{"id":100314,"date":"2026-02-15T20:09:49","date_gmt":"2026-02-15T20:09:49","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100314"},"modified":"2026-02-15T20:09:49","modified_gmt":"2026-02-15T20:09:49","slug":"worm-gear-calculator","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/bn\/calculators\/worm-gear-calculator\/","title":{"rendered":"\u0995\u09c3\u09ae\u09bf \u0997\u09bf\u09af\u09bc\u09be\u09b0 \u0995\u09cd\u09af\u09be\u09b2\u0995\u09c1\u09b2\u09c7\u099f\u09b0 | \u09a6\u0995\u09cd\u09b7\u09a4\u09be &#038; \u09b8\u09cd\u09ac-\u09b2\u0995 | \u09ac\u09bf\u09a8\u09be\u09ae\u09c2\u09b2\u09cd\u09af\u09c7 \u0985\u09a8\u09b2\u09be\u0987\u09a8 \u099f\u09c1\u09b2"},"content":{"rendered":"\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Worm Gear Calculator\",\"description\":\"Free worm gear design calculator with efficiency and self-locking analysis.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/worm-gear-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}<\/script>\n\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[\n{\"@type\":\"Question\",\"name\":\"What is a worm gear and when is it used?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"A worm gear consists of a worm (screw) meshing with a worm wheel (gear). Used for high reduction ratios (5:1 to 100:1) in a single stage, compact right-angle drives, and applications requiring self-locking (hoists, conveyors).\"}},\n{\"@type\":\"Question\",\"name\":\"What determines worm gear efficiency?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Efficiency depends mainly on lead angle (\u03b3) and friction coefficient (\u03bc). \u03b7 = tan(\u03b3)\/tan(\u03b3+\u03c1) where \u03c1=arctan(\u03bc). Higher lead angles (more starts) give better efficiency. Single-start: 40-65%, double-start: 60-80%, quad-start: 75-92%.\"}},\n{\"@type\":\"Question\",\"name\":\"What is self-locking in worm gears?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Self-locking occurs when the worm wheel cannot drive the worm \u2014 the friction angle exceeds the lead angle (\u03c1 > \u03b3). This typically happens when efficiency is below ~50%. Useful for hoists and holding loads, but generates significant heat.\"}},\n{\"@type\":\"Question\",\"name\":\"How do I calculate worm gear ratio?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Gear ratio i = Z2\/z1, where Z2 is the number of worm wheel teeth and z1 is the number of worm starts. For a single-start worm with a 40-tooth wheel: i = 40\/1 = 40:1.\"}},\n{\"@type\":\"Question\",\"name\":\"What is the lead angle of a worm?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Lead angle \u03b3 = arctan(z1\u00d7m \/ d1), where z1 is number of starts, m is axial module, and d1 is worm reference diameter. Higher lead angle = better efficiency but no self-locking.\"}}\n]}<\/script>\n\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"BreadcrumbList\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/vibromera.eu\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Calculators\",\"item\":\"https:\/\/vibromera.eu\/calculators\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Worm Gear Calculator\",\"item\":\"https:\/\/vibromera.eu\/calculators\/worm-gear-calculator\/\"}]}<\/script>\n\n<link rel=\"preconnect\" href=\"https:\/\/fonts.googleapis.com\">\n\n<link rel=\"preconnect\" href=\"https:\/\/fonts.gstatic.com\" crossorigin>\n\n<link href=\"https:\/\/fonts.googleapis.com\/css2?family=DM+Sans:ital,opsz,wght@0,9..40,300;0,9..40,400;0,9..40,500;0,9..40,600;0,9..40,700;1,9..40,400&#038;family=JetBrains+Mono:wght@400;500;600&#038;family=Fraunces:opsz,wght@9..144,700;9..144,800&#038;display=swap\" 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class=\"vc-header-subtitle\">Design worm gear drives. Enter module, worm starts, wheel teeth, and speed to calculate ratio, efficiency, lead angle, and self-locking check. Efficiency typically 50\u201390%.