{"id":100035,"date":"2026-02-15T20:07:35","date_gmt":"2026-02-15T20:07:35","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100035"},"modified":"2026-07-11T20:38:09","modified_gmt":"2026-07-11T20:38:09","slug":"belt-tension-calculator","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/tr\/calculators\/belt-tension-calculator\/","title":{"rendered":"Belt Span Frequency Tension Estimator | Optibelt Formula"},"content":{"rendered":"\r\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Belt Span Frequency Tension Estimator\",\"description\":\"Estimate static belt span tension from measured fundamental frequency, free span length and belt metre weight using the Optibelt relation.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/belt-tension-calculator\/\",\"applicationCategory\":\"Engineering Calculator\",\"operatingSystem\":\"Any (Web Browser)\",\"offers\":{\"@type\":\"Offer\",\"price\":\"0\",\"priceCurrency\":\"EUR\"},\"creator\":{\"@type\":\"Organization\",\"name\":\"Vibromera\",\"url\":\"https:\/\/vibromera.eu\/\"},\"dateModified\":\"2026-07-12\",\"inLanguage\":\"en\",\"isAccessibleForFree\":true}<\/script>\r\n\r\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[{\"@type\":\"Question\",\"name\":\"What formula is used?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"T=4\u00d710^-6 k L^2 f^2 for T in newtons, metre weight k in kg\/m, free span L in mm and fundamental frequency f in hertz, as published in the Optibelt V-belt technical manual.\"}},{\"@type\":\"Question\",\"name\":\"Does the result define the correct installation tension?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"No. It estimates the tension corresponding to the measured span frequency. The required target must come from the exact belt product and drive design.\"}},{\"@type\":\"Question\",\"name\":\"Why was the deflection-force method removed?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"A manufacturer force-deflection procedure compares force at a specified deflection with product-specific data. The former ideal-string equation did not account for belt axial and bending stiffness and could not generally infer installed static tension.\"}},{\"@type\":\"Question\",\"name\":\"Which frequency should be entered?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Use the measured fundamental transverse frequency of the specified free unloaded span under the instrument and product procedure, not an arbitrary spectral peak.\"}},{\"@type\":\"Question\",\"name\":\"Can the same generic limits be used for every belt?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"No. Target frequency or tension depends on belt product, width or belt count, span, drive geometry, power and installation state.\"}}]}<\/script>\r\n\r\n<script type=\"application\/ld+json\">\r\n{\"@context\":\"https:\/\/schema.org\",\"@type\":\"BreadcrumbList\",\"itemListElement\":[\r\n{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/vibromera.eu\/\"},\r\n{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Calculators\",\"item\":\"https:\/\/vibromera.eu\/calculators\/\"},\r\n{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Belt Tension Calculator\",\"item\":\"https:\/\/vibromera.eu\/calculators\/belt-tension-calculator\/\"}\r\n]}\r\n<\/script>\r\n\r\n<link rel=\"preconnect\" href=\"https:\/\/fonts.googleapis.com\">\r\n\r\n<link rel=\"preconnect\" href=\"https:\/\/fonts.gstatic.com\" crossorigin>\r\n\r\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\" rel=\"stylesheet\">\r\n\r\n<link