{"id":66706,"date":"2026-10-13T08:41:11","date_gmt":"2026-10-13T05:41:11","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=66706"},"modified":"2026-10-13T08:41:11","modified_gmt":"2026-10-13T05:41:11","slug":"belt-length","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/engineering\/belt-length\/","title":{"rendered":"Belt Length"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 id=\"calculator-title\" class=\"text-lg font-display font-bold\">Find the Belt Length for Two Pulleys<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"66706\" data-favorite-title=\"Belt Length\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/engineering\/belt-length\/\" data-favorite-excerpt=\"Calculate the required belt length for a two-pulley drive from the pulley diameters and center distance. Supports open and crossed belt arrangements in metric or imperial units.\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-civil\">\n    <span class=\"icon icon-shape-star-empty\" aria-hidden=\"true\"><\/span>\n  <\/button>\n  <div class=\"calcdash-favorite__tip\" aria-hidden=\"true\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n  <span class=\"sr-only\" role=\"status\" id=\"favorite-status\"><\/span>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/en\/engineering\/belt-length\/\" method=\"POST\" class=\"calculator\" id=\"calculator-66706\" data-post=\"66706\"><fieldset class=\"fieldset-input is-1\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"is-single field\" id=\"input-1\"><span class=\"font-semibold\">Pulleys<\/span><\/div><div class=\"field is-single has-term\" id=\"input-2\"><label for=\"field-2\">Large pulley diameter (D)<\/label><div class=\"term\">D<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"large_pulley_diameter_d\" id=\"field-2\" aria-describedby=\"calc-info-2\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 200\" min=\"0\" value=\"200\"\/><div class=\"grid grid-cols-1\"><select id=\"field-3\" name=\"unit\" aria-label=\"Unit\"><option value=\"mm\" selected>mm<\/option><option value=\"cm\">cm<\/option><option value=\"m\">m<\/option><option value=\"in\">in<\/option><option value=\"ft\">ft<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-2\">Pitch (effective) diameter of the larger pulley.<\/small><\/div><div class=\"field is-single has-term\" id=\"input-3\"><label for=\"field-4\">Small pulley diameter (d)<\/label><div class=\"term\">d<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"small_pulley_diameter_d\" id=\"field-4\" aria-describedby=\"calc-info-4\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 100\" min=\"0\" value=\"100\"\/><div class=\"grid grid-cols-1\"><select id=\"field-5\" name=\"unit\" aria-label=\"Unit\"><option value=\"mm\" selected>mm<\/option><option value=\"cm\">cm<\/option><option value=\"m\">m<\/option><option value=\"in\">in<\/option><option value=\"ft\">ft<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-4\">Pitch (effective) diameter of the smaller pulley.<\/small><\/div><div class=\"is-single field\" id=\"input-4\"><span class=\"font-semibold\">Layout<\/span><\/div><div class=\"field is-single has-term\" id=\"input-5\"><label for=\"field-7\">Center distance (C)<\/label><div class=\"term\">C<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"center_distance_c\" id=\"field-7\" aria-describedby=\"calc-info-7\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 500\" min=\"0\" value=\"500\"\/><div class=\"grid grid-cols-1\"><select id=\"field-8\" name=\"unit\" aria-label=\"Unit\"><option value=\"mm\" selected>mm<\/option><option value=\"cm\">cm<\/option><option value=\"m\">m<\/option><option value=\"in\">in<\/option><option value=\"ft\">ft<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-7\">Distance between the centers (rotation axes) of the two pulleys.<\/small><\/div><div class=\"field is-single\" id=\"input-6\"><label for=\"field-9\">Belt arrangement<\/label><div class=\"grid grid-cols-1\"><select id=\"field-9\" name=\"belt_arrangement\"><option value=\"open\" selected>Open belt \u2014 pulleys rotate the same way<\/option><option value=\"crossed\">Crossed belt \u2014 pulleys rotate opposite ways<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"66706\">Calculate<\/button><button type=\"reset\">Reset<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Calculate automatically<\/label><small>If enabled, the result will update automatically when you change any value.