{"id":100062,"date":"2026-02-15T20:10:03","date_gmt":"2026-02-15T20:10:03","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100062"},"modified":"2026-07-11T23:43:40","modified_gmt":"2026-07-11T23:43:40","slug":"compression-spring-design","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/it\/calculators\/compression-spring-design\/","title":{"rendered":"Compression Spring Preliminary Calculator | Rate, Deflection &#038; Stress"},"content":{"rendered":"\r\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Cold-Formed Helical Compression Spring Preliminary Calculator\",\"description\":\"Calculate linear spring rate, load deflection and Wahl-corrected shear stress for a close-coiled round-wire cold-formed compression spring within declared geometric limits.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/compression-spring-design\/\",\"applicationCategory\":\"Engineering Calculator\",\"operatingSystem\":\"Any\",\"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<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[{\"@type\":\"Question\",\"name\":\"Does this calculate a safe maximum load?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"No. It evaluates a user-supplied axial load. Allowable load requires material strength, manufacturing condition, temperature, relaxation, fatigue, tolerances, end geometry, buckling and safety criteria.\"}},{\"@type\":\"Question\",\"name\":\"Is the result ISO certified?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"No. ISO 22705-1 specifies measurement and test methods, not this simplified design formula. EN 13906-1 is the relevant European calculation and design standard for cylindrical compression springs within its scope.\"}},{\"@type\":\"Question\",\"name\":\"Why are material presets omitted?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Shear modulus and allowable stress depend on material specification, product form, condition, temperature and source. Enter a traceable project value.\"}}]}<\/script>\r\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\":\"Compression Spring Preliminary Calculation\",\"item\":\"https:\/\/vibromera.eu\/calculators\/compression-spring-design\/\"}]}<\/script>\r\n<link rel=\"preconnect\" 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16px;font-family:var(--vc-font);font-size:13px;font-weight:600;background:var(--vc-surface-alt);color:var(--vc-ink-secondary);border:1px solid var(--vc-border);border-radius:var(--vc-radius);text-decoration:none;transition:all 0.15s}.vc-related-link:hover{border-color:var(--vc-accent);color:var(--vc-accent);background:var(--vc-accent-light)}\r\n.vc-promo{margin-top:24px;padding:20px;background:linear-gradient(135deg,var(--vc-accent-light),var(--vc-surface));border:1px solid var(--vc-border);border-radius:var(--vc-radius-lg);display:flex;align-items:center;gap:16px}.vc-promo-text{flex:1;font-size:14px;color:var(--vc-ink-secondary)}.vc-promo-text strong{color:var(--vc-ink)}.vc-promo-link{padding:8px 20px;font-size:13px;font-weight:700;color:#fff;background:var(--vc-accent);border-radius:var(--vc-radius);text-decoration:none;white-space:nowrap;transition:background 0.15s}.vc-promo-link:hover{background:var(--vc-accent-hover)}\r\n.vc-footer{text-align:center;padding:32px 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}\r\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}}\r\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}\r\n<\/style>\r\n<div class=\"vc-calculator\" id=\"vc-compression-spring\"><header class=\"vc-header\"><p class=\"vc-header-eyebrow\">Bounded preliminary mechanics<\/p><h1 class=\"vc-header-title\">Compression Spring Preliminary Calculator<\/h1><p class=\"vc-header-subtitle\">For a close-coiled, round-wire, cylindrical cold-formed spring with linear axial response. Calculate rate, deflection at a supplied load and an estimated Wahl-corrected shear stress\u2014not a safe maximum load.