rel=\"stylesheet\" href=\"https:\/\/cdn.jsdelivr.net\/npm\/katex@0.16.11\/dist\/katex.min.css\">\r\n\r\n<style>\r\n:root {\r\n    --vc-bg: #f4f1ec;\r\n    --vc-surface: #ffffff;\r\n    --vc-surface-alt: #f8f6f2;\r\n    --vc-ink: #1a1a1a;\r\n    --vc-ink-secondary: #5a5650;\r\n    --vc-ink-muted: #8a857e;\r\n    --vc-accent: #c85a2a;\r\n    --vc-accent-hover: #b04d22;\r\n    --vc-accent-light: #fdf0ea;\r\n    --vc-blue: #2a5c8c;\r\n    --vc-blue-light: #eaf1f8;\r\n    --vc-green: #2a7a4b;\r\n    --vc-green-light: #eaf8ef;\r\n    --vc-yellow: #a67c00;\r\n    --vc-yellow-light: #fef9e8;\r\n    --vc-red: #b91c1c;\r\n    --vc-red-light: #fef2f2;\r\n    --vc-border: #d9d4cc;\r\n    --vc-border-light: #e8e4dd;\r\n    --vc-shadow: 0 1px 3px rgba(26,26,26,0.06), 0 4px 12px rgba(26,26,26,0.04);\r\n    --vc-shadow-lg: 0 4px 12px rgba(26,26,26,0.08), 0 16px 40px rgba(26,26,26,0.06);\r\n    --vc-radius: 8px;\r\n    --vc-radius-lg: 12px;\r\n    --vc-font: 'DM Sans', -apple-system, BlinkMacSystemFont, 'Segoe UI', sans-serif;\r\n    --vc-mono: 'JetBrains Mono', 'Consolas', 'Monaco', monospace;\r\n    --vc-display: 'Fraunces', Georgia, serif;\r\n}\r\n\r\n.vc-calculator {\r\n    font-family: var(--vc-font);\r\n    font-size: 15px;\r\n    line-height: 1.65;\r\n    color: var(--vc-ink);\r\n    max-width: 960px;\r\n    margin: 0 auto;\r\n    padding: 20px 16px 40px;\r\n    -webkit-font-smoothing: antialiased;\r\n}\r\n.vc-calculator *, .vc-calculator *::before, .vc-calculator *::after { box-sizing: border-box; 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}\r\n\r\n\/* \u2500\u2500 PRINT \u2500\u2500 *\/\r\n@media print {\r\n    .vc-section-body { max-height:none!important; }\r\n    .vc-faq-a { max-height:none!important; }\r\n    .vc-results { max-height:none!important; padding:24px!important; }\r\n    .vc-copy-btn, .vc-section-chevron, .vc-faq-chevron, .vc-presets, .vc-promo { display:none!important; }\r\n}\r\n<\/style>\r\n\r\n<div class=\"vc-calculator\" id=\"vc-belt-tension\">\r\n\r\n<!-- Header -->\r\n<header class=\"vc-header\"><p class=\"vc-header-eyebrow\">Free Engineering Tool<\/p><h1 class=\"vc-header-title\">Belt Span Frequency Tension Estimator<\/h1><p class=\"vc-header-subtitle\">Estimate static span tension from the measured fundamental frequency, free span length and manufacturer belt metre weight.<\/p><div class=\"vc-badges\"><span class=\"vc-badge\">Optibelt Frequency Relation<\/span><span class=\"vc-badge\">Unit-Safe<\/span><span class=\"vc-badge\">No Universal Target<\/span><\/div><\/header>\r\n\r\n<!-- Calculator Card -->\r\n<div class=\"vc-card\"><form class=\"vc-form\" id=\"vc-form\" autocomplete=\"off\"><div class=\"vc-form-grid\">\r\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-mass\">Belt metre weight k<\/label><div style=\"display:flex;gap:8px\"><input class=\"vc-input\" type=\"text\" id=\"vc-mass\" inputmode=\"decimal\" value=\"0.377\"><select class=\"vc-select\" id=\"vc-mass-unit\" style=\"max-width:120px\"><option value=\"kgm\" selected>kg\/m<\/option><option value=\"gm\">g\/m<\/option><\/select><\/div><\/div>\r\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-span\">Free oscillating span L<\/label><div style=\"display:flex;gap:8px\"><input class=\"vc-input\" type=\"text\" id=\"vc-span\" inputmode=\"decimal\" value=\"2189.3\"><select class=\"vc-select\" id=\"vc-span-unit\" style=\"max-width:100px\"><option value=\"mm\" selected>mm<\/option><option value=\"m\">m<\/option><\/select><\/div><\/div>\r\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-freq\">Measured fundamental frequency f <span class=\"vc-label-hint\">(Hz)<\/span><\/label><input class=\"vc-input\" type=\"text\" id=\"vc-freq\" inputmode=\"decimal\" value=\"14.33\"><\/div>\r\n<\/div><div class=\"vc-warning-box\"><p><strong>Use the exact product procedure:<\/strong> metre weight must match belt profile and width; span must be the free measured span; frequency must be the fundamental transverse mode. The result estimates measured static span tension and does not generate an installation target.