<\/p>\n    <div class=\"vc-badges\"><span class=\"vc-badge\">Worm Drive<\/span><span class=\"vc-badge\">Self-Locking<\/span><span class=\"vc-badge\">Efficiency<\/span><\/div>\n<\/header>\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\"><label class=\"vc-label\" for=\"vc-mod\">Axial Module <span class=\"vc-label-hint\">(mm)<\/span><\/label><input class=\"vc-input\" type=\"number\" id=\"vc-mod\" inputmode=\"decimal\" step=\"any\" min=\"0.5\" placeholder=\"e.g. 4\" value=\"4\"><\/div>\n            <div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-z1\">Worm Starts <span class=\"vc-label-hint\">(z\u2081)<\/span><\/label><select class=\"vc-select\" id=\"vc-z1\"><option value=\"1\">1 start<\/option><option value=\"2\" selected>2 starts<\/option><option value=\"3\">3 starts<\/option><option value=\"4\">4 starts<\/option><\/select><\/div>\n            <div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-z2\">Worm Wheel Teeth <span class=\"vc-label-hint\">(Z\u2082)<\/span><\/label><input class=\"vc-input\" type=\"number\" id=\"vc-z2\" inputmode=\"decimal\" step=\"1\" min=\"15\" placeholder=\"e.g. 40\" value=\"40\"><\/div>\n            <div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-d1\">Worm Reference \u2300 <span class=\"vc-label-hint\">(mm)<\/span><\/label><input class=\"vc-input\" type=\"number\" id=\"vc-d1\" inputmode=\"decimal\" step=\"any\" min=\"10\" placeholder=\"e.g. 50\" value=\"50\"><\/div>\n            <div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-speed\">Worm Speed <span class=\"vc-label-hint\">(RPM)<\/span><\/label><input class=\"vc-input\" type=\"number\" id=\"vc-speed\" inputmode=\"decimal\" step=\"any\" min=\"1\" placeholder=\"e.g. 1500\" value=\"1500\"><\/div>\n            <div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-mu\">Friction Coefficient <span class=\"vc-label-hint\">(\u03bc)<\/span><\/label><input class=\"vc-input\" type=\"number\" id=\"vc-mu\" inputmode=\"decimal\" step=\"any\" min=\"0.01\" max=\"0.3\" placeholder=\"e.g. 0.05\" value=\"0.05\"><\/div>\n        <\/div>\n        <div class=\"vc-presets\">\n            <div class=\"vc-presets-label\">Quick presets<\/div>\n            <button type=\"button\" class=\"vc-preset-btn\" data-m=\"3\" data-z1=\"1\" data-z2=\"40\" data-d1=\"30\" data-n=\"1500\" data-mu=\"0.08\">1-start, 40:1 (self-lock)<\/button>\n            <button type=\"button\" class=\"vc-preset-btn\" data-m=\"4\" data-z1=\"2\" data-z2=\"40\" data-d1=\"50\" data-n=\"1500\" data-mu=\"0.05\">2-start, 20:1<\/button>\n            <button type=\"button\" class=\"vc-preset-btn\" data-m=\"5\" data-z1=\"4\" data-z2=\"40\" data-d1=\"60\" data-n=\"1000\" data-mu=\"0.04\">4-start, 10:1 (high eff)<\/button>\n        <\/div>\n    <\/form>\n    <div class=\"vc-results\" id=\"vc-results\">\n        <div class=\"vc-results-head\"><h2 class=\"vc-results-title\">Results<\/h2><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><\/div>\n        <div class=\"vc-result-grid\">\n            <div class=\"vc-rcard vc-rcard-primary\"><div class=\"vc-rcard-label\">Gear Ratio &amp; Efficiency<\/div><div