<\/p><div class=\"vc-badges\"><span class=\"vc-badge\">SI units<\/span><span class=\"vc-badge\">User-supplied load<\/span><span class=\"vc-badge\">Not strength certification<\/span><\/div><\/header>\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-d\">Wire diameter d <span class=\"vc-label-hint\">(mm; \u226420)<\/span><\/label><input class=\"vc-input\" type=\"text\" id=\"vc-d\" inputmode=\"decimal\"><\/div>\r\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-D\">Mean coil diameter D <span class=\"vc-label-hint\">(mm)<\/span><\/label><input class=\"vc-input\" type=\"text\" id=\"vc-D\" inputmode=\"decimal\"><\/div>\r\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-n\">Active coils n <span class=\"vc-label-hint\">(\u22652)<\/span><\/label><input class=\"vc-input\" type=\"text\" id=\"vc-n\" inputmode=\"decimal\"><\/div>\r\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-G\">Shear modulus G <span class=\"vc-label-hint\">(MPa)<\/span><\/label><input class=\"vc-input\" type=\"text\" id=\"vc-G\" inputmode=\"decimal\"><\/div>\r\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-F\">Applied axial load F <span class=\"vc-label-hint\">(N; may be zero)<\/span><\/label><input class=\"vc-input\" type=\"text\" id=\"vc-F\" inputmode=\"decimal\"><\/div>\r\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-source\">G \/ material data source<\/label><input class=\"vc-input\" type=\"text\" id=\"vc-source\" maxlength=\"200\" placeholder=\"Specification, certificate, temperature\"><\/div>\r\n<\/div><p id=\"vc-error\" role=\"alert\" style=\"margin:.75rem 0 0;color:#b42318\"><\/p><div class=\"vc-warning-box\"><p style=\"margin:0\"><strong>Scope gate:<\/strong> this page enforces the cold-formed EN 13906-1:2013 geometry limits d\u226420 mm, n\u22652 and 4\u2264D\/d\u226420. It does not establish material allowables, life, buckling, clash\/solid height or compliance.<\/p><\/div><\/form>\r\n<div class=\"vc-results\" id=\"vc-results\"><div class=\"vc-results-head\"><h2 class=\"vc-results-title\">Preliminary linear result<\/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\">Spring rate k<\/div><div class=\"vc-rcard-value\" id=\"vc-r-k\">\u2014<\/div><\/div>\r\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Deflection at supplied load s=F\/k<\/div><div class=\"vc-rcard-value\" id=\"vc-r-s\">\u2014<\/div><\/div>\r\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Wahl-corrected shear stress estimate<\/div><div class=\"vc-rcard-value\" id=\"vc-r-tau\">\u2014<\/div><\/div>\r\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Spring index C=D\/d<\/div><div class=\"vc-rcard-value\" id=\"vc-r-C\">\u2014<\/div><\/div>\r\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Wahl factor K<sub>w<\/sub><\/div><div class=\"vc-rcard-value\" id=\"vc-r-Kw\">\u2014<\/div><\/div>\r\n<\/div><p id=\"vc-r-note\" style=\"margin:0;color:var(--vc-ink-secondary)\"><\/p><\/div><\/div>\r\n<div class=\"vc-section vc-open\"><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\">Equations, standards and exclusions<\/span><\/span><\/button><div class=\"vc-section-body\"><div class=\"vc-section-inner vc-theory\">\r\n<div class=\"vc-formula-box\">C=D\/d; &nbsp; k=Gd\u2074\/(8D\u00b3n); &nbsp; s=F\/k<\/div><div class=\"vc-formula-box\">K<sub>w<\/sub>=(4C\u22121)\/(4C\u22124)+0.615\/C; &nbsp; \u03c4<sub>est<\/sub>=K<sub>w<\/sub>\u00b78FD\/(\u03c0d\u00b3)<\/div>\r\n<p>The equations are a close-coiled linear-elastic approximation. A NASA technical report documents the Wahl-corrected compression-spring stress form. <a href=\"https:\/\/www.dinmedia.de\/de\/norm\/din-en-13906-1\/189797622\" target=\"_blank\" rel=\"noopener\">DIN EN 13906-1:2013<\/a> is the current European calculation\/design standard for linear cylindrical helical compression springs made from constant-diameter round wire\/bar; its cold-formed scope includes d\u226420 mm, n\u22652 and spring index 4\u201320.<\/p>\r\n<p><a href=\"https:\/\/www.iso.org\/standard\/73723.html\" target=\"_blank\" rel=\"noopener\">ISO 22705-1:2021<\/a> specifies measurement and test methods for general characteristics of cold-formed round-wire cylindrical compression springs and excludes dynamic testing. It is not a source for claiming this simplified calculator is an ISO design.<\/p>\r\n<div class=\"vc-warning-box\"><p style=\"margin:0\"><strong>Required engineering checks outside this calculator:<\/strong> material\/product standard and certificate, strength and safety factor, static or dynamic duty and cycle count, fatigue and shot peening, temperature and relaxation, tolerances, end form, actual solid height\/clash allowance, free length and buckling\/guidance, natural frequency\/surge, corrosion and validation test.<\/p><\/div>\r\n<\/div><\/div><\/div>\r\n<div class=\"vc-section\"><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><\/button><div class=\"vc-section-body\"><div class=\"vc-section-inner\"><div class=\"vc-faq-list\" id=\"vc-faq-list\"><\/div><\/div><\/div><\/div>\r\n<footer class=\"vc-footer\"><p>\u00a9 2024\u20132026 <a href=\"https:\/\/vibromera.eu\/\">Vibromera<\/a><\/p><p>Preliminary linear mechanics only. Scientific review: July 2026.<\/p><\/footer><\/div>\r\n<script>(function(){'use strict';function $(i){return document.getElementById(i)}function pos(v){var s=String(v).trim().replace(\/\\s+\/g,'');if(!