Belt length and transmission geometry 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 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center;\n gap: 7px;\n border: none;\n background: none;\n cursor: pointer;\n padding: 8px 16px;\n border-radius: var(--radius-sm);\n font-family: inherit;\n font-size: 13.5px;\n font-weight: 600;\n color: var(--text-secondary);\n transition: color 0.15s, background 0.15s, box-shadow 0.15s;\n }\n .ci-tab:hover { color: var(--text-primary); }\n .ci-tab--active {\n background: var(--green);\n color: #fff;\n box-shadow: 0 1px 3px rgba(0, 0, 0, 0.08);\n }\n\n .ci-tab-blurb {\n margin: 0;\n max-width: 820px;\n font-size: 13px;\n line-height: 1.55;\n color: var(--text-secondary);\n }\n\n \/* \u2500\u2500 Unit selector \u2500\u2500 *\/\n .ci-unit-row {\n display: flex;\n align-items: center;\n justify-content: space-between;\n gap: 10px;\n }\n .ci-unit-label { font-size: 13px; font-weight: 500; color: var(--text-secondary); }\n .ci-unit-seg {\n display: inline-flex;\n border: 1px solid var(--border-mid);\n border-radius: var(--radius-sm);\n overflow: hidden;\n }\n .ci-unit-btn {\n border: none;\n background: var(--bg);\n cursor: pointer;\n padding: 6px 13px;\n font-family: ui-monospace, 'SF Mono', Menlo, Consolas, monospace;\n font-size: 13px;\n font-weight: 500;\n color: var(--text-secondary);\n border-left: 1px solid var(--border-mid);\n transition: background 0.15s, color 0.15s;\n }\n .ci-unit-btn:first-child { border-left: none; }\n .ci-unit-btn:hover { background: var(--bg-soft); }\n .ci-unit-btn--active { background: var(--green); color: #fff; }\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, 0.05);\n }\n\n .ci-params {\n padding: 22px 22px 20px;\n display: flex;\n flex-direction: column;\n gap: 18px;\n }\n .ci-params-head { display: flex; align-items: center; justify-content: space-between; }\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 .ci-field { display: flex; flex-direction: column; gap: 6px; cursor: auto; }\n .ci-field-head {\n display: flex;\n align-items: baseline;\n justify-content: space-between;\n gap: 8px;\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 -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 .ci-field-input--invalid { border-color: #dc2626; }\n .ci-field-input--invalid:focus { border-color: #dc2626; box-shadow: 0 0 0 3px rgba(220,38,38,.15); }\n\n .ci-field-error { font-size: 11.5px; color: #dc2626; line-height: 1.4; }\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-results { display: flex; flex-direction: column; gap: 14px; }\n\n .ci-readouts { padding: 6px 22px 12px; flex: 1; }\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 .ci-readout-label { font-size: 12px; font-weight: 500; color: var(--text-secondary); line-height: 1.4; }\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 .ci-readout-val-wrap { display: flex; align-items: baseline; gap: 5px; flex-shrink: 0; }\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 { font-size: 42px; font-weight: 700; letter-spacing: -0.03em; }\n .ci-readout-val--accent { color: var(--green); }\n .ci-readout-unit { font-size: 13px; color: var(--gray-650); font-weight: 500; }\n .ci-readout--big .ci-readout-unit { font-size: 15px; }\n\n .ci-warn {\n display: flex;\n align-items: flex-start;\n gap: 8px;\n padding: 10px 14px;\n background: #fffbeb;\n border: 1px solid #f59e0b;\n border-radius: var(--radius-sm);\n font-size: 12.5px;\n color: #78350f;\n line-height: 1.5;\n }\n .ci-warn svg { flex-shrink: 0; margin-top: 1px; }\n\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 .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 .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 .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 .ci-formula-panel { border: 1px solid var(--border); border-radius: var(--radius-md); overflow: hidden; }\n\n .ci-ftable { width: 100%; border-collapse: collapse; font-size: 12.5px; }\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 .ci-tr--alt { background: var(--bg-soft); }\n .ci-ftd { padding: 9px 16px; border-top: 1px solid var(--border); color: var(--text-secondary); vertical-align: middle; }\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 white-space: nowrap;\n }\n\n \/* \u2500\u2500 SVG pulley diagram \u2500\u2500 *\/\n .ci-diagram { padding: 12px 14px 6px; }\n .ci-svg { width: 100%; height: auto; display: block; }\n .ci-svg-pulley { fill: var(--bg-soft); stroke: var(--text-secondary); stroke-width: 2; }\n .ci-svg-dot { fill: var(--text-secondary); }\n .ci-svg-diam-line { stroke: var(--text-secondary); stroke-width: 1.2; }\n .ci-svg-diam-label {\n fill: var(--text-primary);\n font-family: ui-monospace, 'SF Mono', Menlo, Consolas, monospace;\n font-size: 18px;\n font-weight: 700;\n }\n .ci-svg-belt { fill: none; stroke: var(--green); stroke-width: 5; stroke-linejoin: round; }\n .ci-svg-center-line { stroke: var(--text-muted); stroke-width: 1; stroke-dasharray: 4 4; }\n .ci-svg-label--l {\n fill: var(--green);\n font-weight: 600;\n font-family: ui-monospace, 'SF Mono', Menlo, Consolas, monospace;\n font-size: 16px;\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-readout--big .ci-readout-val { font-size: 30px; }\n .ci-unit-row { flex-direction: column; align-items: flex-start; gap: 6px; }\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-belt-length\",\n \"name\": \"Belt length and transmission geometry calculator\",\n \"description\": \"Calculate the belt length, transmission ratio and wrap angles of a two-pulley drive, starting from the pulley diameters and the center distance.