<\/p><\/div><\/form>\r\n<div class=\"vc-results\" id=\"vc-results\"><div class=\"vc-results-head\"><h2 class=\"vc-results-title\">Estimated Span Tension<\/h2><button type=\"button\" class=\"vc-copy-btn\" id=\"vc-copy-btn\">Copy<\/button><\/div><div class=\"vc-result-grid\">\r\n<div class=\"vc-rcard vc-rcard-primary\"><div class=\"vc-rcard-label\">Static span tension T<\/div><div class=\"vc-rcard-value\" id=\"vc-r-tension\">\u2014<\/div><\/div>\r\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Reference force unit<\/div><div class=\"vc-rcard-value\" id=\"vc-r-kgf\">\u2014<\/div><\/div>\r\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Normalized metre weight<\/div><div class=\"vc-rcard-value\" id=\"vc-r-mass\">\u2014<\/div><\/div>\r\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Normalized span<\/div><div class=\"vc-rcard-value\" id=\"vc-r-span\">\u2014<\/div><\/div><\/div><\/div><\/div>\r\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\">Formula, Measurement &amp; Source<\/span><\/span><\/button><div class=\"vc-section-body\"><div class=\"vc-section-inner vc-theory\">\r\n<h3>Frequency relation<\/h3><div class=\"vc-formula-box\">T = 4 \u00d7 10<sup>\u22126<\/sup> \u00d7 k \u00d7 L\u00b2 \u00d7 f\u00b2<\/div><ul><li><strong>T<\/strong> \u2014 static belt span tension (N)<\/li><li><strong>k<\/strong> \u2014 metre weight of the exact belt (kg\/m)<\/li><li><strong>L<\/strong> \u2014 free oscillating span length (mm)<\/li><li><strong>f<\/strong> \u2014 measured fundamental frequency (Hz)<\/li><\/ul>\r\n<p>The relation is equivalent to the ideal stretched-string fundamental f=(1\/(2L))\u221a(T\/k), with the unit factor for L in millimetres. Real belt stiffness and measurement conditions can create small deviations; use the manufacturer procedure and actual metre weight.<\/p>\r\n<h3>Published verification example<\/h3><p>Optibelt gives k=0.377 kg\/m, L=2189.3 mm and f=14.33 Hz, producing T=1484.24 N (approximately 1484 N).<\/p>\r\n<p>Source: <a href=\"https:\/\/www.optibelt.com\/fileadmin\/pdf\/produkte\/keilriemen\/Optibelt-TM-v-belt-drives.pdf\" target=\"_blank\" rel=\"noopener\">Optibelt Technical Manual V-Belt Drives, frequency meter\/tension tester section<\/a>.<\/p>\r\n<div class=\"vc-info-box\"><p><strong>Not a target selector:<\/strong> obtain required first-install and re-tension values from the exact belt and drive calculation. Do not apply generic ranges, universal new-belt multipliers or maintenance intervals.<\/p><\/div>\r\n<\/div><\/div><\/div><div class=\"vc-section\" id=\"vc-sec-related\">\r\n    <button type=\"button\" class=\"vc-section-toggle\" aria-expanded=\"false\">\r\n        <span class=\"vc-section-toggle-text\">\r\n            <span class=\"vc-section-icon\">\ud83d\udd17<\/span>\r\n            <span class=\"vc-section-title\">Related Calculators<\/span>\r\n        <\/span>\r\n        <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>\r\n    <\/button>\r\n    <div class=\"vc-section-body\">\r\n        <div class=\"vc-section-inner\">\r\n            <div class=\"vc-related\">\r\n                <a class=\"vc-related-link\" href=\"\/calculators\/power-unit-converter\/\">Power Unit Converter<\/a>\r\n                <a class=\"vc-related-link\" href=\"\/calculators\/thread-size-converter\/\">Thread Size Converter<\/a>\r\n                <a class=\"vc-related-link\" href=\"\/calculators\/shaft-radial-runout\/\">Shaft Radial Runout<\/a>\r\n            <\/div>\r\n        <\/div>\r\n    <\/div>\r\n<\/div>\r\n\r\n<!