{"id":100114,"date":"2026-02-15T20:18:35","date_gmt":"2026-02-15T20:18:35","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100114"},"modified":"2026-02-15T20:18:35","modified_gmt":"2026-02-15T20:18:35","slug":"gear-ratio-calculator","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/bn\/calculators\/gear-ratio-calculator\/","title":{"rendered":"\u0997\u09bf\u09af\u09bc\u09be\u09b0 \u0985\u09a8\u09c1\u09aa\u09be\u09a4 \u0995\u09cd\u09af\u09be\u09b2\u0995\u09c1\u09b2\u09c7\u099f\u09b0 | \u09ac\u09b9\u09c1-\u09b8\u09cd\u09a4\u09b0\u09c0\u09af\u09bc | \u09ac\u09bf\u09a8\u09be\u09ae\u09c2\u09b2\u09cd\u09af\u09c7\u09b0 \u0985\u09a8\u09b2\u09be\u0987\u09a8 \u09b8\u09b0\u099e\u09cd\u099c\u09be\u09ae"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Gear Ratio Calculator\",\"alternateName\":[\"Transmission Ratio Calculator\",\"Gear Train Calculator\",\"Speed Ratio Calculator\"],\"description\":\"Free online gear ratio calculator supporting multi-stage gear trains. Calculate ratio from speed, teeth count, or diameters.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/gear-ratio-calculator\/\",\"applicationCategory\":\"Engineering Calculator\",\"operatingSystem\":\"Any (Web Browser)\",\"offers\":{\"@type\":\"Offer\",\"price\":\"0\",\"priceCurrency\":\"EUR\"},\"creator\":{\"@type\":\"Organization\",\"name\":\"Vibromera\",\"url\":\"https:\/\/vibromera.eu\/\"},\"datePublished\":\"2024-01-01\",\"dateModified\":\"2025-02-14\",\"inLanguage\":\"en\",\"isAccessibleForFree\":true,\"featureList\":[\"Single and multi-stage support\",\"Teeth count calculation\",\"Speed ratio calculation\",\"Diameter-based ratio\",\"Up to 5 stages\",\"Auto-calculation\"],\"keywords\":\"gear ratio, transmission ratio, gear train, multi-stage\"}\n<\/script>\n\n<script type=\"application\/ld+json\">\n{\"@context\":\"https:\/\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[\n{\"@type\":\"Question\",\"name\":\"What is a gear ratio?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Gear ratio (i) is the ratio of angular velocities between input and output shafts. It equals the ratio of teeth counts i = Z2\/Z1 or speed ratio i = n1\/n2. A ratio greater than 1 means speed reduction (torque multiplication).\"}},\n{\"@type\":\"Question\",\"name\":\"How do I calculate multi-stage gear ratio?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"For a multi-stage gear train, the total ratio is the product of individual stage ratios: i_total = i1 \u00d7 i2 \u00d7 i3 \u00d7 ... For example, two stages with i=3 and i=4 give i_total = 12.\"}},\n{\"@type\":\"Question\",\"name\":\"What is the difference between gear ratio and speed ratio?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"They express the same relationship differently. Gear ratio i = Z_driven\/Z_driver = n_input\/n_output. Speed ratio is the inverse: output_speed\/input_speed = 1\/i. Both describe the same gear mesh.\"}},\n{\"@type\":\"Question\",\"name\":\"What is a typical gear ratio range for single stage?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Single-stage spur gears typically achieve ratios of 1:1 to 6:1. Helical gears can go to 10:1. For higher ratios, use multi-stage (e.g., two-stage gearbox: up to 36:1) or worm gears (5:1 to 100:1).\"}},\n{\"@type\":\"Question\",\"name\":\"How does gear ratio affect torque?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Torque is multiplied by the gear ratio (minus losses): T_output = T_input \u00d7 i \u00d7 \u03b7. A 3:1 reduction triples the torque while reducing speed by 3. 