\",\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 \"Belt length\",\n \"Transmission ratio\",\n \"Pulley wrap angle\"\n ],\n \"about\": [\n {\n \"@type\": \"Thing\",\n \"name\": \"Belt length\"\n },\n {\n \"@type\": \"Thing\",\n \"name\": \"Transmission ratio\"\n },\n {\n \"@type\": \"Thing\",\n \"name\": \"Wrap angle\"\n }\n ]\n}\n <\/script>\n\n <h1 class=\"article__title\">Belt length calculator<\/h1>\n <p class=\"article__subtitle\">\n Calculate the belt length, the transmission ratio and the wrap angles of a\n two-pulley drive, starting from the pulley diameters and the center distance.\n <\/p>\n\n <div class=\"ci-host\">\n\n \n <div class=\"ci-tabs\" role=\"tablist\" id=\"tabs\"><\/div>\n\n <p class=\"ci-tab-blurb\" id=\"tab-blurb\"><\/p>\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\" id=\"parameters\">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-unit-row\">\n <span class=\"ci-unit-label\">Units<\/span>\n <div class=\"ci-unit-seg\" role=\"group\" aria-label=\"Units\" id=\"unit-seg\"><\/div>\n <\/div>\n\n \n <label class=\"ci-field\">\n <div class=\"ci-field-head\">\n <span class=\"ci-field-label\">Driving pulley diameter<\/span>\n <span class=\"ci-field-hint\" id=\"hint-dm\">d (driving)<\/span>\n <\/div>\n <div class=\"ci-field-input-wrap\">\n <input class=\"ci-field-input\" id=\"input-dm\" type=\"number\" step=\"1\" min=\"0\" placeholder=\"\u2014\" \/>\n <span class=\"ci-field-suffix suffix\">mm<\/span>\n <\/div>\n <\/label>\n\n \n <label class=\"ci-field\">\n <div class=\"ci-field-head\">\n <span class=\"ci-field-label\">Driven pulley diameter<\/span>\n <span class=\"ci-field-hint\" id=\"hint-dc\">D (driven)<\/span>\n <\/div>\n <div class=\"ci-field-input-wrap\">\n <input class=\"ci-field-input\" id=\"input-dc\" type=\"number\" step=\"1\" min=\"0\" placeholder=\"\u2014\" \/>\n <span class=\"ci-field-suffix suffix\">mm<\/span>\n <\/div>\n <span class=\"ci-field-error hidden\" id=\"err-dc\"><\/span>\n <\/label>\n\n \n <label class=\"ci-field\">\n <div class=\"ci-field-head\">\n <span class=\"ci-field-label\">Center distance<\/span>\n <span class=\"ci-field-hint\">C<\/span>\n <\/div>\n <div class=\"ci-field-input-wrap\">\n <input class=\"ci-field-input\" id=\"input-a\" type=\"number\" step=\"1\" min=\"0\" placeholder=\"\u2014\" \/>\n <span class=\"ci-field-suffix suffix\">mm<\/span>\n <\/div>\n <\/label>\n <\/section>\n\n \n <section class=\"ci-results\">\n <div class=\"ci-card ci-diagram\" id=\"diagram\"><\/div>\n\n <div class=\"ci-card ci-readouts\">\n <div class=\"ci-readout ci-readout--big\">\n <span class=\"ci-readout-label\">Belt length L<\/span>\n <div class=\"ci-readout-val-wrap\">\n <span class=\"ci-readout-val ci-readout-val--accent\" id=\"out-L\">\u2014<\/span>\n <span class=\"ci-readout-unit unit-out\">mm<\/span>\n <\/div>\n <\/div>\n <div class=\"ci-readout\">\n <span class=\"ci-readout-label\">Transmission ratio i<\/span>\n <div class=\"ci-readout-val-wrap\">\n <span class=\"ci-readout-val\" id=\"out-i\">\u2014<\/span>\n <\/div>\n <\/div>\n <div class=\"ci-readout\">\n <span class=\"ci-readout-label\">Small pulley wrap \u03b1<\/span>\n <div class=\"ci-readout-val-wrap\">\n <span class=\"ci-readout-val\" id=\"out-a\">\u2014<\/span>\n <span class=\"ci-readout-unit\">\u00b0<\/span>\n <\/div>\n <\/div>\n <\/div>\n\n <div id=\"warnings\"><\/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\">\n <polyline points=\"6 9 12 15 18 9\"><\/polyline>\n <\/svg>\n <\/button>\n <\/div>\n\n <div class=\"ci-formula-panel hidden\" id=\"formula-panel\">\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\">Calculated value<\/th>\n <\/tr>\n <\/thead>\n <tbody id=\"formula-rows\"><\/tbody>\n <\/table>\n <\/div>\n\n <\/div>\n\n <script>\n \/\/ \u2500\u2500 SVG icons \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 const ICON_TREND_DOWN = `<svg width=\"15\" height=\"15\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><polyline points=\"23 18 13.5 8.5 8.5 13.5 1 6\"><\/polyline><polyline points=\"17 18 23 18 23 12\"><\/polyline><\/svg>`;\n const ICON_TREND_UP = `<svg width=\"15\" height=\"15\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><polyline points=\"23 6 13.5 15.5 8.5 10.5 1 18\"><\/polyline><polyline points=\"17 6 23 6 23 12\"><\/polyline><\/svg>`;\n const ICON_WARN = `<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\n \/\/ \u2500\u2500 Units \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 const UNITS = [\n { id: 'mm', label: 'mm', toMm: 1 },\n { id: 'cm', label: 'cm', toMm: 10 },\n { id: 'm', label: 'm', toMm: 1000 },\n ];\n\n \/\/ \u2500\u2500 Tabs \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 const TABS = {\n reduction: {\n id: 'reduction',\n label: 'Reduction',\n icon: ICON_TREND_DOWN,\n blurb: 'The driven pulley is larger than the driving one: output speed decreases and torque increases. Typical uses: conveyor belts, mixers, winches, reducers for electric motors.',\n rLeft: 46, rRight: 76,\n },\n multiplication: {\n id: 'multiplication',\n label: 'Overdrive',\n icon: ICON_TREND_UP,\n blurb: 'The driven pulley is smaller than the driving one: output speed increases and torque decreases. Typical uses: fans, centrifugal pumps and compressors, spindles, centrifuges.',\n rLeft: 76, rRight: 46,\n },\n };\n\n \/\/ \u2500\u2500 Helpers \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 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 \/\/ \u2500\u2500 State \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 let state = {\n tab: 'reduction',\n unitId: 'mm',\n vals: { dm: undefined, dc: undefined, a: undefined },\n formulasOpen: false,\n };\n\n \/\/ \u2500\u2500 Solver \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 function solve({ dm, dc, a }) {\n const ok = [dm, dc, a].every(n => Number.isFinite(n) && n > 0);\n if (!ok) return { ok: false };\n\n const D = Math.max(dm, dc);\n const d = Math.min(dm, dc);\n const L = 2 * a + (Math.PI \/ 2) * (D + d) + Math.pow(D - d, 2) \/ (4 * a);\n\n const ratioSin = (D - d) \/ (2 * a);\n const geomValid = Math.abs(ratioSin) <= 1;\n const beta = geomValid ? (Math.asin(ratioSin) * 180) \/ Math.PI : NaN;\n const alphaSmall = 180 - 2 * beta;\n const alphaBig = 180 + 2 * beta;\n\n const i = dc \/ dm;\n\n return { ok: true, L, D, d, alphaSmall, alphaBig, i, geomValid };\n }\n\n \/\/ \u2500\u2500 Belt-path geometry \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 function buildBelt(x1, r1, x2, r2, cy) {\n const D = x2 - x1;\n const theta = Math.acos((r1 - r2) \/ D);\n const c = Math.cos(theta), s = Math.sin(theta);\n const T1u = [x1 + r1 * c, cy - r1 * s];\n const T2u = [x2 + r2 * c, cy - r2 * s];\n const T1l = [x1 + r1 * c, cy + r1 * s];\n const T2l = [x2 + r2 * c, cy + r2 * s];\n const rightLarge = r2 > r1 ? 