=\"1\" min=\"6\" max=\"500\"\n style=\"padding-right:13px\" \/>\n <\/div>\n <\/label>\n <\/div>\n\n <label class=\"ci-field\">\n <div class=\"ci-field-head\">\n <span class=\"ci-field-label\">Input speed<\/span>\n <span class=\"ci-field-hint\">n\u2081<\/span>\n <\/div>\n <div class=\"ci-field-input-wrap\">\n <input class=\"ci-field-input\" id=\"input-n1\" type=\"number\"\n placeholder=\"\u2014\" step=\"50\" min=\"0\"\n style=\"padding-right:52px\" \/>\n <span class=\"ci-field-suffix\">rpm<\/span>\n <\/div>\n <\/label>\n <\/section>\n\n \n <section class=\"ci-results\">\n\n \n <div class=\"ci-card ci-readouts\" id=\"panel-readouts\">\n \n <\/div>\n\n \n <div class=\"ci-card ci-diam-card\">\n <div class=\"ci-diam-head\">\n <h3 class=\"ci-diam-title\">Diameters<\/h3>\n <span class=\"ci-diam-unit\">mm<\/span>\n <\/div>\n <table class=\"ci-table\">\n <thead>\n <tr>\n <th class=\"ci-th ci-th--label\"><\/th>\n <th class=\"ci-th ci-th--val\">Pinion z\u2081<\/th>\n <th class=\"ci-th ci-th--val\">Gear z\u2082<\/th>\n <\/tr>\n <\/thead>\n <tbody id=\"diam-tbody\">\n \n <\/tbody>\n <\/table>\n <\/div>\n <\/section>\n <\/div>\n\n \n <div class=\"ci-formula-bar\">\n <span class=\"ci-formula-tag\">Formula<\/span>\n <span class=\"ci-formula-text\" id=\"formula-main\"><\/span>\n <div class=\"ci-formula-spacer\"><\/div>\n <button class=\"ci-formula-toggle\" id=\"btn-formulas\" type=\"button\">\n <span id=\"formula-toggle-label\">All formulas<\/span>\n <svg width=\"14\" height=\"14\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><polyline points=\"6 9 12 15 18 9\"><\/polyline><\/svg>\n <\/button>\n <\/div>\n\n \n <div class=\"ci-formula-panel hidden\" id=\"panel-formulas\">\n <table class=\"ci-ftable\">\n <thead>\n <tr>\n <th class=\"ci-fth\">Quantity<\/th>\n <th class=\"ci-fth\">Formula<\/th>\n <th class=\"ci-fth ci-fth--right\">Pinion z\u2081<\/th>\n <th class=\"ci-fth ci-fth--right\">Gear z\u2082<\/th>\n <\/tr>\n <\/thead>\n <tbody id=\"ftable-tbody\">\n \n <\/tbody>\n <\/table>\n <\/div>\n\n <\/div>\n\n <script>\n const DEFAULTS = { mode: 'modulo', m: undefined, aIn: undefined, z1: undefined, z2: undefined, alpha: undefined, n1: undefined };\n let state = { ...DEFAULTS };\n let formulasOpen = false;\n\n function fmt(n, d = 2) {\n if (!Number.isFinite(n)) return '\u2014';\n return n.toFixed(d);\n }\n\n function tex(el, str) {\n if (window.katex) katex.render(str, el, { throwOnError: false });\n else el.textContent = str;\n }\n\n function compute(s) {\n const mod = s.mode === 'modulo' ? s.m : (2 * s.aIn) \/ (s.z1 + s.z2);\n const a = s.mode === 'modulo' ? (mod * (s.z1 + s.z2)) \/ 2 : s.aIn;\n const alphaRad = (s.alpha * Math.PI) \/ 180;\n const d1 = mod * s.z1;\n const d2 = mod * s.z2;\n const da1 = d1 + 2 * mod;\n const da2 = d2 + 2 * mod;\n const df1 = d1 - 2.5 * mod;\n const df2 = d2 - 2.5 * mod;\n const db1 = d1 * Math.cos(alphaRad);\n const db2 = d2 * Math.cos(alphaRad);\n const i = s.z2 \/ s.z1;\n const n2 = s.n1 \/ i;\n const v = (Math.PI * d1 * s.n1) \/ 60000;\n return { mod, a, d1, d2, da1, da2, df1, df2, db1, db2, i, n2, v };\n }\n\n function render() {\n const s = state;\n const c = compute(s);\n\n \/\/ Mode toggle\n document.getElementById('seg-modulo').classList.toggle('ci-seg-btn--active', s.mode === 'modulo');\n document.getElementById('seg-interasse').classList.toggle('ci-seg-btn--active', s.mode === 'interasse');\n document.getElementById('field-m').classList.toggle('hidden', s.mode !== 'modulo');\n document.getElementById('field-a').classList.toggle('hidden', s.mode !== 'interasse');\n\n \/\/ Warnings\n const wz1 = document.getElementById('warn-z1');\n const wz2 = document.getElementById('warn-z2');\n const wdf = document.getElementById('warn-df');\n\n if (s.z1 < 17) {\n document.getElementById('warn-z1-text').textContent =\n `z\u2081 = ${s.z1} < 17: risk of undercut on the pinion`;\n wz1.classList.remove('hidden');\n } else { wz1.classList.add('hidden'); }\n\n if (s.z2 < 17) {\n document.getElementById('warn-z2-text').textContent =\n `z\u2082 = ${s.z2} < 17: risk of undercut on the gear`;\n wz2.classList.remove('hidden');\n } else { wz2.classList.add('hidden'); }\n\n if (Number.isFinite(c.df1) && c.df1 <= 0) {\n wdf.classList.remove('hidden');\n } else { wdf.classList.add('hidden'); }\n\n \/\/ Primary readouts\n const isModMode = s.mode === 'modulo';\n const bigLabel = isModMode ? 'Center distance a \u00b7 calculated'\n : 'Module m \u00b7 calculated';\n const bigVal = isModMode ? fmt(c.a) : fmt(c.mod, 3);\n const bigUnit = isModMode ? 'mm' : '';\n const secLabel = isModMode ? 