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16px;font-size:13px;color:var(--vc-ink-muted)}.vc-footer a{color:var(--vc-accent);text-decoration:none}.vc-footer a:hover{text-decoration:underline}.vc-footer-links{margin-top:8px;font-size:12px}.vc-footer-links a{margin:0 8px}\n.vc-stage-row{display:grid;grid-template-columns:1fr 1fr auto;gap:10px;align-items:end;margin-bottom:10px;padding:12px;background:var(--vc-surface-alt);border:1px solid var(--vc-border-light);border-radius:6px}\n.vc-stage-label{font-family:var(--vc-mono);font-size:11px;font-weight:600;color:var(--vc-accent);margin-bottom:4px}\n.vc-add-btn,.vc-remove-btn{padding:8px 14px;border:1px solid var(--vc-border);border-radius:6px;background:var(--vc-surface);font-family:var(--vc-font);font-size:12px;font-weight:600;cursor:pointer;transition:all .15s}\n.vc-add-btn:hover{border-color:var(--vc-accent);color:var(--vc-accent)}.vc-remove-btn{color:var(--vc-red);padding:8px 10px}.vc-remove-btn:hover{background:var(--vc-red-light);border-color:var(--vc-red)}\n@media print{.vc-section-body{max-height:none!important}.vc-faq-a{max-height:none!important}.vc-results{max-height:none!important;padding:24px!important}.vc-copy-btn,.vc-section-chevron,.vc-faq-chevron,.vc-presets,.vc-promo{display:none!important}}\n.vc-viz{margin:20px 0;background:var(--vc-surface);border:1px solid var(--vc-border-light);border-radius:var(--vc-radius);padding:16px;overflow:hidden}.vc-viz svg{width:100%;height:auto;display:block}.vc-viz-title{font-family:var(--vc-mono);font-size:11px;font-weight:500;letter-spacing:0.1em;text-transform:uppercase;color:var(--vc-ink-muted);margin-bottom:12px}\n<\/style>\n\n<div class=\"vc-calculator\" id=\"vc-gear-ratio\">\n\n<header class=\"vc-header\">\n    <p class=\"vc-header-eyebrow\">Free Engineering Tool #086<\/p>\n    <h1 class=\"vc-header-title\">Gear Ratio Calculator<\/h1>\n    <p class=\"vc-header-subtitle\">Calculate gear transmission ratio from speeds, teeth count, or diameters. Supports multi-stage gear trains with up to 5 stages. i&nbsp;=&nbsp;Z<sub>2<\/sub>\/Z<sub>1<\/sub>&nbsp;=&nbsp;n<sub>1<\/sub>\/n<sub>2<\/sub>.<\/p>\n    <div class=\"vc-badges\">\n        <span class=\"vc-badge\">i = Z\u2082\/Z\u2081<\/span>\n        <span class=\"vc-badge\">Multi-Stage<\/span>\n        <span class=\"vc-badge\">Speed &amp; Torque<\/span>\n    <\/div>\n<\/header>\n\n<div class=\"vc-card\">\n    <form class=\"vc-form\" id=\"vc-form\" autocomplete=\"off\">\n        <div class=\"vc-form-grid\">\n            <div class=\"vc-field\">\n                <label class=\"vc-label\" for=\"vc-n1\">Input Speed <span class=\"vc-label-hint\">(RPM)<\/span><\/label>\n                <input class=\"vc-input\" type=\"number\" id=\"vc-n1\" inputmode=\"decimal\" step=\"any\" min=\"0.1\" placeholder=\"e.g. 1500\" value=\"1500\">\n            <\/div>\n            <div class=\"vc-field\">\n                <label class=\"vc-label\" for=\"vc-power\">Input Power <span class=\"vc-label-hint\">(kW, optional)<\/span><\/label>\n                <input class=\"vc-input\" type=\"number\" id=\"vc-power\" inputmode=\"decimal\" step=\"any\" min=\"0\" placeholder=\"e.g. 15\" value=\"15\">\n            <\/div>\n        <\/div>\n\n        <div style=\"margin-top:18px\">\n            <div class=\"vc-label\" style=\"margin-bottom:12px\">Gear Stages <span class=\"vc-label-hint\">(enter teeth counts Z\u2081 and Z\u2082 for each stage)<\/span><\/div>\n            <div id=\"vc-stages\">\n                <div