1 : 0;\n const leftLarge = r1 > r2 ? 1 : 0;\n const p = (x) => `${x[0].toFixed(1)} ${x[1].toFixed(1)}`;\n return `M ${p(T1u)} L ${p(T2u)} ` +\n `A ${r2} ${r2} 0 ${rightLarge} 1 ${p(T2l)} ` +\n `L ${p(T1l)} ` +\n `A ${r1} ${r1} 0 ${leftLarge} 1 ${p(T1u)} Z`;\n }\n\n function diagramSVG(tabId) {\n const t = TABS[tabId];\n const cy = 150;\n const x1 = 160, x2 = 400;\n const beltPath = buildBelt(x1, t.rLeft, x2, t.rRight, cy);\n\n const bigger = t.rLeft >= t.rRight;\n const leftDia = bigger ? 'D' : 'd';\n const rightDia = bigger ? 'd' : 'D';\n const maxR = Math.max(t.rLeft, t.rRight);\n\n const ANGLE = -40 * Math.PI \/ 180;\n const dx = Math.cos(ANGLE);\n const dy = Math.sin(ANGLE);\n\n function pulley(cx, r, label) {\n const ax = cx + r * dx, ay = cy + r * dy;\n const bx = cx - r * dx, by = cy - r * dy;\n const lx = cx - (r + 12) * dx, ly = cy - (r + 12) * dy;\n return `<g>\n <circle cx=\"${cx}\" cy=\"${cy}\" r=\"${r}\" class=\"ci-svg-pulley\" \/>\n <line x1=\"${ax.toFixed(1)}\" y1=\"${ay.toFixed(1)}\" x2=\"${bx.toFixed(1)}\" y2=\"${by.toFixed(1)}\" class=\"ci-svg-diam-line\" \/>\n <circle cx=\"${cx}\" cy=\"${cy}\" r=\"2.5\" class=\"ci-svg-dot\" \/>\n <text x=\"${lx.toFixed(1)}\" y=\"${(ly + 4).toFixed(1)}\" text-anchor=\"end\" class=\"ci-svg-diam-label\">${label}<\/text>\n <\/g>`;\n }\n\n return `<svg viewBox=\"0 0 560 300\" class=\"ci-svg\" role=\"img\" aria-label=\"Belt drive diagram\">\n <path d=\"${beltPath}\" class=\"ci-svg-belt\" \/>\n <text x=\"${(x1 + x2) \/ 2}\" y=\"${cy - maxR - 12}\" text-anchor=\"middle\" class=\"ci-svg-label--l\">L<\/text>\n ${pulley(x1, t.rLeft, leftDia)}\n ${pulley(x2, t.rRight, rightDia)}\n <line x1=\"${x1}\" y1=\"${cy}\" x2=\"${x2}\" y2=\"${cy}\" class=\"ci-svg-center-line\" \/>\n <circle cx=\"${x1}\" cy=\"${cy}\" r=\"2.5\" class=\"ci-svg-dot\" \/>\n <circle cx=\"${x2}\" cy=\"${cy}\" r=\"2.5\" class=\"ci-svg-dot\" \/>\n <text x=\"${(x1 + x2) \/ 2}\" y=\"${cy - 14}\" text-anchor=\"middle\" class=\"ci-svg-diam-label\">C<\/text>\n <\/svg>`;\n }\n\n \/\/ \u2500\u2500 Build static UI \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n function buildTabs() {\n const wrap = document.getElementById('tabs');\n wrap.innerHTML = Object.values(TABS).map(t => `\n <button role=\"tab\" type=\"button\" data-tab=\"${t.id}\"\n class=\"ci-tab${state.tab === t.id ? ' ci-tab--active' : ''}\"\n aria-selected=\"${state.tab === t.id}\">\n ${t.icon}${t.label}\n <\/button>`).join('');\n wrap.querySelectorAll('.ci-tab').forEach(btn => {\n btn.addEventListener('click', () => { state.tab = btn.dataset.tab; render(); });\n });\n }\n\n function buildUnits() {\n const wrap = document.getElementById('unit-seg');\n wrap.innerHTML = UNITS.map(un => `\n <button type=\"button\" data-unit=\"${un.id}\"\n class=\"ci-unit-btn${state.unitId === un.id ? ' ci-unit-btn--active' : ''}\">${un.label}<\/button>`).join('');\n wrap.querySelectorAll('.ci-unit-btn').forEach(btn => {\n btn.addEventListener('click', () => changeUnit(btn.dataset.unit));\n });\n }\n\n function changeUnit(newId) {\n if (newId === state.unitId) return;\n const from = UNITS.find(u => u.id === state.unitId);\n const to = UNITS.find(u => u.id === newId);\n const factor = from.toMm \/ to.toMm;\n const conv = v => (v === undefined ? undefined : Number((v * factor).toFixed(6)));\n state.vals = { dm: conv(state.vals.dm), dc: conv(state.vals.dc), a: conv(state.vals.a) };\n state.unitId = newId;\n syncInputs();\n render();\n }\n\n function syncInputs() {\n document.getElementById('input-dm').value = state.vals.dm !== undefined ? state.vals.dm : '';\n document.getElementById('input-dc').value = state.vals.dc !== undefined ? state.vals.dc : '';\n document.getElementById('input-a').value = state.vals.a !== undefined ? state.vals.a : '';\n }\n\n function parseField(v) {\n const raw = v.trim();\n if (raw === '') return undefined;\n const n = parseFloat(raw);\n return Number.isFinite(n) ? n : undefined;\n }\n\n \/\/ \u2500\u2500 Render \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 function render() {\n const { tab, vals } = state;\n const unit = UNITS.find(u => u.id === state.unitId);\n const u = unit.label;\n const calc = solve(vals);\n\n \/\/ tabs active state\n document.querySelectorAll('.ci-tab').forEach(btn => {\n const active = btn.dataset.tab === tab;\n btn.classList.toggle('ci-tab--active', active);\n btn.setAttribute('aria-selected', active);\n });\n document.querySelectorAll('.ci-unit-btn').forEach(btn => {\n btn.classList.toggle('ci-unit-btn--active', btn.dataset.unit === state.unitId);\n });\n\n document.getElementById('tab-blurb').textContent = TABS[tab].blurb;\n\n \/\/ hints\n const drivingDia = tab === 'reduction' ? 'd' : 'D';\n const drivenDia = tab === 'reduction' ? 'D' : 'd';\n document.getElementById('hint-dm').textContent = `${drivingDia} (driving)`;\n document.getElementById('hint-dc').textContent = `${drivenDia} (driven)`;\n\n \/\/ unit suffixes\n document.querySelectorAll('.suffix').forEach(s => s.textContent = u);\n document.querySelectorAll('.unit-out').forEach(s => s.textContent = u);\n\n \/\/ diagram\n document.getElementById('diagram').innerHTML = diagramSVG(tab);\n\n \/\/ constraint\n const bothDiam = Number.isFinite(vals.dm) && Number.isFinite(vals.dc);\n const violatesReduction = bothDiam && vals.dc < vals.dm;\n const violatesMultiplication = bothDiam && vals.dc > vals.dm;\n const violated = tab === 'reduction' ? violatesReduction : violatesMultiplication;\n const constraintError = tab === 'reduction'\n ? 