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Belt Length Results<\/h3><div class=\"result-box\"><div class=\"field-result is-column\" id=\"output-1\"><span class=\"field-title\"><span>Approximate required belt length (L)<\/span><span class=\"result-term\">L<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-2\"><span class=\"field-title\"><span>Belt geometry details<\/span><\/span><span class=\"field-value\" id=\"result-2\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><\/div><div class=\"result-actions\"><button type=\"button\" class=\"copy-link\"><svg viewBox=\"0 0 20 20\" fill=\"currentColor\" aria-hidden=\"true\"><path d=\"M12.232 4.232a2.5 2.5 0 0 1 3.536 3.536l-1.225 1.224a.75.75 0 0 0 1.061 1.06l1.224-1.224a4 4 0 0 0-5.656-5.656l-3 3a4 4 0 0 0 .225 5.865.75.75 0 0 0 .977-1.138 2.5 2.5 0 0 1-.142-3.667l3-3Z\"\/><path d=\"M11.603 7.963a.75.75 0 0 0-.977 1.138 2.5 2.5 0 0 1 .142 3.667l-3 3a2.5 2.5 0 0 1-3.536-3.536l1.225-1.224a.75.75 0 0 0-1.061-1.06l-1.224 1.224a4 4 0 1 0 5.656 5.656l3-3a4 4 0 0 0-.225-5.865Z\"\/><\/svg><span class=\"copy-link__text\">Copy link to this calculation<\/span><\/button><span class=\"sr-only\" role=\"status\" id=\"copy-link-status\"><\/span><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Leave a Comment<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"66706\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">How did this result make you feel?<\/p><div role=\"group\" aria-labelledby=\"calc-reactions-title\" class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Like <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">Helpful <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"confused\"><span class=\"reaction-count\" data-reaction-count=\"confused\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Confused <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"disappointed\"><span class=\"reaction-count\" data-reaction-count=\"disappointed\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">Disappointed <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\u274c <\/span><span class=\"reaction-description font-medium\">Inaccurate <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><div class=\"calcdash-ad not-prose calcdash-ad--calc_result calcdash-ad--in-article\"><ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-1721569815777345\" data-ad-slot=\"6317458308\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\"><\/ins><script>(adsbygoogle = window.adsbygoogle || []).push({});<\/script><\/div>\n<style id=\"wpcoderpro-inline-1\">.formula-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>Belt Length Formula<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Formula<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n\\[ L \\approx 2C + \\frac{\\pi}{2}(D + d) + \\frac{(D \\mp d)^2}{4C} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(L\\) \u2014 required belt length (same unit as the inputs)<\/li>\n<li>\\(C\\) \u2014 center distance between the two pulley axes<\/li>\n<li>\\(D\\) \u2014 pitch (effective) diameter of the large pulley<\/li>\n<li>\\(d\\) \u2014 pitch (effective) diameter of the small pulley<\/li>\n<\/ul>\n<p>Use the minus sign \\((D - d)\\) for an open belt and the plus sign \\((D + d)\\) for a crossed belt. The formula is the standard engineering approximation: \\(2C\\) covers the two straight spans, the arc term wraps the belt around both pulleys, and the squared term corrects for the extra length caused by unequal pulley sizes.<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-459\">.calculation-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>Belt Length \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> an open belt connects a 200 mm pulley to a 100 mm pulley whose shafts are 500 mm apart.<\/p>\n<p>\\[ L \\approx 2(500) + \\frac{\\pi}{2}(200 + 100) + \\frac{(200 - 100)^2}{4 \\times 500} \\]<\/p>\n<p>\\[ L \\approx 1000 + 471.24 + 5 = 1476.24 \\text{ mm} \\]<\/p>\n<p><strong>Result:<\/strong> the required belt length is approximately <strong>1476 mm (1.476 m, or 58.1 in)<\/strong>. You can reproduce this by leaving the calculator's default values unchanged and pressing Calculate.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to use the calculator<\/h2>\n<ol>\n<li>Enter the <strong>Large pulley diameter (D)<\/strong> \u2014 the pitch (effective) diameter of the bigger pulley \u2014 and pick its unit (mm, cm, m, in, or ft).<\/li>\n<li>Enter the <strong>Small pulley diameter (d)<\/strong> with its unit.<\/li>\n<li>Enter the <strong>Center distance (C)<\/strong>, the distance between the rotation axes of the two pulleys.<\/li>\n<li>Choose the <strong>Belt arrangement<\/strong>: <em>Open belt<\/em> if the pulleys rotate the same way, or <em>Crossed belt<\/em> if the belt is twisted into a figure-eight so the pulleys rotate in opposite directions.