class=\"vc-stage-row\" data-stage=\"1\">\n                    <div><div class=\"vc-stage-label\">Stage 1 \u2014 Driver Z\u2081<\/div><input class=\"vc-input vc-z1\" type=\"number\" inputmode=\"decimal\" step=\"1\" min=\"6\" placeholder=\"Z\u2081\" value=\"20\"><\/div>\n                    <div><div class=\"vc-stage-label\">Driven Z\u2082<\/div><input class=\"vc-input vc-z2\" type=\"number\" inputmode=\"decimal\" step=\"1\" min=\"6\" placeholder=\"Z\u2082\" value=\"80\"><\/div>\n                    <button type=\"button\" class=\"vc-remove-btn\" title=\"Remove stage\" style=\"visibility:hidden\">\u2715<\/button>\n                <\/div>\n            <\/div>\n            <button type=\"button\" class=\"vc-add-btn\" id=\"vc-add-stage\" style=\"margin-top:8px\">+ Add Stage<\/button>\n        <\/div>\n\n        <div class=\"vc-presets\">\n            <div class=\"vc-presets-label\">Quick presets<\/div>\n            <button type=\"button\" class=\"vc-preset-btn\" data-stages=\"[[20,80]]\" data-n=\"1500\" data-p=\"15\">4:1 Single Stage<\/button>\n            <button type=\"button\" class=\"vc-preset-btn\" data-stages=\"[[18,72],[20,60]]\" data-n=\"1500\" data-p=\"15\">12:1 Two Stage<\/button>\n            <button type=\"button\" class=\"vc-preset-btn\" data-stages=\"[[17,51],[19,57],[20,80]]\" data-n=\"1500\" data-p=\"30\">36:1 Three Stage<\/button>\n        <\/div>\n    <\/form>\n\n    <div class=\"vc-results\" id=\"vc-results\">\n        <div class=\"vc-results-head\">\n            <h2 class=\"vc-results-title\">Results<\/h2>\n            <button type=\"button\" class=\"vc-copy-btn\" id=\"vc-copy-btn\"><svg width=\"14\" height=\"14\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><rect x=\"9\" y=\"9\" width=\"13\" height=\"13\" rx=\"2\"\/><path d=\"M5 15H4a2 2 0 01-2-2V4a2 2 0 012-2h9a2 2 0 012 2v1\"\/><\/svg> Copy<\/button>\n        <\/div>\n        <div class=\"vc-result-grid\">\n            <div class=\"vc-rcard vc-rcard-primary\">\n                <div class=\"vc-rcard-label\">Total Gear Ratio<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-ratio\">\u2014<\/div>\n            <\/div>\n            <div class=\"vc-rcard\">\n                <div class=\"vc-rcard-label\">Output Speed<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-nout\">\u2014<\/div>\n            <\/div>\n            <div class=\"vc-rcard\">\n                <div class=\"vc-rcard-label\">Output Torque (\u03b7\u224897%\/stage)<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-tout\">\u2014<\/div>\n            <\/div>\n            <div class=\"vc-rcard\">\n                <div class=\"vc-rcard-label\">Per-Stage Ratios<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-stages\" style=\"font-size:16px\">\u2014<\/div>\n            <\/div>\n        <\/div>\n        <div class=\"vc-viz\" id=\"vc-viz\"><div class=\"vc-viz-title\">Gear Mesh (First Stage)<\/div><div id=\"vc-viz-svg\"><\/div><\/div>\n    <\/div>\n<\/div>\n\n<div class=\"vc-section vc-open\" id=\"vc-sec-theory\">\n    <button type=\"button\" class=\"vc-section-toggle\" aria-expanded=\"true\"><span class=\"vc-section-toggle-text\"><span class=\"vc-section-icon\">\ud83d\udcd8<\/span><span class=\"vc-section-title\">Theory &amp; Formulas<\/span><\/span><svg class=\"vc-section-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg><\/button>\n    <div class=\"vc-section-body\">\n        <div class=\"vc-section-inner vc-theory\">\n            <h3>Single-Stage Gear Ratio<\/h3>\n            <div class=\"vc-formula-box\" id=\"vc-katex-1\"><\/div>\n            <h3>Multi-Stage Total Ratio<\/h3>\n            <div class=\"vc-formula-box\" id=\"vc-katex-2\"><\/div>\n            <h3>Output Torque<\/h3>\n            <div class=\"vc-formula-box\" id=\"vc-katex-3\"><\/div>\n            <p>Where \u03b7 is efficiency per stage (typically 97\u201399% for spur gears).