'In reduction the driven pulley must be \u2265 the driving one.'\n : 'In overdrive the driven pulley must be \u2264 the driving one.';\n\n const dcInput = document.getElementById('input-dc');\n const errDc = document.getElementById('err-dc');\n dcInput.classList.toggle('ci-field-input--invalid', violated);\n if (violated) { errDc.textContent = constraintError; errDc.classList.remove('hidden'); }\n else { errDc.classList.add('hidden'); }\n\n const showResults = calc.ok && !violated;\n\n \/\/ readouts\n document.getElementById('out-L').textContent = showResults ? fmt(calc.L) : '\u2014';\n document.getElementById('out-i').textContent = showResults ? fmt(calc.i, 3) : '\u2014';\n document.getElementById('out-a').textContent = showResults ? fmt(calc.alphaSmall) : '\u2014';\n\n \/\/ warnings\n const warnings = [];\n if (violated) warnings.push(constraintError + ' Correct the diameters or switch tab.');\n if (showResults && calc.ok && !calc.geomValid)\n warnings.push('Center distance too small for the chosen diameters: the belt cannot wrap both pulleys.');\n if (showResults && Number.isFinite(calc.alphaSmall) && calc.alphaSmall < 120)\n warnings.push(`\u03b1 (small pulley) = ${fmt(calc.alphaSmall)}\u00b0 < 120\u00b0 \u2014 low wrap angle, risk of slippage under load.`);\n\n document.getElementById('warnings').innerHTML = warnings.map(w =>\n `<div class=\"ci-warn\">${ICON_WARN}<span>${w}<\/span><\/div>`).join('');\n\n \/\/ formula panel values\n const FORMULA_ROWS = [\n { g: 'Belt length L', t: 'L = 2C + \\\\dfrac{\\\\pi}{2}\\\\,(D + d) + \\\\dfrac{(D - d)^2}{4C}', v: showResults ? fmt(calc.L) + ' ' + u : '\u2014' },\n { g: 'Transmission ratio i', t: 'i = \\\\dfrac{d_{driven}}{d_{driving}}', v: showResults ? fmt(calc.i, 3) : '\u2014' },\n { g: 'Small pulley wrap', t: '\\\\alpha_{s} = 180^\\\\circ - 2\\\\arcsin\\\\!\\\\left(\\\\dfrac{D - d}{2C}\\\\right)', v: showResults ? fmt(calc.alphaSmall) + '\u00b0' : '\u2014' },\n { g: 'Large pulley wrap', t: '\\\\alpha_{l} = 180^\\\\circ + 2\\\\arcsin\\\\!\\\\left(\\\\dfrac{D - d}{2C}\\\\right)', v: showResults ? fmt(calc.alphaBig) + '\u00b0' : '\u2014' },\n ];\n const rowsWrap = document.getElementById('formula-rows');\n rowsWrap.innerHTML = FORMULA_ROWS.map((r, idx) => `\n <tr class=\"${idx % 2 === 1 ? 'ci-tr--alt' : ''}\">\n <td class=\"ci-ftd\">${r.g}<\/td>\n <td class=\"ci-ftd ci-ftd--tex\"><\/td>\n <td class=\"ci-ftd ci-ftd--val\">${r.v}<\/td>\n <\/tr>`).join('');\n rowsWrap.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 function wireInput(id, key) {\n document.getElementById(id).addEventListener('input', e => {\n state.vals[key] = parseField(e.target.value);\n render();\n });\n }\n\n function init() {\n buildTabs();\n buildUnits();\n wireInput('input-dm', 'dm');\n wireInput('input-dc', 'dc');\n wireInput('input-a', 'a');\n\n document.getElementById('btn-reset').addEventListener('click', () => {\n state.vals = { dm: undefined, dc: undefined, a: undefined };\n syncInputs();\n render();\n });\n\n const panel = document.getElementById('formula-panel');\n const toggle = document.getElementById('btn-formulas');\n toggle.addEventListener('click', () => {\n state.formulasOpen = !state.formulasOpen;\n panel.classList.toggle('hidden', !state.formulasOpen);\n toggle.classList.toggle('ci-formula-toggle--open', state.formulasOpen);\n document.getElementById('formula-toggle-label').textContent =\n state.formulasOpen ? 'Hide' : 'All formulas';\n });\n\n tex(document.getElementById('formula-main'), 'L = 2C + \\\\dfrac{\\\\pi}{2}\\\\,(D + d) + \\\\dfrac{(D - d)^2}{4C}');\n render();\n }\n\n if (document.readyState === 'loading') {\n window.addEventListener('DOMContentLoaded', () => {\n \/\/ ensure katex is ready (deferred); render text falls back gracefully\n init();\n });\n } else {\n init();\n }\n\n \/\/ re-render formulas once KaTeX finishes loading, in case it wasn't ready\n window.addEventListener('load', () => {\n tex(document.getElementById('formula-main'), 'L = 2C + \\\\dfrac{\\\\pi}{2}\\\\,(D + d) + \\\\dfrac{(D - d)^2}{4C}');\n render();\n });\n <\/script>\n<\/body>\n<\/html>\n\n","protected":false},"excerpt":{"rendered":"<p>Calculate the belt length, transmission ratio and wrap angles of a two-pulley drive, starting from the pulley diameters and the center distance.<\/p>\n","protected":false},"parent":0,"template":"","meta":{"_acf_changed":false},"campo-applicazione":[5452],"categoria-ct":[5447],"class_list":["post-25647","centro-tecnico","type-centro-tecnico","status-publish","hentry","campo-applicazione-calcolo","categoria-ct-belts-pulleys-and-belt-drives"],"acf":[],"yoast_head":"\n<title>Belt Length Calculator | Stagnoli Gears Shop<\/title>\n<meta name=\"description\" content=\"Calculate belt length, transmission ratio and wrap angles for two-pulley belt drives.