class=\"vc-rcard-value\" id=\"vc-r-main\">\u2014<\/div><\/div>\n            <div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Lead Angle (\u03b3)<\/div><div class=\"vc-rcard-value\" id=\"vc-r-gamma\">\u2014<\/div><\/div>\n            <div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Self-Locking<\/div><div class=\"vc-rcard-value\" id=\"vc-r-lock\">\u2014<\/div><\/div>\n            <div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Output Speed<\/div><div class=\"vc-rcard-value\" id=\"vc-r-nout\">\u2014<\/div><\/div>\n            <div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Wheel Pitch Diameter<\/div><div class=\"vc-rcard-value\" id=\"vc-r-d2\">\u2014<\/div><\/div>\n            <div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Center Distance<\/div><div class=\"vc-rcard-value\" id=\"vc-r-a\">\u2014<\/div><\/div>\n        <\/div>\n    <\/div>\n<\/div>\n<div class=\"vc-section vc-open\" id=\"vc-sec-theory\"><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><div class=\"vc-section-body\"><div class=\"vc-section-inner vc-theory\">\n    <h3>Gear Ratio<\/h3><div class=\"vc-formula-box\" id=\"vc-katex-1\"><\/div>\n    <h3>Lead Angle<\/h3><div class=\"vc-formula-box\" id=\"vc-katex-2\"><\/div>\n    <h3>Efficiency<\/h3><div class=\"vc-formula-box\" id=\"vc-katex-3\"><\/div>\n    <p>Self-locking occurs when \u03b3 &lt; \u03c1 (friction angle), i.e., efficiency &lt; ~50%.<\/p>\n    <table class=\"vc-table\"><thead><tr><th>Starts<\/th><th>Typical Lead Angle<\/th><th>Typical Efficiency<\/th><th>Self-Locking?<\/th><\/tr><\/thead><tbody>\n        <tr><td>1<\/td><td>2\u20136\u00b0<\/td><td>40\u201365%<\/td><td>Usually yes<\/td><\/tr>\n        <tr><td>2<\/td><td>6\u201312\u00b0<\/td><td>60\u201380%<\/td><td>Sometimes<\/td><\/tr>\n        <tr><td>3<\/td><td>10\u201318\u00b0<\/td><td>70\u201385%<\/td><td>Rarely<\/td><\/tr>\n        <tr><td>4<\/td><td>14\u201325\u00b0<\/td><td>75\u201392%<\/td><td>No<\/td><\/tr>\n    <\/tbody><\/table>\n<\/div><\/div><\/div>\n<div class=\"vc-section\" id=\"vc-sec-related\"><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><div class=\"vc-section-body\"><div class=\"vc-section-inner\"><div class=\"vc-related\"><a class=\"vc-related-link\" href=\"\/calculators\/spur-gear-calculator\/\">Spur Gear Calculator<\/a><a class=\"vc-related-link\" href=\"\/calculators\/gear-ratio-calculator\/\">Gear Ratio Calculator<\/a><a class=\"vc-related-link\" href=\"\/calculators\/drive-efficiency-calculator\/\">Drive Efficiency Calculator<\/a><\/div><\/div><\/div><\/div>\n<div class=\"vc-section\" id=\"vc-sec-faq\"><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><div class=\"vc-section-body\"><div class=\"vc-section-inner\"><div class=\"vc-faq-list\" id=\"vc-faq-list\"><\/div><\/div><\/div><\/div>\n<div class=\"vc-promo\"><div class=\"vc-promo-text\"><strong>Vibromera \u2014 Portable Balancing &amp; Vibration Analysis<\/strong><br>Professional instruments. Used in 50+ countries.<\/div><a class=\"vc-promo-link\" href=\"https:\/\/vibromera.eu\/\" target=\"_blank\" rel=\"noopener\">Learn More<\/a><\/div>\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<\/div>\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    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    function calculate(){\n        var m=parseFloat($('vc-mod').value),z1=parseInt($('vc-z1').value),z2=parseInt($('vc-z2').value);\n        var d1=parseFloat($('vc-d1').value),n1=parseFloat($('vc-speed').value),mu=parseFloat($('vc-mu').value);\n        