<\/li>\n<li>Read the approximate belt length, shown in your chosen unit plus a table of all common units, along with the geometry details (wrap angles, straight span length, and arc lengths on each pulley).<\/li>\n<\/ol>\n<h2>What the belt length calculation means<\/h2>\n<p>A belt drive transfers power between two shafts by friction (flat and V-belts) or by teeth (timing belts). To size or order a belt you need its total length, which is the sum of three parts: the two straight spans running between the pulleys, and the two arcs of contact wrapped around each pulley. Because the pulleys usually have different diameters, the belt leaves each pulley at a slight angle rather than along the line of centers \u2014 this is what the \\((D \\mp d)^2\/(4C)\\) correction term accounts for.<\/p>\n<p>The geometry details tell you how well the drive will actually work. The <strong>angle of contact<\/strong> (wrap angle) is how many degrees of each pulley circumference the belt grips. In an open belt the small pulley always has the smaller wrap; if it falls below roughly 120\u2013130\u00b0, the belt may slip under load. A crossed belt gives both pulleys a wrap angle larger than 180\u00b0, improving grip at the cost of faster wear where the belt rubs against itself at the crossing point.<\/p>\n<p>The <strong>center distance ratio<\/strong> \\(C\/d\\) is a useful design check: most practical two-pulley drives work best with \\(C\/d\\) between about 1.5 and 5. Very short center distances force extreme wrap angles and flex the belt too often around the small pulley, while very long distances make the belt sag and flap. Note that the pulley speed ratio is fixed by the diameters alone, \\(n_1\/n_2 = D\/d\\) \u2014 the belt length does not change it.<\/p>\n<h2>Assumptions, limitations and practical tips<\/h2>\n<ul>\n<li><strong>Approximate formula.<\/strong> The formula used here is the classic engineering approximation. It is accurate to well under 1% for typical layouts (center distance larger than the pulley diameters) and becomes exact when the pulleys are equal in size.<\/li>\n<li><strong>Pitch diameter, not outside diameter.<\/strong> For V-belts and timing belts, use the pitch (effective) diameter from the manufacturer's data \u2014 typically 5\u201310 mm smaller than the outside diameter for a V-belt pulley. Using the outside diameter will overestimate the length.<\/li>\n<li><strong>Minimum center distance.<\/strong> Geometrically, an open belt needs \\(C &gt; |D - d|\/2\\) and a crossed belt needs \\(C &gt; (D + d)\/2\\); the calculator warns you if the layout is impossible.<\/li>\n<li><strong>No sag, thickness, or tension allowance.<\/strong> The result is the neutral-axis length of an ideal belt. Real belts stretch slightly and take-up (adjustable) pulley mounts are recommended so you can set the tension after installation. For a V-belt, choose the nearest standard belt section and length from a manufacturer's catalogue rather than ordering a custom length.<\/li>\n<li><strong>Buying a joined (endless) belt?<\/strong> Its length is measured under a specified tension and may differ by a fraction of a percent from the calculated geometric length \u2014 always check the catalogue tolerance.<\/li>\n<\/ul>\n<p>If you are designing the wider mechanical or fluid system around the belt drive, you may also find our <a href=\"https:\/\/wpcalc.com\/en\/engineering\/pump-power\/\">Pump Power<\/a> calculator useful for sizing the motor that drives the pulley, and the <a href=\"https:\/\/wpcalc.com\/en\/engineering\/reynolds-number\/\">Reynolds Number<\/a> and <a href=\"https:\/\/wpcalc.com\/en\/engineering\/pipe-pressure-drop\/\">Pipe Pressure Drop<\/a> calculators for the flow side of the system.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Calculate the required belt length for a two-pulley drive from the pulley diameters and center distance. Supports open and crossed belt arrangements in metric or imperial units.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[4],"tags":[19],"class_list":["post-66706","post","type-post","status-publish","format-standard","hentry","category-engineering","tag-civil"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66706","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/comments?post=66706"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66706\/revisions"}],"predecessor-version":[{"id":66707,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66706\/revisions\/66707"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=66706"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=66706"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=66706"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}