\" \/>\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\/belt-length-and-transmission-geometry-calculator\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Belt Length Calculator | Stagnoli Gears Shop\" \/>\n<meta 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{"id":25647,"date":"2026-07-02T15:36:10","date_gmt":"2026-07-02T13:36:10","guid":{"rendered":"https:\/\/shop.stagnoligears.com\/?post_type=centro-tecnico&p=25647"},"modified":"2026-07-10T13:48:55","modified_gmt":"2026-07-10T11:48:55","slug":"belt-length-and-transmission-geometry-calculator","status":"publish","type":"centro-tecnico","link":"https:\/\/shop.stagnoligears.com\/en\/technical-hub\/belt-length-and-transmission-geometry-calculator\/","title":{"rendered":"Belt length and transmission geometry calculator"},"content":{"rendered":"\n\n\n\n \n \n \n Belt length and transmission geometry 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 }\n\n body { min-height: 100vh; padding: 40px 28px 64px; \n font-family: 'Inter', sans-serif;\n font-size: 14px;\n letter-spacing: 0.02em;\n color: var(--text-primary);}\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 Shell \u2500\u2500 *\/\n .ci-host { display: flex; flex-direction: column; gap: 14px; margin-top: 4px; }\n\n \/* \u2500\u2500 Mode tabs \u2500\u2500 *\/\n .ci-tabs {\n display: inline-flex;\n gap: 4px;\n padding: 4px;\n background: var(--bg-soft);\n border: 1px solid var(--border);\n border-radius: var(--radius-md);\n align-self: flex-start;\n }\n .ci-tab {\n display: inline-flex;\n align-items: center;\n gap: 7px;\n border: none;\n background: none;\n cursor: pointer;\n padding: 8px 16px;\n border-radius: var(--radius-sm);\n font-family: inherit;\n font-size: 13.5px;\n font-weight: 600;\n color: var(--text-secondary);\n transition: color 0.15s, background 0.15s, box-shadow 0.15s;\n }\n .ci-tab:hover { color: var(--text-primary); }\n .ci-tab--active {\n background: var(--green);\n color: #fff;\n box-shadow: 0 1px 3px rgba(0, 0, 0, 0.08);\n }\n\n .ci-tab-blurb {\n margin: 0;\n max-width: 820px;\n font-size: 13px;\n line-height: 1.55;\n color: var(--text-secondary);\n }\n\n \/* \u2500\u2500 Unit selector \u2500\u2500 *\/\n .ci-unit-row {\n display: flex;\n align-items: center;\n justify-content: space-between;\n gap: 10px;\n }\n .ci-unit-label { font-size: 13px; font-weight: 500; color: var(--text-secondary); }\n .ci-unit-seg {\n display: inline-flex;\n border: 1px solid var(--border-mid);\n border-radius: var(--radius-sm);\n overflow: hidden;\n }\n .ci-unit-btn {\n border: none;\n background: var(--bg);\n cursor: pointer;\n padding: 6px 13px;\n font-family: ui-monospace, 'SF Mono', Menlo, Consolas, monospace;\n font-size: 13px;\n font-weight: 500;\n color: var(--text-secondary);\n border-left: 1px solid var(--border-mid);\n transition: background 0.15s, color 0.15s;\n }\n .ci-unit-btn:first-child { border-left: none; }\n .ci-unit-btn:hover { background: var(--bg-soft); }\n .ci-unit-btn--active { background: var(--green); color: #fff; }\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, 0.05);\n }\n\n .ci-params {\n padding: 22px 22px 20px;\n display: flex;\n flex-direction: column;\n gap: 18px;\n }\n .ci-params-head { display: flex; align-items: center; justify-content: space-between; }\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 .ci-field { display: flex; flex-direction: column; gap: 6px; cursor: auto; }\n .ci-field-head {\n display: flex;\n align-items: baseline;\n justify-content: space-between;\n gap: 8px;\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 -moz-appearance: textfield;\n }\n 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border-bottom: none; }\n .ci-readout--big { padding: 18px 0 20px; }\n .ci-readout-label { font-size: 12px; font-weight: 500; color: var(--text-secondary); line-height: 1.4; }\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 .ci-readout-val-wrap { display: flex; align-items: baseline; gap: 5px; flex-shrink: 0; }\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 { font-size: 42px; font-weight: 700; letter-spacing: -0.03em; }\n .ci-readout-val--accent { color: var(--green); }\n .ci-readout-unit { font-size: 13px; color: var(--gray-650); font-weight: 500; }\n .ci-readout--big .ci-readout-unit { font-size: 15px; }\n\n .ci-warn {\n display: flex;\n align-items: flex-start;\n gap: 8px;\n padding: 10px 14px;\n background: #fffbeb;\n border: 1px solid #f59e0b;\n border-radius: var(--radius-sm);\n font-size: 12.5px;\n color: #78350f;\n line-height: 1.5;\n }\n .ci-warn svg { flex-shrink: 0; margin-top: 1px; }\n\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 .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 .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 .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 .ci-formula-panel { border: 1px solid var(--border); border-radius: var(--radius-md); overflow: hidden; }\n\n .ci-ftable { width: 100%; border-collapse: collapse; font-size: 12.5px; }\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 .ci-tr--alt { background: var(--bg-soft); }\n .ci-ftd { padding: 9px 16px; border-top: 1px solid var(--border); color: var(--text-secondary); vertical-align: middle; }\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 white-space: nowrap;\n }\n\n \/* \u2500\u2500 SVG pulley diagram \u2500\u2500 *\/\n .ci-diagram { padding: 12px 14px 6px; }\n .ci-svg { width: 100%; height: auto; display: block; }\n .ci-svg-pulley { fill: var(--bg-soft); stroke: var(--text-secondary); stroke-width: 2; }\n .ci-svg-dot { fill: var(--text-secondary); }\n .ci-svg-diam-line { stroke: var(--text-secondary); stroke-width: 1.2; }\n .ci-svg-diam-label {\n fill: var(--text-primary);\n font-family: ui-monospace, 'SF Mono', Menlo, Consolas, monospace;\n font-size: 18px;\n font-weight: 700;\n }\n .ci-svg-belt { fill: none; stroke: var(--green); stroke-width: 5; stroke-linejoin: round; }\n .ci-svg-center-line { stroke: var(--text-muted); stroke-width: 1; stroke-dasharray: 4 4; }\n .ci-svg-label--l {\n fill: var(--green);\n font-weight: 600;\n font-family: ui-monospace, 'SF Mono', Menlo, Consolas, monospace;\n font-size: 16px;\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-readout--big .ci-readout-val { font-size: 30px; }\n .ci-unit-row { flex-direction: column; align-items: flex-start; gap: 6px; }\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-belt-length\",\n \"name\": \"Belt length and transmission geometry calculator\",\n \"description\": \"Calculate the belt length, transmission ratio and wrap angles of a two-pulley drive, starting from the pulley diameters and the center distance.