'Module m' : 'Center distance a';\n const secVal = isModMode ? fmt(c.mod, 3) : fmt(c.a);\n const secUnit = isModMode ? '' : 'mm';\n\n document.getElementById('panel-readouts').innerHTML = `\n <div class=\"ci-readout ci-readout--big\">\n <span class=\"ci-readout-label\">${bigLabel}<\/span>\n <div class=\"ci-readout-val-wrap\">\n <span class=\"ci-readout-val ci-readout-val--accent\">${bigVal}<\/span>\n ${bigUnit ? `<span class=\"ci-readout-unit\">${bigUnit}<\/span>` : ''}\n <\/div>\n <\/div>\n <div class=\"ci-readout\">\n <span class=\"ci-readout-label\">${secLabel}<\/span>\n <div class=\"ci-readout-val-wrap\">\n <span class=\"ci-readout-val\">${secVal}<\/span>\n ${secUnit ? `<span class=\"ci-readout-unit\">${secUnit}<\/span>` : ''}\n <\/div>\n <\/div>\n <div class=\"ci-readout\">\n <span class=\"ci-readout-label\">Gear ratio i = z\u2082\/z\u2081<\/span>\n <div class=\"ci-readout-val-wrap\">\n <span class=\"ci-readout-val\">${fmt(c.i, 3)}<\/span>\n <\/div>\n <\/div>\n <div class=\"ci-readout\">\n <span class=\"ci-readout-label\">Output speed n\u2082<\/span>\n <div class=\"ci-readout-val-wrap\">\n <span class=\"ci-readout-val\">${fmt(c.n2, 1)}<\/span>\n <span class=\"ci-readout-unit\">rpm<\/span>\n <\/div>\n <\/div>\n <div class=\"ci-readout\">\n <span class=\"ci-readout-label\">Pitch line velocity v<\/span>\n <div class=\"ci-readout-val-wrap\">\n <span class=\"ci-readout-val\">${fmt(c.v, 2)}<\/span>\n <span class=\"ci-readout-unit\">m\/s<\/span>\n <\/div>\n <\/div>`;\n\n \/\/ Diameters table\n const DIAM_ROWS = [\n ['Reference d', c.d1, c.d2],\n ['Tip d\u2090', c.da1, c.da2],\n ['Root d<sub>f<\/sub>', c.df1, c.df2],\n ['Base d<sub>b<\/sub>', c.db1, c.db2],\n ];\n document.getElementById('diam-tbody').innerHTML = DIAM_ROWS.map(([label, v1, v2], idx) => `\n <tr class=\"ci-tr${idx % 2 === 1 ? ' ci-tr--alt' : ''}\">\n <td class=\"ci-td--label\">${label}<\/td>\n <td class=\"ci-td--val\">${fmt(v1)}<\/td>\n <td class=\"ci-td--val\">${fmt(v2)}<\/td>\n <\/tr>`).join('');\n\n \/\/ Formula bar\n tex(document.getElementById('formula-main'), isModMode\n ? 'a = \\\\dfrac{m\\\\,(z_1 + z_2)}{2}'\n : 'm = \\\\dfrac{2a}{z_1 + z_2}');\n\n \/\/ Formula table\n const FORMULA_ROWS = [\n { g: 'Module m', t: 'm = \\\\dfrac{2a}{z_1 + z_2}', v1: fmt(c.mod, 3), v2: null },\n { g: 'Center distance a', t: 'a = \\\\dfrac{m\\\\,(z_1 + z_2)}{2}', v1: fmt(c.a) + ' mm', v2: null },\n { g: 'Reference dia. d', t: 'd = m\\\\,z', v1: fmt(c.d1) + ' mm', v2: fmt(c.d2) + ' mm' },\n { g: 'Tip dia. d\u2090', t: 'd_a = d + 2m = m\\\\,(z + 2)', v1: fmt(c.da1) + ' mm', v2: fmt(c.da2) + ' mm' },\n { g: 'Root dia. d_f', t: 'd_f = d - 2.5\\\\,m = m\\\\,(z - 2.5)', v1: fmt(c.df1) + ' mm', v2: fmt(c.df2) + ' mm' },\n { g: 'Base dia. d_b', t: 'd_b = d\\\\cos\\\\alpha', v1: fmt(c.db1) + ' mm', v2: fmt(c.db2) + ' mm' },\n { g: 'Ratio i', t: 'i = \\\\dfrac{z_2}{z_1} = \\\\dfrac{n_1}{n_2}', v1: fmt(c.i, 3), v2: null },\n { g: 'Pitch line vel. v', t: 'v = \\\\dfrac{\\\\pi\\\\,d_1\\\\,n_1}{60\\\\,000}', v1: fmt(c.v, 3) + ' m\/s', v2: null },\n ];\n const ftbody = document.getElementById('ftable-tbody');\n ftbody.innerHTML = FORMULA_ROWS.map(({ g, v1, v2 }, idx) => `\n <tr class=\"${idx % 2 === 1 ? 'ci-tr--alt' : ''}\">\n <td class=\"ci-ftd\">${g}<\/td>\n <td class=\"ci-ftd ci-ftd--tex\"><\/td>\n <td class=\"ci-ftd ci-ftd--val\"${v2 ? '' : ' colspan=\"2\"'}>${v1}<\/td>\n ${v2 ? `<td class=\"ci-ftd ci-ftd--val\">${v2}<\/td>` : ''}\n <\/tr>`).join('');\n ftbody.querySelectorAll('.ci-ftd--tex').forEach((cell, idx) => tex(cell, FORMULA_ROWS[idx].t));\n }\n\n \/\/ \u2500\u2500 Wire inputs \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n document.getElementById('seg-modulo').addEventListener('click', () => {\n state.mode = 'modulo'; render();\n });\n document.getElementById('seg-interasse').addEventListener('click', () => {\n state.mode = 'interasse'; render();\n });\n\n document.getElementById('input-m').addEventListener('input', e => {\n const v = parseFloat(e.target.value);\n state.m = (Number.isFinite(v) && v > 0) ? v : undefined; render();\n });\n document.getElementById('input-a').addEventListener('input', e => {\n const v = parseFloat(e.target.value);\n state.aIn = (Number.isFinite(v) && v > 0) ? v : undefined; render();\n });\n document.getElementById('input-alpha').addEventListener('input', e => {\n const v = parseFloat(e.target.value);\n state.alpha = Number.isFinite(v) ? v : undefined; render();\n });\n document.getElementById('input-z1').addEventListener('input', e => {\n const v = parseFloat(e.target.value);\n state.z1 = Number.isFinite(v) ? Math.max(6, Math.round(v)) : undefined; render();\n });\n document.getElementById('input-z2').addEventListener('input', e => {\n const v = parseFloat(e.target.value);\n state.z2 = Number.isFinite(v) ? Math.max(6, Math.round(v)) : undefined; render();\n });\n document.getElementById('input-n1').addEventListener('input', e => {\n const v = parseFloat(e.target.value);\n state.n1 = (Number.isFinite(v) && v >= 0) ? v : undefined; render();\n });\n\n document.getElementById('btn-reset').addEventListener('click', () => {\n state = { ...DEFAULTS };\n document.getElementById('input-m').value = '';\n document.getElementById('input-a').value = '';\n document.getElementById('input-alpha').value = '';\n document.getElementById('input-z1').value = '';\n document.getElementById('input-z2').value = '';\n document.getElementById('input-n1').value = '';\n render();\n });\n\n document.getElementById('btn-formulas').addEventListener('click', () => {\n formulasOpen = !formulasOpen;\n document.getElementById('panel-formulas').classList.toggle('hidden', !formulasOpen);\n document.getElementById('btn-formulas').classList.toggle('ci-formula-toggle--open', formulasOpen);\n document.getElementById('formula-toggle-label').textContent =\n formulasOpen ? 