<\/p>\n            <div class=\"vc-example-box\">\n                <div class=\"vc-example-title\">Example \u2014 Two-Stage Gearbox<\/div>\n                <p><strong>Given:<\/strong> Stage 1: Z\u2081=18, Z\u2082=72; Stage 2: Z\u2081=20, Z\u2082=60; Input = 1500 RPM, 15 kW<\/p>\n                <p>i\u2081 = 72\/18 = 4.0, i\u2082 = 60\/20 = 3.0<\/p>\n                <p>i_total = 4.0 \u00d7 3.0 = <strong>12.0<\/strong><\/p>\n                <p>n_out = 1500 \/ 12 = <strong>125 RPM<\/strong><\/p>\n                <p>T_out = 9549 \u00d7 15 \/ 125 \u00d7 0.97\u00b2 = <strong>1080 N\u00b7m<\/strong><\/p>\n            <\/div>\n        <\/div>\n    <\/div>\n<\/div>\n\n<div class=\"vc-section\" id=\"vc-sec-related\">\n    <button type=\"button\" class=\"vc-section-toggle\" aria-expanded=\"false\"><span class=\"vc-section-toggle-text\"><span class=\"vc-section-icon\">\ud83d\udd17<\/span><span class=\"vc-section-title\">Related Calculators<\/span><\/span><svg class=\"vc-section-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg><\/button>\n    <div class=\"vc-section-body\"><div class=\"vc-section-inner\"><div class=\"vc-related\">\n        <a class=\"vc-related-link\" href=\"\/calculators\/spur-gear-calculator\/\">Spur Gear Calculator<\/a>\n        <a class=\"vc-related-link\" href=\"\/calculators\/worm-gear-calculator\/\">Worm Gear Calculator<\/a>\n        <a class=\"vc-related-link\" href=\"\/calculators\/belt-drive-calculator\/\">Belt Drive Calculator<\/a>\n        <a class=\"vc-related-link\" href=\"\/calculators\/coupling-torque-calculator\/\">Coupling Torque Calculator<\/a>\n    <\/div><\/div><\/div>\n<\/div>\n\n<div class=\"vc-section\" id=\"vc-sec-faq\">\n    <button type=\"button\" class=\"vc-section-toggle\" aria-expanded=\"false\"><span class=\"vc-section-toggle-text\"><span class=\"vc-section-icon\">\u2753<\/span><span class=\"vc-section-title\">Frequently Asked Questions<\/span><\/span><svg class=\"vc-section-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg><\/button>\n    <div class=\"vc-section-body\"><div class=\"vc-section-inner\"><div class=\"vc-faq-list\" id=\"vc-faq-list\"><\/div><\/div><\/div>\n<\/div>\n\n<div class=\"vc-promo\"><div class=\"vc-promo-text\"><strong>Vibromera \u2014 Portable Balancing &amp; Vibration Analysis<\/strong><br>Professional field balancing instruments and software. Used in 50+ countries.<\/div><a class=\"vc-promo-link\" href=\"https:\/\/vibromera.eu\/\" target=\"_blank\" rel=\"noopener\">Learn More<\/a><\/div>\n\n<footer class=\"vc-footer\"><p>\u00a9 2024\u20132025 <a href=\"https:\/\/vibromera.eu\/\">Vibromera<\/a> \u2014 Engineering Calculators<\/p><p style=\"font-size:12px;margin-top:4px;\">Last updated: February 2025<\/p><div class=\"vc-footer-links\"><a href=\"\/calculators\/engineering-calculators\/\">All Calculators<\/a><a href=\"https:\/\/vibromera.eu\/contacts\/\">Contact<\/a><\/div><\/footer>\n\n<\/div>\n\n<script src=\"https:\/\/cdn.jsdelivr.net\/npm\/katex@0.16.11\/dist\/katex.min.js\"><\/script>\n<script>\n(function(){\n    'use strict';\n    var SLUG='gear-ratio-calculator';\n    function $(id){return document.getElementById(id)}\n    function fmt(n,d){if(isNaN(n)||!isFinite(n))return '\u2014';var f=n.toFixed(d===undefined?2:d);return f.replace(\/(\\.