\",\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 \"Belt length\",\n \"Transmission ratio\",\n \"Pulley wrap angle\"\n ],\n \"about\": [\n {\n \"@type\": \"Thing\",\n \"name\": \"Belt length\"\n },\n {\n \"@type\": \"Thing\",\n \"name\": \"Transmission ratio\"\n },\n {\n \"@type\": \"Thing\",\n \"name\": \"Wrap angle\"\n }\n ]\n}\n <\/script>\n\n <h1 class=\"article__title\">Belt length calculator<\/h1>\n <p class=\"article__subtitle\">\n Calculate the belt length, the transmission ratio and the wrap angles of a\n two-pulley drive, starting from the pulley diameters and the center distance.\n <\/p>\n\n <div class=\"ci-host\">\n\n \n <div class=\"ci-tabs\" role=\"tablist\" id=\"tabs\"><\/div>\n\n <p class=\"ci-tab-blurb\" id=\"tab-blurb\"><\/p>\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\" id=\"parameters\">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-unit-row\">\n <span class=\"ci-unit-label\">Units<\/span>\n <div class=\"ci-unit-seg\" role=\"group\" aria-label=\"Units\" id=\"unit-seg\"><\/div>\n <\/div>\n\n \n <label class=\"ci-field\">\n <div class=\"ci-field-head\">\n <span class=\"ci-field-label\">Driving pulley diameter<\/span>\n <span class=\"ci-field-hint\" id=\"hint-dm\">d (driving)<\/span>\n <\/div>\n <div class=\"ci-field-input-wrap\">\n <input class=\"ci-field-input\" id=\"input-dm\" type=\"number\" step=\"1\" min=\"0\" placeholder=\"\u2014\" \/>\n <span class=\"ci-field-suffix suffix\">mm<\/span>\n <\/div>\n <\/label>\n\n \n <label class=\"ci-field\">\n <div class=\"ci-field-head\">\n <span class=\"ci-field-label\">Driven pulley diameter<\/span>\n <span class=\"ci-field-hint\" id=\"hint-dc\">D (driven)<\/span>\n <\/div>\n <div class=\"ci-field-input-wrap\">\n <input class=\"ci-field-input\" id=\"input-dc\" type=\"number\" step=\"1\" min=\"0\" placeholder=\"\u2014\" \/>\n <span class=\"ci-field-suffix suffix\">mm<\/span>\n <\/div>\n <span class=\"ci-field-error hidden\" id=\"err-dc\"><\/span>\n <\/label>\n\n \n <label class=\"ci-field\">\n <div class=\"ci-field-head\">\n <span class=\"ci-field-label\">Center distance<\/span>\n <span class=\"ci-field-hint\">C<\/span>\n <\/div>\n <div class=\"ci-field-input-wrap\">\n <input class=\"ci-field-input\" id=\"input-a\" type=\"number\" step=\"1\" min=\"0\" placeholder=\"\u2014\" \/>\n <span class=\"ci-field-suffix suffix\">mm<\/span>\n <\/div>\n <\/label>\n <\/section>\n\n \n <section class=\"ci-results\">\n <div class=\"ci-card ci-diagram\" id=\"diagram\"><\/div>\n\n <div class=\"ci-card ci-readouts\">\n <div class=\"ci-readout ci-readout--big\">\n <span class=\"ci-readout-label\">Belt length L<\/span>\n <div class=\"ci-readout-val-wrap\">\n <span class=\"ci-readout-val ci-readout-val--accent\" id=\"out-L\">\u2014<\/span>\n <span class=\"ci-readout-unit unit-out\">mm<\/span>\n <\/div>\n <\/div>\n <div class=\"ci-readout\">\n <span class=\"ci-readout-label\">Transmission ratio i<\/span>\n <div class=\"ci-readout-val-wrap\">\n <span class=\"ci-readout-val\" id=\"out-i\">\u2014<\/span>\n <\/div>\n <\/div>\n <div class=\"ci-readout\">\n <span class=\"ci-readout-label\">Small pulley wrap \u03b1<\/span>\n <div class=\"ci-readout-val-wrap\">\n <span class=\"ci-readout-val\" id=\"out-a\">\u2014<\/span>\n <span class=\"ci-readout-unit\">\u00b0<\/span>\n <\/div>\n <\/div>\n <\/div>\n\n <div id=\"warnings\"><\/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\">\n <polyline points=\"6 9 12 15 18 9\"><\/polyline>\n <\/svg>\n <\/button>\n <\/div>\n\n <div class=\"ci-formula-panel hidden\" id=\"formula-panel\">\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\">Calculated value<\/th>\n <\/tr>\n <\/thead>\n <tbody id=\"formula-rows\"><\/tbody>\n <\/table>\n <\/div>\n\n <\/div>\n\n <script>\n \/\/ \u2500\u2500 SVG icons \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 const ICON_TREND_DOWN = `<svg width=\"15\" height=\"15\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><polyline points=\"23 18 13.5 8.5 8.5 13.5 1 6\"><\/polyline><polyline points=\"17 18 23 18 23 12\"><\/polyline><\/svg>`;\n const ICON_TREND_UP = `<svg width=\"15\" height=\"15\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><polyline points=\"23 6 13.5 15.5 8.5 10.5 1 18\"><\/polyline><polyline points=\"17 6 23 6 23 12\"><\/polyline><\/svg>`;\n const ICON_WARN = `<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\n \/\/ \u2500\u2500 Units \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 const UNITS = [\n { id: 'mm', label: 'mm', toMm: 1 },\n { id: 'cm', label: 'cm', toMm: 10 },\n { id: 'm', label: 'm', toMm: 1000 },\n ];\n\n \/\/ \u2500\u2500 Tabs \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 const TABS = {\n reduction: {\n id: 'reduction',\n label: 'Reduction',\n icon: ICON_TREND_DOWN,\n blurb: 'The driven pulley is larger than the driving one: output speed decreases and torque increases. Typical uses: conveyor belts, mixers, winches, reducers for electric motors.',\n rLeft: 46, rRight: 76,\n },\n multiplication: {\n id: 'multiplication',\n label: 'Overdrive',\n icon: ICON_TREND_UP,\n blurb: 'The driven pulley is smaller than the driving one: output speed increases and torque decreases. Typical uses: fans, centrifugal pumps and compressors, spindles, centrifuges.',\n rLeft: 76, rRight: 46,\n },\n };\n\n \/\/ \u2500\u2500 Helpers \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 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 \/\/ \u2500\u2500 State \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 let state = {\n tab: 'reduction',\n unitId: 'mm',\n vals: { dm: undefined, dc: undefined, a: undefined },\n formulasOpen: false,\n };\n\n \/\/ \u2500\u2500 Solver \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 function solve({ dm, dc, a }) {\n const ok = [dm, dc, a].every(n => Number.isFinite(n) && n > 0);\n if (!ok) return { ok: false };\n\n const D = Math.max(dm, dc);\n const d = Math.min(dm, dc);\n const L = 2 * a + (Math.PI \/ 2) * (D + d) + Math.pow(D - d, 2) \/ (4 * a);\n\n const ratioSin = (D - d) \/ (2 * a);\n const geomValid = Math.abs(ratioSin) <= 1;\n const beta = geomValid ? (Math.asin(ratioSin) * 180) \/ Math.PI : NaN;\n const alphaSmall = 180 - 2 * beta;\n const alphaBig = 180 + 2 * beta;\n\n const i = dc \/ dm;\n\n return { ok: true, L, D, d, alphaSmall, alphaBig, i, geomValid };\n }\n\n \/\/ \u2500\u2500 Belt-path geometry \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 function buildBelt(x1, r1, x2, r2, cy) {\n const D = x2 - x1;\n const theta = Math.acos((r1 - r2) \/ D);\n const c = Math.cos(theta), s = Math.sin(theta);\n const T1u = [x1 + r1 * c, cy - r1 * s];\n const T2u = [x2 + r2 * c, cy - r2 * s];\n const T1l = [x1 + r1 * c, cy + r1 * s];\n const T2l = [x2 + r2 * c, cy + r2 * s];\n const rightLarge = r2 > r1 ? 1 : 0;\n const leftLarge = r1 > r2 ? 1 : 0;\n const p = (x) => `${x[0].toFixed(1)} ${x[1].toFixed(1)}`;\n return `M ${p(T1u)} L ${p(T2u)} ` +\n `A ${r2} ${r2} 0 ${rightLarge} 1 ${p(T2l)} ` +\n `L ${p(T1l)} ` +\n `A ${r1} ${r1} 0 ${leftLarge} 1 ${p(T1u)} Z`;\n }\n\n function diagramSVG(tabId) {\n const t = TABS[tabId];\n const cy = 150;\n const x1 = 160, x2 = 400;\n const beltPath = buildBelt(x1, t.rLeft, x2, t.rRight, cy);\n\n const bigger = t.rLeft >= t.rRight;\n const leftDia = bigger ? 'D' : 'd';\n const rightDia = bigger ? 'd' : 'D';\n const maxR = Math.max(t.rLeft, t.rRight);\n\n const ANGLE = -40 * Math.PI \/ 180;\n const dx = Math.cos(ANGLE);\n const dy = Math.sin(ANGLE);\n\n function pulley(cx, r, label) {\n const ax = cx + r * dx, ay = cy + r * dy;\n const bx = cx - r * dx, by = cy - r * dy;\n const lx = cx - (r + 12) * dx, ly = cy - (r + 12) * dy;\n return `<g>\n <circle cx=\"${cx}\" cy=\"${cy}\" r=\"${r}\" class=\"ci-svg-pulley\" \/>\n <line x1=\"${ax.toFixed(1)}\" y1=\"${ay.toFixed(1)}\" x2=\"${bx.toFixed(1)}\" y2=\"${by.toFixed(1)}\" class=\"ci-svg-diam-line\" \/>\n <circle cx=\"${cx}\" cy=\"${cy}\" r=\"2.5\" class=\"ci-svg-dot\" \/>\n <text x=\"${lx.toFixed(1)}\" y=\"${(ly + 4).toFixed(1)}\" text-anchor=\"end\" class=\"ci-svg-diam-label\">${label}<\/text>\n <\/g>`;\n }\n\n return `<svg viewBox=\"0 0 560 300\" class=\"ci-svg\" role=\"img\" aria-label=\"Belt drive diagram\">\n <path d=\"${beltPath}\" class=\"ci-svg-belt\" \/>\n <text x=\"${(x1 + x2) \/ 2}\" y=\"${cy - maxR - 12}\" text-anchor=\"middle\" class=\"ci-svg-label--l\">L<\/text>\n ${pulley(x1, t.rLeft, leftDia)}\n ${pulley(x2, t.rRight, rightDia)}\n <line x1=\"${x1}\" y1=\"${cy}\" x2=\"${x2}\" y2=\"${cy}\" class=\"ci-svg-center-line\" \/>\n <circle cx=\"${x1}\" cy=\"${cy}\" r=\"2.5\" class=\"ci-svg-dot\" \/>\n <circle cx=\"${x2}\" cy=\"${cy}\" r=\"2.5\" class=\"ci-svg-dot\" \/>\n <text x=\"${(x1 + x2) \/ 2}\" y=\"${cy - 14}\" text-anchor=\"middle\" class=\"ci-svg-diam-label\">C<\/text>\n <\/svg>`;\n }\n\n \/\/ \u2500\u2500 Build static UI \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n function buildTabs() {\n const wrap = document.getElementById('tabs');\n wrap.innerHTML = Object.values(TABS).map(t => `\n <button role=\"tab\" type=\"button\" data-tab=\"${t.id}\"\n class=\"ci-tab${state.tab === t.id ? ' ci-tab--active' : ''}\"\n aria-selected=\"${state.tab === t.id}\">\n ${t.icon}${t.label}\n <\/button>`).join('');\n wrap.querySelectorAll('.ci-tab').forEach(btn => {\n btn.addEventListener('click', () => { state.tab = btn.dataset.tab; render(); });\n });\n }\n\n function buildUnits() {\n const wrap = document.getElementById('unit-seg');\n wrap.innerHTML = UNITS.map(un => `\n <button type=\"button\" data-unit=\"${un.id}\"\n class=\"ci-unit-btn${state.unitId === un.id ? ' ci-unit-btn--active' : ''}\">${un.label}<\/button>`).join('');\n wrap.querySelectorAll('.ci-unit-btn').forEach(btn => {\n btn.addEventListener('click', () => changeUnit(btn.dataset.unit));\n });\n }\n\n function changeUnit(newId) {\n if (newId === state.unitId) return;\n const from = UNITS.find(u => u.id === state.unitId);\n const to = UNITS.find(u => u.id === newId);\n const factor = from.toMm \/ to.toMm;\n const conv = v => (v === undefined ? undefined : Number((v * factor).toFixed(6)));\n state.vals = { dm: conv(state.vals.dm), dc: conv(state.vals.dc), a: conv(state.vals.a) };\n state.unitId = newId;\n syncInputs();\n render();\n }\n\n function syncInputs() {\n document.getElementById('input-dm').value = state.vals.dm !== undefined ? state.vals.dm : '';\n document.getElementById('input-dc').value = state.vals.dc !== undefined ? state.vals.dc : '';\n document.getElementById('input-a').value = state.vals.a !== undefined ? state.vals.a : '';\n }\n\n function parseField(v) {\n const raw = v.trim();\n if (raw === '') return undefined;\n const n = parseFloat(raw);\n return Number.isFinite(n) ? n : undefined;\n }\n\n \/\/ \u2500\u2500 Render \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 function render() {\n const { tab, vals } = state;\n const unit = UNITS.find(u => u.id === state.unitId);\n const u = unit.label;\n const calc = solve(vals);\n\n \/\/ tabs active state\n document.querySelectorAll('.ci-tab').forEach(btn => {\n const active = btn.dataset.tab === tab;\n btn.classList.toggle('ci-tab--active', active);\n btn.setAttribute('aria-selected', active);\n });\n document.querySelectorAll('.ci-unit-btn').forEach(btn => {\n btn.classList.toggle('ci-unit-btn--active', btn.dataset.unit === state.unitId);\n });\n\n document.getElementById('tab-blurb').textContent = TABS[tab].blurb;\n\n \/\/ hints\n const drivingDia = tab === 'reduction' ? 'd' : 'D';\n const drivenDia = tab === 'reduction' ? 