'Hide' : 'All formulas';\n });\n\n \/\/ \u2500\u2500 Boot \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n render();\n\n \/\/ re-render once KaTeX finishes loading (deferred), in case it wasn't ready\n window.addEventListener('load', render);\n <\/script>\n<\/body>\n<\/html>\n\n","protected":false},"excerpt":{"rendered":"<p>Fundamental geometric relationships to quickly derive diameters and center distances during new design or validation phases.<\/p>\n","protected":false},"parent":0,"template":"","meta":{"_acf_changed":false},"campo-applicazione":[5455],"categoria-ct":[5442],"class_list":["post-25583","centro-tecnico","type-centro-tecnico","status-publish","hentry","campo-applicazione-design","categoria-ct-gear-fundamentals"],"acf":[],"yoast_head":"\n<title>Quick Calculation Formulas for Gears | Stagnoli Gears Shop<\/title>\n<meta name=\"description\" content=\"Find essential formulas for gear calculations, including module, pitch diameter, center distance, transmission ratio, speed and torque.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/shop.stagnoligears.com\/en\/technical-hub\/quick-calculation-formulas-for-gears\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Quick Calculation Formulas for Gears 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{"id":25583,"date":"2026-06-30T09:43:00","date_gmt":"2026-06-30T07:43:00","guid":{"rendered":"https:\/\/shop.stagnoligears.com\/?post_type=centro-tecnico&p=25583"},"modified":"2026-07-10T15:00:09","modified_gmt":"2026-07-10T13:00:09","slug":"quick-calculation-formulas-for-gears","status":"publish","type":"centro-tecnico","link":"https:\/\/shop.stagnoligears.com\/en\/technical-hub\/quick-calculation-formulas-for-gears\/","title":{"rendered":"Quick calculation formulas for gears"},"content":{"rendered":"\n\n\n\n \n \n \n Spur gear center distance calculator<\/title>\n\n <link rel=\"preconnect\" href=\"https:\/\/fonts.googleapis.com\" \/>\n <link rel=\"preconnect\" href=\"https:\/\/fonts.gstatic.com\" crossorigin \/>\n <link href=\"https:\/\/fonts.googleapis.com\/css2?family=Inter:wght@400;500;600;700&display=swap\" rel=\"stylesheet\" \/>\n\n \n <link rel=\"stylesheet\" href=\"https:\/\/cdn.jsdelivr.net\/npm\/katex@0.16.9\/dist\/katex.min.css\" crossorigin=\"anonymous\" \/>\n <script defer src=\"https:\/\/cdn.jsdelivr.net\/npm\/katex@0.16.9\/dist\/katex.min.js\" crossorigin=\"anonymous\"><\/script>\n\n <style>\n *, *::before, *::after { box-sizing: border-box; margin: 0; padding: 0; }\n\n :root {\n --green: #1a6b3c;\n --green-dark: #0f4a28;\n --green-mid: #2d8a55;\n --green-light: #e8f4ed;\n --green-xlight: #f2faf5;\n --amber: #b45309;\n --amber-light: #fef3c7;\n --red: #b91c1c;\n --bg: #ffffff;\n --bg-soft: #f8f9fa;\n --bg-muted: #f1f3f5;\n --border: #e5e7eb;\n --border-mid: #d1d5db;\n --text-primary: #111827;\n --text-secondary: #4b5563;\n --text-muted: #9ca3af;\n --gray-650: #4b5563;\n --radius-sm: 6px;\n --radius-md: 8px;\n\n font-family: 'Inter', sans-serif;\n font-size: 14px;\n letter-spacing: 0.02em;\n color: var(--text-primary);\n background: var(--bg-soft);\n }\n\n body { background: var(--bg-soft); min-height: 100vh; padding: 40px 28px 64px; }\n\n .article__title {\n font-size: 22px;\n font-weight: 700;\n color: var(--text-primary);\n line-height: 1.3;\n margin-bottom: 8px;\n }\n\n .article__subtitle {\n font-size: 14px;\n color: var(--text-secondary);\n line-height: 1.75;\n margin-bottom: 24px;\n }\n\n \/* \u2500\u2500 Infobox \/ Warnbox \u2500\u2500 *\/\n .infobox {\n display: flex;\n flex-direction: column;\n gap: 4px;\n padding: 12px 14px;\n background: var(--green-xlight);\n border: 1px solid var(--green-light);\n border-radius: var(--radius-sm);\n color: var(--green-dark);\n }\n .infobox__title {\n display: flex;\n align-items: center;\n gap: 6px;\n font-size: 12.5px;\n font-weight: 600;\n }\n .infobox__text { font-size: 12px; line-height: 1.6; }\n\n .warnbox {\n display: flex;\n flex-direction: column;\n gap: 4px;\n padding: 12px 14px;\n background: #fffbeb;\n border: 1px solid #f59e0b;\n border-radius: var(--radius-sm);\n color: #78350f;\n }\n .warnbox__title {\n display: flex;\n align-items: center;\n gap: 6px;\n font-size: 12.5px;\n font-weight: 600;\n }\n .warnbox__text { font-size: 12px; line-height: 1.6; }\n\n \/* \u2500\u2500 Shell \u2500\u2500 *\/\n .ci-host { display: flex; flex-direction: column; gap: 14px; margin-top: 4px; }\n\n .ci-layout {\n display: grid;\n grid-template-columns: repeat(auto-fit, minmax(300px, 1fr));\n gap: 22px;\n align-items: stretch;\n }\n\n .ci-card {\n background: var(--bg);\n border: 1px solid var(--border);\n border-radius: var(--radius-md);\n box-shadow: 0 1px 3px rgba(0,0,0,.05);\n }\n\n \/* \u2500\u2500 Parameters panel \u2500\u2500 *\/\n .ci-params {\n padding: 22px 22px 20px;\n display: flex;\n flex-direction: column;\n gap: 18px;\n }\n\n .ci-params-head { display: flex; align-items: center; justify-content: space-between; }\n\n .ci-params-title {\n font-size: 16px;\n font-weight: 700;\n color: var(--text-primary);\n letter-spacing: -0.01em;\n }\n\n .ci-reset-btn {\n display: inline-flex;\n align-items: center;\n gap: 5px;\n background: none;\n border: none;\n cursor: pointer;\n color: var(--text-secondary);\n font-family: inherit;\n font-size: 12.5px;\n font-weight: 500;\n padding: 4px 8px;\n border-radius: var(--radius-sm);\n transition: color 0.15s, background 0.15s;\n }\n .ci-reset-btn:hover { color: var(--text-primary); background: var(--bg-soft); }\n\n \/* \u2500\u2500 Segmented toggle \u2500\u2500 *\/\n .ci-seg-wrap { display: flex; flex-direction: column; gap: 7px; }\n\n .ci-seg {\n display: flex;\n gap: 3px;\n padding: 3px;\n background: var(--bg-muted);\n border: 1px solid var(--border);\n border-radius: var(--radius-sm);\n }\n\n .ci-seg-btn {\n flex: 1;\n padding: 7px 8px;\n border: none;\n cursor: pointer;\n background: transparent;\n color: var(--text-secondary);\n font-family: inherit;\n font-size: 12px;\n font-weight: 500;\n border-radius: 4px;\n transition: background 0.12s, color 0.12s, box-shadow 0.12s;\n white-space: nowrap;\n line-height: 1.3;\n }\n .ci-seg-btn--active {\n background: var(--bg);\n color: var(--text-primary);\n box-shadow: 0 1px 3px rgba(0,0,0,.08);\n }\n\n \/* \u2500\u2500 Number input field \u2500\u2500 *\/\n .ci-field { display: flex; flex-direction: column; gap: 6px; cursor: auto; }\n\n .ci-field-head {\n display: flex;\n align-items: baseline;\n justify-content: space-between;\n gap: 8px;\n }\n\n .ci-field-label { font-size: 13px; font-weight: 500; color: var(--text-secondary); }\n .ci-field-hint { font-size: 11px; color: var(--gray-650); flex-shrink: 0; }\n\n .ci-field-input-wrap { position: relative; display: flex; align-items: center; }\n\n .ci-field-input {\n width: 100%;\n padding: 10px 50px 10px 13px;\n border: 1px solid var(--border-mid);\n border-radius: var(--radius-sm);\n font-family: ui-monospace, 'SF Mono', Menlo, Consolas, monospace;\n font-size: 15px;\n font-weight: 500;\n color: var(--text-primary);\n background: var(--bg);\n outline: none;\n transition: border-color 0.15s, box-shadow 0.15s;\n appearance: textfield;\n -moz-appearance: textfield;\n }\n .ci-field-input::-webkit-outer-spin-button,\n .ci-field-input::-webkit-inner-spin-button { -webkit-appearance: none; margin: 0; }\n .ci-field-input:hover { border-color: var(--green-mid); }\n .ci-field-input:focus { border-color: var(--green); box-shadow: 0 0 0 3px rgba(26,107,60,.15); }\n\n .ci-field-suffix {\n position: absolute;\n right: 12px;\n font-size: 12px;\n color: var(--gray-650);\n pointer-events: none;\n user-select: none;\n }\n\n .ci-field-grid {\n display: grid;\n grid-template-columns: 1fr 1fr;\n gap: 12px;\n }\n\n .ci-divider { height: 1px; background: var(--border); }\n\n \/* \u2500\u2500 Results column \u2500\u2500 *\/\n .ci-results { display: flex; flex-direction: column; gap: 14px; }\n\n \/* \u2500\u2500 Readout rows \u2500\u2500 *\/\n .ci-readouts { padding: 6px 22px 12px; flex: 1; }\n\n .ci-readout {\n display: flex;\n align-items: baseline;\n justify-content: space-between;\n padding: 11px 0;\n border-bottom: 1px solid var(--border);\n gap: 12px;\n }\n .ci-readout:last-child { border-bottom: none; }\n .ci-readout--big { padding: 18px 0 20px; }\n\n .ci-readout-label {\n font-size: 12px;\n font-weight: 500;\n color: var(--text-secondary);\n line-height: 1.4;\n }\n .ci-readout--big .ci-readout-label {\n font-size: 12px;\n font-weight: 600;\n text-transform: uppercase;\n letter-spacing: 0.05em;\n }\n\n .ci-readout-val-wrap {\n display: flex;\n align-items: baseline;\n gap: 5px;\n flex-shrink: 0;\n }\n\n .ci-readout-val {\n font-family: ui-monospace, 'SF Mono', Menlo, Consolas, monospace;\n font-size: 17px;\n font-weight: 600;\n color: var(--text-primary);\n font-variant-numeric: tabular-nums;\n letter-spacing: -0.01em;\n line-height: 1;\n }\n .ci-readout--big .ci-readout-val {\n font-size: 42px;\n font-weight: 700;\n letter-spacing: -0.03em;\n }\n .ci-readout-val--accent { color: var(--green); }\n\n .ci-readout-unit {\n font-size: 13px;\n color: var(--gray-650);\n font-weight: 500;\n }\n .ci-readout--big .ci-readout-unit { font-size: 15px; }\n\n \/* \u2500\u2500 Diameters table card \u2500\u2500 *\/\n .ci-diam-card { overflow: hidden; }\n\n .ci-diam-head {\n display: flex;\n align-items: center;\n justify-content: space-between;\n padding: 13px 18px 10px;\n }\n\n .ci-diam-title {\n font-size: 14px;\n font-weight: 700;\n color: var(--text-primary);\n }\n\n .ci-diam-unit {\n font-size: 11px;\n color: var(--gray-650);\n }\n\n \/* \u2500\u2500 Table \u2500\u2500 *\/\n .ci-table {\n width: 100%;\n border-collapse: collapse;\n font-size: 13px;\n font-variant-numeric: tabular-nums;\n }\n .ci-th {\n