\\d*?)0+$\/,'$1').replace(\/\\.$\/,'')}\n\n    var stageCount=1;\n    var stagesEl=$('vc-stages');\n\n    function addStage(z1,z2){\n        if(stageCount>=5) return;\n        stageCount++;\n        var row=document.createElement('div');\n        row.className='vc-stage-row';\n        row.setAttribute('data-stage',stageCount);\n        row.innerHTML='<div><div class=\"vc-stage-label\">Stage '+stageCount+' \u2014 Driver Z\u2081<\/div><input class=\"vc-input vc-z1\" type=\"number\" inputmode=\"decimal\" step=\"1\" min=\"6\" placeholder=\"Z\u2081\" value=\"'+(z1||20)+'\"><\/div><div><div class=\"vc-stage-label\">Driven Z\u2082<\/div><input class=\"vc-input vc-z2\" type=\"number\" inputmode=\"decimal\" step=\"1\" min=\"6\" placeholder=\"Z\u2082\" value=\"'+(z2||60)+'\"><\/div><button type=\"button\" class=\"vc-remove-btn\" title=\"Remove stage\">\u2715<\/button>';\n        stagesEl.appendChild(row);\n        updateRemoveButtons();\n        calculate();\n    }\n\n    function updateRemoveButtons(){\n        var rows=stagesEl.querySelectorAll('.vc-stage-row');\n        rows.forEach(function(r,i){\n            var btn=r.querySelector('.vc-remove-btn');\n            btn.style.visibility=rows.length>1?'visible':'hidden';\n        });\n    }\n\n    stagesEl.addEventListener('click',function(e){\n        if(e.target.classList.contains('vc-remove-btn')){\n            e.target.closest('.vc-stage-row').remove();\n            stageCount--;\n            \/\/ Renumber\n            stagesEl.querySelectorAll('.vc-stage-row').forEach(function(r,i){\n                r.setAttribute('data-stage',i+1);\n                r.querySelector('.vc-stage-label').textContent='Stage '+(i+1)+' \u2014 Driver Z\u2081';\n            });\n            updateRemoveButtons();\n            calculate();\n        }\n    });\n\n    $('vc-add-stage').addEventListener('click',function(){addStage()});\n\n    function calculate(){\n        var n1=parseFloat($('vc-n1').value);\n        var P=parseFloat($('vc-power').value)||0;\n        var rows=stagesEl.querySelectorAll('.vc-stage-row');\n        var totalRatio=1;\n        var stageRatios=[];\n        var valid=true;\n\n        rows.forEach(function(r){\n            var z1=parseFloat(r.querySelector('.vc-z1').value);\n            var z2=parseFloat(r.querySelector('.vc-z2').value);\n            if(!z1||z1<=0||!z2||z2<=0){valid=false;return}\n            var ri=z2\/z1;\n            stageRatios.push(ri);\n            totalRatio*=ri;\n        });\n\n        if(!valid||!n1||n1<=0){$('vc-results').classList.remove('vc-visible');return}\n\n        var nOut=n1\/totalRatio;\n        var eta=Math.pow(0.97,stageRatios.length);\n        var tOut=P>0?9549*P\/nOut*eta:0;\n\n        $('vc-r-ratio').innerHTML=fmt(totalRatio,3)+' <span class=\"vc-rcard-unit\">: 1<\/span>';\n        $('vc-r-nout').innerHTML=fmt(nOut,1)+' <span class=\"vc-rcard-unit\">RPM<\/span>';\n        $('vc-r-tout').innerHTML=tOut>0?fmt(tOut,1)+' <span class=\"vc-rcard-unit\">N\u00b7m<\/span>':'\u2014';\n        $('vc-r-stages').innerHTML=stageRatios.map(function(r,i){return 'i<sub>'+(i+1)+'<\/sub> = '+fmt(r,3)}).join(' &nbsp;\u00d7&nbsp; ');\n\n        $('vc-results').classList.add('vc-visible');\n        \/\/ Draw gear viz for first stage\n        var firstZ1 = parseFloat(rows[0].querySelector('.vc-z1').value) || 20;\n        var firstZ2 = parseFloat(rows[0].querySelector('.vc-z2').value) || 60;\n        