'D' : 'd';\n document.getElementById('hint-dm').textContent = `${drivingDia} (driving)`;\n document.getElementById('hint-dc').textContent = `${drivenDia} (driven)`;\n\n \/\/ unit suffixes\n document.querySelectorAll('.suffix').forEach(s => s.textContent = u);\n document.querySelectorAll('.unit-out').forEach(s => s.textContent = u);\n\n \/\/ diagram\n document.getElementById('diagram').innerHTML = diagramSVG(tab);\n\n \/\/ constraint\n const bothDiam = Number.isFinite(vals.dm) && Number.isFinite(vals.dc);\n const violatesReduction = bothDiam && vals.dc < vals.dm;\n const violatesMultiplication = bothDiam && vals.dc > vals.dm;\n const violated = tab === 'reduction' ? violatesReduction : violatesMultiplication;\n const constraintError = tab === 'reduction'\n ? 'In reduction the driven pulley must be \u2265 the driving one.'\n : 'In overdrive the driven pulley must be \u2264 the driving one.';\n\n const dcInput = document.getElementById('input-dc');\n const errDc = document.getElementById('err-dc');\n dcInput.classList.toggle('ci-field-input--invalid', violated);\n if (violated) { errDc.textContent = constraintError; errDc.classList.remove('hidden'); }\n else { errDc.classList.add('hidden'); }\n\n const showResults = calc.ok && !violated;\n\n \/\/ readouts\n document.getElementById('out-L').textContent = showResults ? fmt(calc.L) : '\u2014';\n document.getElementById('out-i').textContent = showResults ? fmt(calc.i, 3) : '\u2014';\n document.getElementById('out-a').textContent = showResults ? fmt(calc.alphaSmall) : '\u2014';\n\n \/\/ warnings\n const warnings = [];\n if (violated) warnings.push(constraintError + ' Correct the diameters or switch tab.');\n if (showResults && calc.ok && !calc.geomValid)\n warnings.push('Center distance too small for the chosen diameters: the belt cannot wrap both pulleys.');\n if (showResults && Number.isFinite(calc.alphaSmall) && calc.alphaSmall < 120)\n warnings.push(`\u03b1 (small pulley) = ${fmt(calc.alphaSmall)}\u00b0 < 120\u00b0 \u2014 low wrap angle, risk of slippage under load.`);\n\n document.getElementById('warnings').innerHTML = warnings.map(w =>\n `<div class=\"ci-warn\">${ICON_WARN}<span>${w}<\/span><\/div>`).join('');\n\n \/\/ formula panel values\n const FORMULA_ROWS = [\n { g: 'Belt length L', t: 'L = 2C + \\\\dfrac{\\\\pi}{2}\\\\,(D + d) + \\\\dfrac{(D - d)^2}{4C}', v: showResults ? fmt(calc.L) + ' ' + u : '\u2014' },\n { g: 'Transmission ratio i', t: 'i = \\\\dfrac{d_{driven}}{d_{driving}}', v: showResults ? fmt(calc.i, 3) : '\u2014' },\n { g: 'Small pulley wrap', t: '\\\\alpha_{s} = 180^\\\\circ - 2\\\\arcsin\\\\!\\\\left(\\\\dfrac{D - d}{2C}\\\\right)', v: showResults ? fmt(calc.alphaSmall) + '\u00b0' : '\u2014' },\n { g: 'Large pulley wrap', t: '\\\\alpha_{l} = 180^\\\\circ + 2\\\\arcsin\\\\!\\\\left(\\\\dfrac{D - d}{2C}\\\\right)', v: showResults ? fmt(calc.alphaBig) + '\u00b0' : '\u2014' },\n ];\n const rowsWrap = document.getElementById('formula-rows');\n rowsWrap.innerHTML = FORMULA_ROWS.map((r, idx) => `\n <tr class=\"${idx % 2 === 1 ? 'ci-tr--alt' : ''}\">\n <td class=\"ci-ftd\">${r.g}<\/td>\n <td class=\"ci-ftd ci-ftd--tex\"><\/td>\n <td class=\"ci-ftd ci-ftd--val\">${r.v}<\/td>\n <\/tr>`).join('');\n rowsWrap.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 function wireInput(id, key) {\n document.getElementById(id).addEventListener('input', e => {\n state.vals[key] = parseField(e.target.value);\n render();\n });\n }\n\n function init() {\n buildTabs();\n buildUnits();\n wireInput('input-dm', 'dm');\n wireInput('input-dc', 'dc');\n wireInput('input-a', 'a');\n\n document.getElementById('btn-reset').addEventListener('click', () => {\n state.vals = { dm: undefined, dc: undefined, a: undefined };\n syncInputs();\n render();\n });\n\n const panel = document.getElementById('formula-panel');\n const toggle = document.getElementById('btn-formulas');\n toggle.addEventListener('click', () => {\n state.formulasOpen = !state.formulasOpen;\n panel.classList.toggle('hidden', !state.formulasOpen);\n toggle.classList.toggle('ci-formula-toggle--open', state.formulasOpen);\n document.getElementById('formula-toggle-label').textContent =\n state.formulasOpen ? 'Hide' : 'All formulas';\n });\n\n tex(document.getElementById('formula-main'), 'L = 2C + \\\\dfrac{\\\\pi}{2}\\\\,(D + d) + \\\\dfrac{(D - d)^2}{4C}');\n render();\n }\n\n if (document.readyState === 'loading') {\n window.addEventListener('DOMContentLoaded', () => {\n \/\/ ensure katex is ready (deferred); render text falls back gracefully\n init();\n });\n } else {\n init();\n }\n\n \/\/ re-render formulas once KaTeX finishes loading, in case it wasn't ready\n window.addEventListener('load', () => {\n tex(document.getElementById('formula-main'), 'L = 2C + \\\\dfrac{\\\\pi}{2}\\\\,(D + d) + \\\\dfrac{(D - d)^2}{4C}');\n render();\n });\n <\/script>\n<\/body>\n<\/html>\n\n","protected":false},"excerpt":{"rendered":"<p>Calculate the belt length, transmission ratio and wrap angles of a two-pulley drive, starting from the pulley diameters and the center distance.<\/p>\n","protected":false},"parent":0,"template":"","meta":{"_acf_changed":false},"campo-applicazione":[5452],"categoria-ct":[5447],"class_list":["post-25647","centro-tecnico","type-centro-tecnico","status-publish","hentry","campo-applicazione-calcolo","categoria-ct-belts-pulleys-and-belt-drives"],"acf":[],"yoast_head":"\n<title>Belt Length Calculator | Stagnoli Gears Shop<\/title>\n<meta name=\"description\" content=\"Calculate belt length, transmission ratio and wrap angles for two-pulley belt drives.\" \/>\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\/belt-length-and-transmission-geometry-calculator\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Belt Length Calculator | Stagnoli Gears Shop\" \/>\n<meta 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