padding: 8px 14px;\n background: var(--green);\n color: #fff;\n font-size: 11px;\n font-weight: 600;\n letter-spacing: 0.04em;\n white-space: nowrap;\n }\n .ci-th--label { text-align: left; }\n .ci-th--val { text-align: right; }\n .ci-tr { border-top: 1px solid var(--border); }\n .ci-tr--alt { background: var(--bg-soft); }\n .ci-td--label {\n padding: 8px 14px;\n font-weight: 500;\n color: var(--text-secondary);\n font-size: 12.5px;\n }\n .ci-td--val {\n padding: 8px 14px;\n text-align: right;\n color: var(--text-primary);\n font-family: ui-monospace, 'SF Mono', Menlo, Consolas, monospace;\n font-size: 13px;\n }\n\n \/* \u2500\u2500 Formula bar \u2500\u2500 *\/\n .ci-formula-bar {\n display: flex;\n align-items: center;\n gap: 16px;\n flex-wrap: wrap;\n padding: 14px 20px;\n background: var(--bg-soft);\n border: 1px solid var(--border);\n border-radius: var(--radius-md);\n }\n\n .ci-formula-tag {\n font-size: 10px;\n font-weight: 700;\n letter-spacing: 0.1em;\n text-transform: uppercase;\n color: var(--gray-650);\n flex-shrink: 0;\n }\n\n .ci-formula-text {\n font-family: ui-monospace, 'SF Mono', Menlo, Consolas, monospace;\n font-size: 15px;\n color: var(--text-primary);\n font-weight: 500;\n }\n\n .ci-formula-spacer { flex: 1; min-width: 0; }\n\n .ci-formula-toggle {\n display: inline-flex;\n align-items: center;\n gap: 5px;\n background: none;\n border: 1px solid var(--green-light);\n border-radius: var(--radius-sm);\n cursor: pointer;\n color: var(--green);\n font-family: inherit;\n font-size: 12.5px;\n font-weight: 600;\n padding: 5px 10px;\n transition: background 0.15s, border-color 0.15s;\n flex-shrink: 0;\n }\n .ci-formula-toggle:hover { background: var(--green-xlight); border-color: var(--green-mid); }\n .ci-formula-toggle svg { transition: transform 0.2s; }\n .ci-formula-toggle--open svg { transform: rotate(180deg); }\n\n \/* \u2500\u2500 Formula reference panel \u2500\u2500 *\/\n .ci-formula-panel {\n border: 1px solid var(--border);\n border-radius: var(--radius-md);\n overflow: hidden;\n }\n\n .ci-ftable { width: 100%; border-collapse: collapse; font-size: 12.5px; }\n\n .ci-fth {\n padding: 9px 16px;\n background: var(--green);\n color: #fff;\n font-weight: 600;\n font-size: 11px;\n letter-spacing: 0.04em;\n text-align: left;\n }\n .ci-fth--right { text-align: right; }\n\n .ci-ftd {\n padding: 9px 16px;\n border-top: 1px solid var(--border);\n color: var(--text-secondary);\n vertical-align: middle;\n }\n .ci-ftd--val {\n text-align: right;\n font-family: ui-monospace, 'SF Mono', Menlo, Consolas, monospace;\n font-weight: 600;\n color: var(--green);\n }\n\n .hidden { display: none; }\n\n @media (max-width: 900px) {\n body { padding: 28px 16px 48px; }\n .ci-layout { grid-template-columns: 1fr; }\n }\n @media (max-width: 540px) {\n .ci-field-grid { grid-template-columns: 1fr; }\n .ci-readout--big .ci-readout-val { font-size: 30px; }\n }\n <\/style>\n<\/head>\n<body>\n\n <script type=\"application\/ld+json\">\n{\n \"@context\": \"https:\/\/schema.org\",\n \"@type\": \"WebApplication\",\n \"@id\": \"#calc-center-distance\",\n \"name\": \"Spur gear center distance calculator\",\n \"description\": \"Calculate the nominal zero-backlash center distance of a pair of spur gears, along with the module, reference, tip, root and base diameters, gear ratio and speeds.\",\n \"applicationCategory\": \"UtilitiesApplication\",\n \"operatingSystem\": \"Web\",\n \"browserRequirements\": \"Requires JavaScript\",\n \"inLanguage\": \"en\",\n \"isAccessibleForFree\": true,\n \"offers\": {\n \"@type\": \"Offer\",\n \"price\": \"0\",\n \"priceCurrency\": \"EUR\"\n },\n \"featureList\": [\n \"Nominal zero-backlash center distance\",\n \"Module\",\n \"Reference, tip, root and base diameters\",\n \"Gear ratio\",\n \"Output speed and pitch line velocity\"\n ],\n \"about\": [\n {\n \"@type\": \"Thing\",\n \"name\": \"Center distance\"\n },\n {\n \"@type\": \"Thing\",\n \"name\": \"Module\"\n },\n {\n \"@type\": \"Thing\",\n \"name\": \"Gear ratio\"\n }\n ]\n}\n <\/script>\n\n <h1 class=\"article__title\">Spur gear center distance calculator<\/h1>\n <p class=\"article__subtitle\">\n Calculate the nominal zero-backlash center distance for a pair of straight-tooth spur gears\n \u2014 module, reference, tip, root and base diameters, gear ratio and speeds.\n <\/p>\n\n <div class=\"ci-host\">\n\n \n <div class=\"infobox\">\n <div class=\"infobox__title\">\n <svg width=\"13\" height=\"13\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><circle cx=\"12\" cy=\"12\" r=\"10\"><\/circle><line x1=\"12\" y1=\"16\" x2=\"12\" y2=\"12\"><\/line><line x1=\"12\" y1=\"8\" x2=\"12.01\" y2=\"8\"><\/line><\/svg>\n Nominal zero-backlash center distance\n <\/div>\n <p class=\"infobox__text\">\n This calculator returns the nominal center distance for standard full-depth gears without\n profile shift, corresponding to theoretical zero backlash. In practice it is good practice to\n allow a small amount of backlash to compensate for machining tolerances and thermal expansion,\n and to ensure adequate lubrication.