drawGearViz(firstZ1, firstZ2);\n    }\n\n    function drawGearViz(z1, z2) {\n        var el = $('vc-viz-svg'); if (!el) return;\n        var W = 500, H = 220;\n        var r1 = 40, r2 = r1 * (z2 \/ z1);\n        if (r2 > 80) { r2 = 80; r1 = r2 * (z1 \/ z2); }\n        if (r1 < 15) r1 = 15;\n        var gap = 3, cx1 = W \/ 2 - r1 - gap \/ 2, cx2 = W \/ 2 + r2 + gap \/ 2, cy = H \/ 2;\n        var s = '<svg viewBox=\"0 0 ' + W + ' ' + H + '\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\">';\n        s += '<rect width=\"' + W + '\" height=\"' + H + '\" fill=\"var(--vc-surface)\" rx=\"4\"\/>';\n        \/\/ Draw gear teeth as circles with notches\n        function drawGear(cx, cy, r, z, color, label) {\n            var toothH = Math.max(r * 0.12, 3), pts = '';\n            for (var i = 0; i < z; i++) {\n                var a1 = (i \/ z) * Math.PI * 2, a2 = ((i + 0.35) \/ z) * Math.PI * 2, a3 = ((i + 0.5) \/ z) * Math.PI * 2, a4 = ((i + 0.85) \/ z) * Math.PI * 2;\n                pts += (i === 0 ? 'M' : 'L') + (cx + (r + toothH) * Math.cos(a1)).toFixed(1) + ',' + (cy + (r + toothH) * Math.sin(a1)).toFixed(1);\n                pts += 'L' + (cx + (r + toothH) * Math.cos(a2)).toFixed(1) + ',' + (cy + (r + toothH) * Math.sin(a2)).toFixed(1);\n                pts += 'L' + (cx + r * Math.cos(a3)).toFixed(1) + ',' + (cy + r * Math.sin(a3)).toFixed(1);\n                pts += 'L' + (cx + r * Math.cos(a4)).toFixed(1) + ',' + (cy + r * Math.sin(a4)).toFixed(1);\n            }\n            pts += 'Z';\n            s += '<path d=\"' + pts + '\" fill=\"' + color + '\" opacity=\"0.15\" stroke=\"' + color + '\" stroke-width=\"1.5\"\/>';\n            s += '<circle cx=\"' + cx + '\" cy=\"' + cy + '\" r=\"4\" fill=\"' + color + '\"\/>';\n            s += '<text x=\"' + cx + '\" y=\"' + (cy - r - toothH - 8) + '\" text-anchor=\"middle\" font-size=\"11\" font-weight=\"600\" font-family=\"var(--vc-mono)\" fill=\"' + color + '\">Z=' + label + '<\/text>';\n        }\n        drawGear(cx1, cy, r1, Math.min(z1, 40), 'var(--vc-blue)', z1);\n        drawGear(cx2, cy, r2, Math.min(z2, 40), 'var(--vc-accent)', z2);\n        \/\/ Rotation arrows\n        s += '<path d=\"M' + (cx1 + r1 + 18) + ',' + (cy - 8) + ' A12,12 0 1,1 ' + (cx1 + r1 + 18) + ',' + (cy + 8) + '\" fill=\"none\" stroke=\"var(--vc-blue)\" stroke-width=\"1.5\" marker-end=\"url(#arrB)\"\/>';\n        s += '<path d=\"M' + (cx2 - r2 - 18) + ',' + (cy + 8) + ' A12,12 0 1,1 ' + (cx2 - r2 - 18) + ',' + (cy - 8) + '\" fill=\"none\" stroke=\"var(--vc-accent)\" stroke-width=\"1.5\" marker-end=\"url(#arrA)\"\/>';\n        s += '<defs><marker id=\"arrB\" markerWidth=\"6\" markerHeight=\"5\" refX=\"6\" refY=\"2.5\" orient=\"auto\"><path d=\"M0,0 L6,2.5 L0,5Z\" fill=\"var(--vc-blue)\"\/><\/marker>';\n        s += '<marker id=\"arrA\" markerWidth=\"6\" markerHeight=\"5\" refX=\"6\" refY=\"2.5\" orient=\"auto\"><path d=\"M0,0 L6,2.5 L0,5Z\" fill=\"var(--vc-accent)\"\/><\/marker><\/defs>';\n        \/\/ Ratio label\n        s += '<text x=\"' + (W \/ 2) + '\" y=\"' + (H - 12) + '\" text-anchor=\"middle\" font-size=\"11\" font-family=\"var(--vc-mono)\" fill=\"var(--vc-ink-secondary)\">i = ' + z2 + '\/' + z1 + ' = ' + (z2 \/ z1).toFixed(2) + '<\/text>';\n        s += '<\/svg>';\n        el.innerHTML = s;\n    }\n\n    \/\/ Presets\n    document.querySelectorAll('.vc-preset-btn').forEach(function(btn){\n        btn.addEventListener('click',function(e){\n            e.preventDefault();\n            var stages=JSON.parse(this.getAttribute('data-stages'));\n            $('vc-n1').value=this.getAttribute('data-n');\n            $('vc-power').value=this.getAttribute('data-p');\n            \/\/ Remove all stage rows, rebuild\n            stagesEl.innerHTML='';\n            stageCount=0;\n            stages.forEach(function(s,i){\n                stageCount++;\n                var row=document.createElement('div');\n                row.className='vc-stage-row';\n                row.setAttribute('data-stage',stageCount);\n                row.innerHTML='<div><div class=\"vc-stage-label\">Stage '+(i+1)+' \u2014 Driver Z\u2081<\/div><input class=\"vc-input vc-z1\" type=\"number\" inputmode=\"decimal\" step=\"1\" min=\"6\" placeholder=\"Z\u2081\" value=\"'+s[0]+'\"><\/div><div><div class=\"vc-stage-label\">Driven Z\u2082<\/div><input class=\"vc-input vc-z2\" type=\"number\" inputmode=\"decimal\" step=\"1\" min=\"6\" placeholder=\"Z\u2082\" value=\"'+s[1]+'\"><\/div><button type=\"button\" class=\"vc-remove-btn\" title=\"Remove stage\">\u2715<\/button>';\n                stagesEl.appendChild(row);\n            });\n            updateRemoveButtons();\n            calculate();\n        });\n    });\n\n    $('vc-form').addEventListener('input',calculate);\n    $('vc-form').addEventListener('change',calculate);\n\n    $('vc-copy-btn').addEventListener('click',function(){\n        var text='Gear Ratio Calculation\\n\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\\nTotal Ratio: '+$('vc-r-ratio').textContent+'\\nOutput Speed: '+$('vc-r-nout').textContent+'\\nOutput Torque: '+$('vc-r-tout').textContent+'\\n\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\\nvibromera.eu\/calculators\/'+SLUG+'\/';\n        if(navigator.clipboard){navigator.clipboard.writeText(text).then(function(){var b=$('vc-copy-btn');b.classList.add('vc-copied');b.innerHTML='<svg width=\"14\" height=\"14\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><polyline points=\"20 6 9 17 4 12\"\/><\/svg> Copied!';setTimeout(function(){b.classList.remove('vc-copied');b.innerHTML='<svg width=\"14\" height=\"14\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><rect x=\"9\" y=\"9\" width=\"13\" height=\"13\" rx=\"2\"\/><path d=\"M5 15H4a2 2 0 01-2-2V4a2 2 0 012-2h9a2 2 0 012 2v1\"\/><\/svg> Copy'},2000)})}\n    });\n\n    document.querySelectorAll('.vc-section-toggle').forEach(function(btn){btn.addEventListener('click',function(){var s=this.closest('.vc-section');s.classList.toggle('vc-open');this.setAttribute('aria-expanded',s.classList.contains('vc-open'))})});\n\n    var faqData=[\n        {q:'What is a gear ratio?',a:'<p>Gear ratio (i) is the ratio of angular velocities between input and output shafts. It equals the ratio of teeth counts i = Z\u2082\/Z\u2081 or speed ratio i = n\u2081\/n\u2082. A ratio greater than 1 means speed reduction (torque multiplication).<\/p>'},\n        {q:'How do I calculate multi-stage gear ratio?',a:'<p>For a multi-stage gear train, the total ratio is the product of individual stage ratios: i_total = i\u2081 \u00d7 i\u2082 \u00d7 i\u2083 \u00d7 \u2026 For example, two stages with i=3 and i=4 give i_total = 12.<\/p>'},\n        {q:'What is the difference between gear ratio and speed ratio?',a:'<p>They express the same relationship differently. Gear ratio i = Z_driven\/Z_driver = n_input\/n_output. Speed ratio is the inverse: output_speed\/input_speed = 1\/i.<\/p>'},\n        {q:'What is a typical gear ratio range for single stage?',a:'<p>Single-stage spur gears: 1:1 to 6:1. Helical gears: up to 10:1. Multi-stage (two-stage): up to 36:1. Worm gears: 5:1 to 100:1 in a single stage.