if(!m||!z1||!z2||!d1||!n1||m<=0||d1<=0||n1<=0||mu<=0){$('vc-results').classList.remove('vc-visible');return}\n\n        var ratio=z2\/z1;\n        var d2=m*z2;\n        var a=(d1+d2)\/2;\n        var gamma=Math.atan(z1*m\/d1); \/\/ lead angle in radians\n        var gammaDeg=gamma*180\/Math.PI;\n        var rho=Math.atan(mu); \/\/ friction angle\n        var eta=Math.tan(gamma)\/Math.tan(gamma+rho);\n        var selfLock=gamma<rho;\n        var n2=n1\/ratio;\n\n        $('vc-r-main').innerHTML='i = '+fmt(ratio,1)+':1 <span class=\"vc-rcard-unit\">&nbsp; \u03b7 = '+fmt(eta*100,1)+'%<\/span>';\n        $('vc-r-gamma').innerHTML=fmt(gammaDeg,2)+'\u00b0 <span class=\"vc-rcard-unit\">('+z1+' start'+(z1>1?'s':'')+')<\/span>';\n        $('vc-r-lock').innerHTML=selfLock?'<span style=\"color:var(--vc-green)\">\u2713 Self-locking<\/span> <span class=\"vc-rcard-unit\">(\u03b3 &lt; \u03c1)<\/span>':'<span style=\"color:var(--vc-yellow)\">\u2717 Not self-locking<\/span> <span class=\"vc-rcard-unit\">(\u03b3 &gt; \u03c1)<\/span>';\n        $('vc-r-nout').innerHTML=fmt(n2,1)+' <span class=\"vc-rcard-unit\">RPM<\/span>';\n        $('vc-r-d2').innerHTML=fmt(d2,1)+' <span class=\"vc-rcard-unit\">mm<\/span>';\n        $('vc-r-a').innerHTML=fmt(a,1)+' <span class=\"vc-rcard-unit\">mm<\/span>';\n        $('vc-results').classList.add('vc-visible');\n    }\n\n    document.querySelectorAll('.vc-preset-btn').forEach(function(btn){btn.addEventListener('click',function(e){e.preventDefault();$('vc-mod').value=this.getAttribute('data-m');$('vc-z1').value=this.getAttribute('data-z1');$('vc-z2').value=this.getAttribute('data-z2');$('vc-d1').value=this.getAttribute('data-d1');$('vc-speed').value=this.getAttribute('data-n');$('vc-mu').value=this.getAttribute('data-mu');calculate()})});\n    $('vc-form').addEventListener('input',calculate);$('vc-form').addEventListener('change',calculate);\n    $('vc-copy-btn').addEventListener('click',function(){var text='Worm Gear Calculation\\n\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\\n'+$('vc-r-main').textContent+'\\nLead Angle: '+$('vc-r-gamma').textContent+'\\nSelf-Lock: '+$('vc-r-lock').textContent+'\\nOutput: '+$('vc-r-nout').textContent+'\\n\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\\nvibromera.eu\/calculators\/worm-gear-calculator\/';if(navigator.clipboard){navigator.clipboard.writeText(text).then(function(){var b=$('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    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    var faqData=[{q:'What is a worm gear and when is it used?',a:'<p>A worm gear uses a screw (worm) meshing with a wheel for high reduction ratios (5:1 to 100:1) in a single stage. Used for compact right-angle drives and self-locking applications.<\/p>'},{q:'What determines worm gear efficiency?',a:'<p>Lead angle and friction coefficient. \u03b7 = tan(\u03b3)\/tan(\u03b3+\u03c1). More starts = higher lead angle = better efficiency. Single-start: 40\u201365%, quad-start: 75\u201392%.<\/p>'},{q:'What is self-locking in worm gears?',a:'<p>When friction angle exceeds lead angle (\u03c1 > \u03b3), the wheel cannot drive the worm. This happens below ~50% efficiency. Useful for hoists.<\/p>'},{q:'How do I calculate worm gear ratio?',a:'<p>i = Z\u2082\/z\u2081 (wheel teeth \/ worm starts). A single-start worm with 40-tooth wheel gives i = 40:1.<\/p>'},{q:'What is the lead angle of a worm?',a:'<p>\u03b3 = arctan(z\u2081\u00d7m\/d\u2081). 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