\n <\/p>\n <\/div>\n\n \n <div id=\"warn-z1\" class=\"warnbox hidden\">\n <div class=\"warnbox__title\">\n <svg width=\"13\" height=\"13\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><path d=\"M10.29 3.86L1.82 18a2 2 0 0 0 1.71 3h16.94a2 2 0 0 0 1.71-3L13.71 3.86a2 2 0 0 0-3.42 0z\"><\/path><line x1=\"12\" y1=\"9\" x2=\"12\" y2=\"13\"><\/line><line x1=\"12\" y1=\"17\" x2=\"12.01\" y2=\"17\"><\/line><\/svg>\n Warning\n <\/div>\n <p class=\"warnbox__text\" id=\"warn-z1-text\"><\/p>\n <\/div>\n <div id=\"warn-z2\" class=\"warnbox hidden\">\n <div class=\"warnbox__title\">\n <svg width=\"13\" height=\"13\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><path d=\"M10.29 3.86L1.82 18a2 2 0 0 0 1.71 3h16.94a2 2 0 0 0 1.71-3L13.71 3.86a2 2 0 0 0-3.42 0z\"><\/path><line x1=\"12\" y1=\"9\" x2=\"12\" y2=\"13\"><\/line><line x1=\"12\" y1=\"17\" x2=\"12.01\" y2=\"17\"><\/line><\/svg>\n Warning\n <\/div>\n <p class=\"warnbox__text\" id=\"warn-z2-text\"><\/p>\n <\/div>\n <div id=\"warn-df\" class=\"warnbox hidden\">\n <div class=\"warnbox__title\">\n <svg width=\"13\" height=\"13\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><path d=\"M10.29 3.86L1.82 18a2 2 0 0 0 1.71 3h16.94a2 2 0 0 0 1.71-3L13.71 3.86a2 2 0 0 0-3.42 0z\"><\/path><line x1=\"12\" y1=\"9\" x2=\"12\" y2=\"13\"><\/line><line x1=\"12\" y1=\"17\" x2=\"12.01\" y2=\"17\"><\/line><\/svg>\n Warning\n <\/div>\n <p class=\"warnbox__text\">Root diameter \u2264 0: module too large for the selected number of teeth<\/p>\n <\/div>\n\n <div class=\"ci-layout\">\n\n \n <section class=\"ci-card ci-params\">\n <div class=\"ci-params-head\">\n <h2 class=\"ci-params-title\">Parameters<\/h2>\n <button class=\"ci-reset-btn\" id=\"btn-reset\" type=\"button\">\n <svg width=\"13\" height=\"13\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\">\n <polyline points=\"1 4 1 10 7 10\"><\/polyline>\n <path d=\"M3.51 15a9 9 0 1 0 .49-5.66\"><\/path>\n <\/svg>\n Reset\n <\/button>\n <\/div>\n\n \n <div class=\"ci-seg-wrap\">\n <span class=\"ci-field-label\">Calculate<\/span>\n <div class=\"ci-seg\">\n <button class=\"ci-seg-btn ci-seg-btn--active\" id=\"seg-modulo\" type=\"button\">Center distance<\/button>\n <button class=\"ci-seg-btn\" id=\"seg-interasse\" type=\"button\">Module<\/button>\n <\/div>\n <\/div>\n\n \n <div class=\"ci-field-grid\">\n <label class=\"ci-field\" id=\"field-m\">\n <div class=\"ci-field-head\">\n <span class=\"ci-field-label\">Module<\/span>\n <span class=\"ci-field-hint\">m<\/span>\n <\/div>\n <div class=\"ci-field-input-wrap\">\n <input class=\"ci-field-input\" id=\"input-m\" type=\"number\"\n placeholder=\"\u2014\" step=\"0.25\" min=\"0.25\" max=\"20\"\n style=\"padding-right:13px\" \/>\n <\/div>\n <\/label>\n <label class=\"ci-field hidden\" id=\"field-a\">\n <div class=\"ci-field-head\">\n <span class=\"ci-field-label\">Center distance<\/span>\n <span class=\"ci-field-hint\">a \u2014 target<\/span>\n <\/div>\n <div class=\"ci-field-input-wrap\">\n <input class=\"ci-field-input\" id=\"input-a\" type=\"number\"\n placeholder=\"\u2014\" step=\"1\" min=\"1\" \/>\n <span class=\"ci-field-suffix\">mm<\/span>\n <\/div>\n <\/label>\n\n <label class=\"ci-field\">\n <div class=\"ci-field-head\">\n <span class=\"ci-field-label\">Pressure angle<\/span>\n <span class=\"ci-field-hint\">\u03b1<\/span>\n <\/div>\n <div class=\"ci-field-input-wrap\">\n <input class=\"ci-field-input\" id=\"input-alpha\" type=\"number\"\n placeholder=\"\u2014\" step=\"0.5\" min=\"0\" max=\"45\" \/>\n <span class=\"ci-field-suffix\">\u00b0<\/span>\n <\/div>\n <\/label>\n <\/div>\n\n <div class=\"ci-divider\"><\/div>\n\n <div class=\"ci-field-grid\">\n <label class=\"ci-field\">\n <div class=\"ci-field-head\">\n <span class=\"ci-field-label\">Pinion teeth<\/span>\n <span class=\"ci-field-hint\">z\u2081<\/span>\n <\/div>\n <div class=\"ci-field-input-wrap\">\n <input class=\"ci-field-input\" id=\"input-z1\" type=\"number\"\n placeholder=\"\u2014\" step=\"1\" min=\"6\" max=\"300\"\n style=\"padding-right:13px\" \/>\n <\/div>\n <\/label>\n <label class=\"ci-field\">\n <div class=\"ci-field-head\">\n <span class=\"ci-field-label\">Gear teeth<\/span>\n <span class=\"ci-field-hint\">z\u2082<\/span>\n <\/div>\n <div class=\"ci-field-input-wrap\">\n <input class=\"ci-field-input\" id=\"input-z2\" type=\"number\"\n placeholder=\"\u2014\" step=\"1\" min=\"6\" max=\"500\"\n style=\"padding-right:13px\" \/>\n <\/div>\n <\/label>\n <\/div>\n\n <label class=\"ci-field\">\n <div class=\"ci-field-head\">\n <span class=\"ci-field-label\">Input speed<\/span>\n <span class=\"ci-field-hint\">n\u2081<\/span>\n <\/div>\n <div class=\"ci-field-input-wrap\">\n <input class=\"ci-field-input\" id=\"input-n1\" type=\"number\"\n placeholder=\"\u2014\" step=\"50\" min=\"0\"\n style=\"padding-right:52px\" \/>\n <span class=\"ci-field-suffix\">rpm<\/span>\n <\/div>\n <\/label>\n <\/section>\n\n \n <section class=\"ci-results\">\n\n \n <div class=\"ci-card ci-readouts\" id=\"panel-readouts\">\n \n <\/div>\n\n \n <div class=\"ci-card ci-diam-card\">\n <div class=\"ci-diam-head\">\n <h3 class=\"ci-diam-title\">Diameters<\/h3>\n <span class=\"ci-diam-unit\">mm<\/span>\n <\/div>\n <table class=\"ci-table\">\n <thead>\n <tr>\n <th class=\"ci-th ci-th--label\"><\/th>\n <th class=\"ci-th ci-th--val\">Pinion z\u2081<\/th>\n <th class=\"ci-th ci-th--val\">Gear z\u2082<\/th>\n <\/tr>\n <\/thead>\n <tbody id=\"diam-tbody\">\n \n <\/tbody>\n <\/table>\n <\/div>\n <\/section>\n <\/div>\n\n \n <div class=\"ci-formula-bar\">\n <span class=\"ci-formula-tag\">Formula<\/span>\n <span class=\"ci-formula-text\" id=\"formula-main\"><\/span>\n <div class=\"ci-formula-spacer\"><\/div>\n <button class=\"ci-formula-toggle\" id=\"btn-formulas\" type=\"button\">\n <span id=\"formula-toggle-label\">All formulas<\/span>\n <svg width=\"14\" height=\"14\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><polyline points=\"6 9 12 15 18 9\"><\/polyline><\/svg>\n <\/button>\n <\/div>\n\n \n <div class=\"ci-formula-panel hidden\" id=\"panel-formulas\">\n <table class=\"ci-ftable\">\n <thead>\n <tr>\n <th class=\"ci-fth\">Quantity<\/th>\n <th class=\"ci-fth\">Formula<\/th>\n <th class=\"ci-fth ci-fth--right\">Pinion z\u2081<\/th>\n <th class=\"ci-fth ci-fth--right\">Gear z\u2082<\/th>\n <\/tr>\n <\/thead>\n <tbody id=\"ftable-tbody\">\n \n <\/tbody>\n <\/table>\n <\/div>\n\n <\/div>\n\n <script>\n const DEFAULTS = { mode: 'modulo', m: undefined, aIn: undefined, z1: undefined, z2: undefined, alpha: undefined, n1: undefined };\n let state = { ...DEFAULTS };\n let formulasOpen = false;\n\n function fmt(n, d = 2) {\n if (!Number.isFinite(n)) return '\u2014';\n return n.toFixed(d);\n }\n\n function tex(el, str) {\n if (window.katex) katex.render(str, el, { throwOnError: false });\n else el.textContent = str;\n }\n\n function compute(s) {\n const mod = s.mode === 'modulo' ? s.m : (2 * s.aIn) \/ (s.z1 + s.z2);\n const a = s.mode === 'modulo' ? (mod * (s.z1 + s.z2)) \/ 2 : s.aIn;\n const alphaRad = (s.alpha * Math.PI) \/ 180;\n const d1 = mod * s.z1;\n const d2 = mod * s.z2;\n const da1 = d1 + 2 * mod;\n const da2 = d2 + 2 * mod;\n const df1 = d1 - 2.5 * mod;\n const df2 = d2 - 2.5 * mod;\n const db1 = d1 * Math.cos(alphaRad);\n const db2 = d2 * Math.cos(alphaRad);\n const i = s.z2 \/ s.z1;\n const n2 = s.n1 \/ i;\n const v = (Math.PI * d1 * s.n1) \/ 60000;\n return { mod, a, d1, d2, da1, da2, df1, df2, db1, db2, i, n2, v };\n }\n\n function render() {\n const s = state;\n const c = compute(s);\n\n \/\/ Mode toggle\n document.getElementById('seg-modulo').classList.toggle('ci-seg-btn--active', s.mode === 'modulo');\n document.getElementById('seg-interasse').classList.toggle('ci-seg-btn--active', s.mode === 'interasse');\n document.getElementById('field-m').classList.toggle('hidden', s.mode !== 'modulo');\n document.getElementById('field-a').classList.toggle('hidden', s.mode !== 'interasse');\n\n \/\/ Warnings\n const wz1 = document.getElementById('warn-z1');\n const wz2 = document.getElementById('warn-z2');\n const wdf = document.getElementById('warn-df');\n\n if (s.z1 < 17) {\n document.getElementById('warn-z1-text').textContent =\n `z\u2081 = ${s.z1} < 17: risk of undercut on the pinion`;\n wz1.classList.remove('hidden');\n } else { wz1.classList.add('hidden'); }\n\n if (s.z2 < 17) {\n document.getElementById('warn-z2-text').textContent =\n `z\u2082 = ${s.z2} < 17: risk of undercut on the gear`;\n wz2.classList.remove('hidden');\n } else { wz2.classList.add('hidden'); }\n\n if (Number.isFinite(c.df1) && c.df1 <= 0) {\n wdf.classList.remove('hidden');\n } else { wdf.classList.add('hidden'); }\n\n \/\/ Primary readouts\n const isModMode = s.mode === 'modulo';\n const bigLabel = isModMode ? 'Center distance a \u00b7 calculated'\n : 'Module m \u00b7 calculated';\n const bigVal = isModMode ? fmt(c.a) : fmt(c.mod, 3);\n const bigUnit = isModMode ? 'mm' : '';\n const secLabel = isModMode ? 'Module m' : 'Center distance a';\n const secVal = isModMode ? fmt(c.mod, 3) : fmt(c.a);\n const secUnit = isModMode ? '' : 'mm';\n\n document.getElementById('panel-readouts').innerHTML = `\n <div class=\"ci-readout ci-readout--big\">\n <span class=\"ci-readout-label\">${bigLabel}<\/span>\n <div class=\"ci-readout-val-wrap\">\n <span class=\"ci-readout-val ci-readout-val--accent\">${bigVal}<\/span>\n ${bigUnit ? `<span class=\"ci-readout-unit\">${bigUnit}<\/span>` : ''}\n <\/div>\n <\/div>\n <div class=\"ci-readout\">\n <span class=\"ci-readout-label\">${secLabel}<\/span>\n <div class=\"ci-readout-val-wrap\">\n <span class=\"ci-readout-val\">${secVal}<\/span>\n ${secUnit ? `<span class=\"ci-readout-unit\">${secUnit}<\/span>` : ''}\n <\/div>\n <\/div>\n <div class=\"ci-readout\">\n <span class=\"ci-readout-label\">Gear ratio i = z\u2082\/z\u2081<\/span>\n <div class=\"ci-readout-val-wrap\">\n <span class=\"ci-readout-val\">${fmt(c.i, 3)}<\/span>\n <\/div>\n <\/div>\n <div class=\"ci-readout\">\n <span class=\"ci-readout-label\">Output speed n\u2082<\/span>\n <div class=\"ci-readout-val-wrap\">\n <span class=\"ci-readout-val\">${fmt(c.n2, 1)}<\/span>\n <span class=\"ci-readout-unit\">rpm<\/span>\n <\/div>\n <\/div>\n <div class=\"ci-readout\">\n <span class=\"ci-readout-label\">Pitch line velocity v<\/span>\n <div class=\"ci-readout-val-wrap\">\n <span class=\"ci-readout-val\">${fmt(c.v, 2)}<\/span>\n <span class=\"ci-readout-unit\">m\/s<\/span>\n <\/div>\n <\/div>`;\n\n \/\/ Diameters table\n const DIAM_ROWS = [\n ['Reference d', c.d1, c.d2],\n ['Tip d\u2090', c.da1, c.da2],\n ['Root d<sub>f<\/sub>', c.df1, c.df2],\n ['Base d<sub>b<\/sub>', c.db1, c.db2],\n ];\n document.getElementById('diam-tbody').innerHTML = DIAM_ROWS.map(([label, v1, v2], idx) => `\n <tr class=\"ci-tr${idx % 2 === 1 ? ' ci-tr--alt' : ''}\">\n <td class=\"ci-td--label\">${label}<\/td>\n <td class=\"ci-td--val\">${fmt(v1)}<\/td>\n <td class=\"ci-td--val\">${fmt(v2)}<\/td>\n <\/tr>`).join('');\n\n \/\/ Formula bar\n tex(document.getElementById('formula-main'), isModMode\n ? 'a = \\\\dfrac{m\\\\,(z_1 + z_2)}{2}'\n : 'm = \\\\dfrac{2a}{z_1 + z_2}');\n\n \/\/ Formula table\n const FORMULA_ROWS = [\n { g: 'Module m', t: 'm = \\\\dfrac{2a}{z_1 + z_2}', v1: fmt(c.mod, 3), v2: null },\n { g: 'Center distance a', t: 'a = \\\\dfrac{m\\\\,(z_1 + z_2)}{2}', v1: fmt(c.a) + ' mm', v2: null },\n { g: 'Reference dia. d', t: 'd = m\\\\,z', v1: fmt(c.d1) + ' mm', v2: fmt(c.d2) + ' mm' },\n { g: 'Tip dia. d\u2090', t: 'd_a = d + 2m = m\\\\,(z + 2)', v1: fmt(c.da1) + ' mm', v2: fmt(c.da2) + ' mm' },\n { g: 'Root dia. d_f', t: 'd_f = d - 2.5\\\\,m = m\\\\,(z - 2.5)', v1: fmt(c.df1) + ' mm', v2: fmt(c.df2) + ' mm' },\n { g: 'Base dia. d_b', t: 'd_b = d\\\\cos\\\\alpha', v1: fmt(c.db1) + ' mm', v2: fmt(c.db2) + ' mm' },\n { g: 'Ratio i', t: 'i = \\\\dfrac{z_2}{z_1} = \\\\dfrac{n_1}{n_2}', v1: fmt(c.i, 3), v2: null },\n { g: 'Pitch line vel. v', t: 'v = \\\\dfrac{\\\\pi\\\\,d_1\\\\,n_1}{60\\\\,000}', v1: fmt(c.v, 3) + ' m\/s', v2: null },\n ];\n const ftbody = document.getElementById('ftable-tbody');\n ftbody.innerHTML = FORMULA_ROWS.map(({ g, v1, v2 }, idx) => `\n <tr class=\"${idx % 2 === 1 ? 'ci-tr--alt' : ''}\">\n <td class=\"ci-ftd\">${g}<\/td>\n <td class=\"ci-ftd ci-ftd--tex\"><\/td>\n <td class=\"ci-ftd ci-ftd--val\"${v2 ? '' : ' colspan=\"2\"'}>${v1}<\/td>\n ${v2 ? `<td class=\"ci-ftd ci-ftd--val\">${v2}<\/td>` : ''}\n <\/tr>`).join('');\n ftbody.querySelectorAll('.ci-ftd--tex').forEach((cell, idx) => tex(cell, FORMULA_ROWS[idx].t));\n }\n\n \/\/ \u2500\u2500 Wire inputs \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n document.getElementById('seg-modulo').addEventListener('click', () => {\n state.mode = 'modulo'; render();\n });\n document.getElementById('seg-interasse').addEventListener('click', () => {\n state.mode = 'interasse'; render();\n });\n\n document.getElementById('input-m').addEventListener('input', e => {\n const v = parseFloat(e.target.value);\n state.m = (Number.isFinite(v) && v > 0) ? v : undefined; render();\n });\n document.getElementById('input-a').addEventListener('input', e => {\n const v = parseFloat(e.target.value);\n state.aIn = (Number.isFinite(v) && v > 0) ? v : undefined; render();\n });\n document.getElementById('input-alpha').addEventListener('input', e => {\n const v = parseFloat(e.target.value);\n state.alpha = Number.isFinite(v) ? v : undefined; render();\n });\n document.getElementById('input-z1').addEventListener('input', e => {\n const v = parseFloat(e.target.value);\n state.z1 = Number.isFinite(v) ? Math.max(6, Math.round(v)) : undefined; render();\n });\n document.getElementById('input-z2').addEventListener('input', e => {\n const v = parseFloat(e.target.value);\n state.z2 = Number.isFinite(v) ? 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'Hide' : 'All formulas';\n });\n\n \/\/ \u2500\u2500 Boot \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n render();\n\n \/\/ re-render once KaTeX finishes loading (deferred), in case it wasn't ready\n window.addEventListener('load', render);\n <\/script>\n<\/body>\n<\/html>\n\n","protected":false},"excerpt":{"rendered":"<p>Fundamental geometric relationships to quickly derive diameters and center distances during new design or validation phases.<\/p>\n","protected":false},"parent":0,"template":"","meta":{"_acf_changed":false},"campo-applicazione":[5455],"categoria-ct":[5442],"class_list":["post-25583","centro-tecnico","type-centro-tecnico","status-publish","hentry","campo-applicazione-design","categoria-ct-gear-fundamentals"],"acf":[],"yoast_head":"\n<title>Quick Calculation Formulas for Gears | Stagnoli Gears Shop<\/title>\n<meta name=\"description\" content=\"Find essential formulas for gear calculations, including module, pitch diameter, center distance, transmission ratio, speed and torque.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/shop.stagnoligears.com\/en\/technical-hub\/quick-calculation-formulas-for-gears\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Quick Calculation Formulas for Gears 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