<\/p>'},\n        {q:'How does gear ratio affect torque?',a:'<p>Torque is multiplied by the gear ratio minus losses: T_output = T_input \u00d7 i \u00d7 \u03b7. A 3:1 reduction triples the torque while reducing speed by 3. Typical efficiency per spur gear stage is 97\u201399%.<\/p>'}\n    ];\n    var fl=$('vc-faq-list');faqData.forEach(function(f){fl.innerHTML+='<div class=\"vc-faq-item\"><button type=\"button\" class=\"vc-faq-q\"><span>'+f.q+'<\/span><svg class=\"vc-faq-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg><\/button><div class=\"vc-faq-a\"><div class=\"vc-faq-a-inner\">'+f.a+'<\/div><\/div><\/div>'});\n    fl.addEventListener('click',function(e){var b=e.target.closest('.vc-faq-q');if(b)b.closest('.vc-faq-item').classList.toggle('vc-open')});\n\n    function renderFormulas(){\n        try{\n            katex.render('i = \\\\frac{Z_2}{Z_1} = \\\\frac{n_1}{n_2} = \\\\frac{d_2}{d_1}',$('vc-katex-1'),{displayMode:true,throwOnError:false});\n            katex.render('i_{total} = i_1 \\\\times i_2 \\\\times i_3 \\\\times \\\\ldots \\\\times i_k',$('vc-katex-2'),{displayMode:true,throwOnError:false});\n            katex.render('T_{out} = \\\\frac{9549 \\\\times P}{n_{out}} \\\\times \\\\eta^k',$('vc-katex-3'),{displayMode:true,throwOnError:false});\n        }catch(e){}\n    }\n\n    function init(){renderFormulas();calculate()}\n    if(document.readyState==='loading'){document.addEventListener('DOMContentLoaded',init)}else{init()}\n})();\n<\/script>\n","protected":false},"excerpt":{"rendered":"<p>\u09ac\u09bf\u09a8\u09be\u09ae\u09c2\u09b2\u09cd\u09af\u09c7 \u0985\u09a8\u09b2\u09be\u0987\u09a8 \u0997\u09bf\u09af\u09bc\u09be\u09b0 \u0985\u09a8\u09c1\u09aa\u09be\u09a4 \u0995\u09cd\u09af\u09be\u09b2\u0995\u09c1\u09b2\u09c7\u099f\u09b0\u0964 \u0997\u09a4\u09bf, \u09a6\u09be\u0981\u09a4 \u0997\u09a3\u09a8\u09be \u09ac\u09be \u09ac\u09cd\u09af\u09be\u09b8 \u09a5\u09c7\u0995\u09c7 \u099f\u09cd\u09b0\u09be\u09a8\u09cd\u09b8\u09ae\u09bf\u09b6\u09a8 \u0985\u09a8\u09c1\u09aa\u09be\u09a4 \u0997\u09a3\u09a8\u09be \u0995\u09b0\u09c1\u09a8\u0964 \u09aa\u09b0\u09cd\u09af\u09be\u09af\u09bc\u0995\u09cd\u09b0\u09ae\u09c7 \u09eb \u09aa\u09b0\u09cd\u09af\u09be\u09af\u09bc \u09aa\u09b0\u09cd\u09af\u09a8\u09cd\u09a4 \u09b8\u09b9 \u09ac\u09b9\u09c1-\u09aa\u09b0\u09cd\u09af\u09be\u09af\u09bc \u0997\u09bf\u09af\u09bc\u09be\u09b0 \u099f\u09cd\u09b0\u09c7\u09a8\u0995\u09c7 \u09b8\u09ae\u09b0\u09cd\u09a5\u09a8 \u0995\u09b0\u09c7\u0964 i = Z2\/Z1 = n1\/n2\u0964<\/p>","protected":false},"featured_media":0,"template":"","meta":{"ai_generated_summary":"","footnotes":""},"categories":[],"tags":[],"class_list":["post-100114","calculator","type-calculator","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/calculator\/100114","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/calculator"}],"about":[{"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/types\/calculator"}],"version-history":[{"count":1,"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/calculator\/100114\/revisions"}],"predecessor-version":[{"id":100428,"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/calculator\/100114\/revisions\/100428"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/media?parent=100114"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/categories?post=100114"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/tags?post=100114"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}