-- FAQ -->\r\n<div class=\"vc-section\" id=\"vc-sec-faq\">\r\n    <button type=\"button\" class=\"vc-section-toggle\" aria-expanded=\"false\">\r\n        <span class=\"vc-section-toggle-text\">\r\n            <span class=\"vc-section-icon\">\u2753<\/span>\r\n            <span class=\"vc-section-title\">Frequently Asked Questions<\/span>\r\n        <\/span>\r\n        <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>\r\n    <\/button>\r\n    <div class=\"vc-section-body\">\r\n        <div class=\"vc-section-inner\">\r\n            <div class=\"vc-faq-list\" id=\"vc-faq-list\"><\/div>\r\n        <\/div>\r\n    <\/div>\r\n<\/div>\r\n\r\n<!-- Promo -->\r\n<div class=\"vc-promo\">\r\n    <div class=\"vc-promo-text\">\r\n        <strong>Vibromera \u2014 Portable Balancing &amp; Vibration Analysis<\/strong><br>\r\n        Professional field balancing instruments and software. Vibration monitoring for belt-driven equipment. Used in 50+ countries.\r\n    <\/div>\r\n    <a class=\"vc-promo-link\" href=\"https:\/\/vibromera.eu\/\" target=\"_blank\" rel=\"noopener\">Learn More<\/a>\r\n<\/div>\r\n\r\n<!-- Footer -->\r\n<footer class=\"vc-footer\"><p>\u00a9 2024\u20132026 <a href=\"https:\/\/vibromera.eu\/\">Vibromera<\/a> \u2014 Engineering Calculators<\/p><p style=\"font-size:12px;margin-top:4px;\">Optibelt frequency relation; product-specific target required. Scientific review: July 2026<\/p><\/footer>\r\n\r\n<\/div>\r\n\r\n<script>(function(){'use strict';var SLUG='belt-tension-calculator';function $(id){return document.getElementById(id)}function parseN(raw){var s=String(raw).trim().replace(\/\\s+\/g,'');if(!\/^[+]?(?:\\d+(?:[.,]\\d*)?|[.,]\\d+)$\/.test(s))return NaN;return Number(s.replace(',','.'))}function fmt(n,d){return n.toFixed(d).replace(\/(\\.\\d*?)0+$\/,'$1').replace(\/\\.$\/,'')}\r\nfunction calculate(){var k=parseN($('vc-mass').value),L=parseN($('vc-span').value),f=parseN($('vc-freq').value);if(![k,L,f].every(function(v){return isFinite(v)&&v>0})){$('vc-results').classList.remove('vc-visible');return}if($('vc-mass-unit').value==='gm')k\/=1000;if($('vc-span-unit').value==='m')L*=1000;var T=4e-6*k*L*L*f*f;if(!isFinite(T)||T<=0){$('vc-results').classList.remove('vc-visible');return}$('vc-r-tension').innerHTML=fmt(T,3)+' <span class=\"vc-rcard-unit\">N<\/span>';$('vc-r-kgf').innerHTML=fmt(T\/9.80665,3)+' <span class=\"vc-rcard-unit\">kgf (standard gravity)<\/span>';$('vc-r-mass').innerHTML=fmt(k,6)+' <span class=\"vc-rcard-unit\">kg\/m<\/span>';$('vc-r-span').innerHTML=fmt(L,3)+' <span class=\"vc-rcard-unit\">mm<\/span>';$('vc-results').classList.add('vc-visible');var u=new URL(location);u.searchParams.set('mass',$('vc-mass').value.trim().replace(',','.'));u.searchParams.set('massUnit',$('vc-mass-unit').value);u.searchParams.set('span',$('vc-span').value.trim().replace(',','.'));u.searchParams.set('spanUnit',$('vc-span-unit').value);u.searchParams.set('freq',$('vc-freq').value.trim().replace(',','.'));history.replaceState(null,'',u.toString());saveHistory({k:k,L:L,f:f,T:T,_summary:fmt(T,2)+' N'})}\r\n$('vc-form').addEventListener('input',calculate);$('vc-form').addEventListener('change',calculate);$('vc-copy-btn').addEventListener('click',function(){var t='Belt span frequency estimate\\nT: '+$('vc-r-tension').textContent+'\\nk: '+$('vc-r-mass').textContent+'\\nL: '+$('vc-r-span').textContent+'\\nf: '+$('vc-freq').value+' Hz';if(navigator.clipboard)navigator.clipboard.writeText(t)});document.querySelectorAll('.vc-section-toggle').forEach(function(b){b.addEventListener('click',function(){this.closest('.vc-section').classList.toggle('vc-open')})});var faqData=[{q:'What equation is used?',a:'<p>T=4\u00d710\u207b\u2076kL\u00b2f\u00b2 for k in kg\/m and L in mm.<\/p>'},{q:'Does this choose the target tension?',a:'<p>No. The exact product and drive calculation supplies the target.<\/p>'},{q:'Which frequency is required?',a:'<p>The fundamental transverse frequency of the specified free span.<\/p>'},{q:'Why is force-deflection absent?',a:'<p>It requires product-specific force at a specified deflection; the former ideal-string shortcut was not a general installation method.<\/p>'},{q:'Can I multiply by belt count?',a:'<p>Measure and set each belt or use the manufacturer procedure for matched sets; do not assume a generic aggregate target.<\/p>'}];var fl=$('vc-faq-list');faqData.forEach(function(f){fl.innerHTML+='<div class=\"vc-faq-item\"><button type=\"button\" class=\"vc-faq-q\">'+f.q+'<\/button><div class=\"vc-faq-a\"><div class=\"vc-faq-a-inner\">'+f.a+'<\/div><\/div><\/div>'});fl.addEventListener('click',function(e){var b=e.target.closest('.vc-faq-q');if(b)b.closest('.vc-faq-item').classList.toggle('vc-open')});function saveHistory(e){var a=[],key='vc_history_'+SLUG;try{a=JSON.parse(localStorage.getItem(key))||[]}catch(x){}e._ts=new Date().toISOString();a.unshift(e);try{localStorage.setItem(key,JSON.stringify(a.slice(0,10)))}catch(x){}}function load(){var p=new URLSearchParams(location.search),m={mass:'vc-mass',massUnit:'vc-mass-unit',span:'vc-span',spanUnit:'vc-span-unit',freq:'vc-freq'};Object.keys(m).forEach(function(k){if(p.has(k))$(m[k]).value=p.get(k)})}function init(){load();calculate()}if(document.readyState==='loading')document.addEventListener('DOMContentLoaded',init);else init()})();<\/script>\r\n","protected":false},"excerpt":{"rendered":"<p>Estimate static belt span tension from measured fundamental frequency, free span and belt metre weight with explicit product-specific limitations.<\/p>","protected":false},"featured_media":0,"template":"","meta":{"ai_generated_summary":"","footnotes":""},"categories":[],"tags":[],"class_list":["post-100035","calculator","type-calculator","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/vibromera.eu\/tr\/wp-json\/wp\/v2\/calculator\/100035","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vibromera.eu\/tr\/wp-json\/wp\/v2\/calculator"}],"about":[{"href":"https:\/\/vibromera.eu\/tr\/wp-json\/wp\/v2\/types\/calculator"}],"version-history":[{"count":2,"href":"https:\/\/vibromera.eu\/tr\/wp-json\/wp\/v2\/calculator\/100035\/revisions"}],"predecessor-version":[{"id":102323,"href":"https:\/\/vibromera.eu\/tr\/wp-json\/wp\/v2\/calculator\/100035\/revisions\/102323"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/tr\/wp-json\/wp\/v2\/media?parent=100035"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/tr\/wp-json\/wp\/v2\/categories?post=100035"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/tr\/wp-json\/wp\/v2\/tags?post=100035"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}