\/^[+]?(?:\\d+(?:[.,]\\d*)?|[.,]\\d+)$\/.test(s))return NaN;var x=Number(s.replace(',','.'));return Number.isFinite(x)&&x>0?x:NaN}function nonneg(v){var s=String(v).trim().replace(\/\\s+\/g,'');if(!\/^[+]?(?:\\d+(?:[.,]\\d*)?|[.,]\\d+)$\/.test(s))return NaN;var x=Number(s.replace(',','.'));return Number.isFinite(x)&&x>=0?x:NaN}function f(x){return x.toFixed(9).replace(\/(\\.\\d*?)0+$\/,'$1').replace(\/\\.$\/,'')}function calc(){var d=pos($('vc-d').value),D=pos($('vc-D').value),n=pos($('vc-n').value),G=pos($('vc-G').value),F=nonneg($('vc-F').value),source=$('vc-source').value.trim(),any=[$('vc-d').value,$('vc-D').value,$('vc-n').value,$('vc-G').value,$('vc-F').value,source].some(function(v){return String(v).trim()});var C=D\/d;if(![d,D,n,G,F].every(Number.isFinite)||!source){$('vc-error').textContent=any?'Enter positive finite d,D,n,G; non-negative F; and a traceable G\/material source.':'';$('vc-results').classList.remove('vc-visible');return}if(d>20||n<2||C<4||C>20){$('vc-error').textContent='Outside the declared cold-formed scope: require d\u226420 mm, n\u22652 and 4\u2264D\/d\u226420.';$('vc-results').classList.remove('vc-visible');return}var Kw=(4*C-1)\/(4*C-4)+0.615\/C,k=G*Math.pow(d,4)\/(8*Math.pow(D,3)*n),s=F\/k,tau=Kw*8*F*D\/(Math.PI*Math.pow(d,3));if(![Kw,k,s,tau].every(Number.isFinite)){$('vc-error').textContent='Values exceed the finite calculation range.';$('vc-results').classList.remove('vc-visible');return}$('vc-error').textContent='';$('vc-r-k').textContent=f(k)+' N\/mm';$('vc-r-s').textContent=f(s)+' mm';$('vc-r-tau').textContent=f(tau)+' MPa';$('vc-r-C').textContent=f(C);$('vc-r-Kw').textContent=f(Kw);$('vc-r-note').textContent='Applied load: '+f(F)+' N | G source: '+source+' | Stress is an estimate, not an allowable.';$('vc-results').classList.add('vc-visible');var u=new URL(location),v={wire_diameter_mm:d,mean_coil_diameter_mm:D,active_coils:n,shear_modulus_mpa:G,applied_axial_load_n:F,material_data_source:source};Object.keys(v).forEach(function(k){u.searchParams.set(k,v[k])});history.replaceState(null,'',u.toString())}$('vc-form').addEventListener('input',calc);$('vc-form').addEventListener('change',calc);$('vc-copy-btn').addEventListener('click',function(){if(navigator.clipboard)navigator.clipboard.writeText($('vc-results').innerText)});document.querySelectorAll('.vc-section-toggle').forEach(function(b){b.addEventListener('click',function(){var s=this.closest('.vc-section');s.classList.toggle('vc-open');this.setAttribute('aria-expanded',s.classList.contains('vc-open'))})});var qa=[['Does this calculate a safe maximum load?','No. It evaluates a supplied load. Strength, life, stability, environment and safety checks are separate.'],['Is this an ISO-certified design?','No. ISO 22705-1 covers measurement\/test methods. EN 13906-1 is the relevant European calculation\/design standard.'],['Why no material presets?','Use a traceable G value for the actual material specification, condition and temperature.']];var l=$('vc-faq-list');qa.forEach(function(v){l.innerHTML+='<div class=\"vc-faq-item\"><button type=\"button\" class=\"vc-faq-q\">'+v[0]+'<\/button><div class=\"vc-faq-a\"><div class=\"vc-faq-a-inner\"><p>'+v[1]+'<\/p><\/div><\/div><\/div>'});l.addEventListener('click',function(e){var b=e.target.closest('.vc-faq-q');if(b)b.closest('.vc-faq-item').classList.toggle('vc-open')});var z=new URLSearchParams(location.search),map={wire_diameter_mm:'vc-d',mean_coil_diameter_mm:'vc-D',active_coils:'vc-n',shear_modulus_mpa:'vc-G',applied_axial_load_n:'vc-F',material_data_source:'vc-source'};Object.keys(map).forEach(function(k){if(z.has(k))$(map[k]).value=z.get(k)});calc()})();<\/script>\r\n","protected":false},"excerpt":{"rendered":"<p>Bounded SI calculation of compression-spring rate, deflection at a supplied axial load and Wahl-corrected stress estimate; not a safe-load or compliance claim.<\/p>","protected":false},"featured_media":0,"template":"","meta":{"ai_generated_summary":"","footnotes":""},"categories":[],"tags":[],"class_list":["post-100062","calculator","type-calculator","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/vibromera.eu\/it\/wp-json\/wp\/v2\/calculator\/100062","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vibromera.eu\/it\/wp-json\/wp\/v2\/calculator"}],"about":[{"href":"https:\/\/vibromera.eu\/it\/wp-json\/wp\/v2\/types\/calculator"}],"version-history":[{"count":2,"href":"https:\/\/vibromera.eu\/it\/wp-json\/wp\/v2\/calculator\/100062\/revisions"}],"predecessor-version":[{"id":102352,"href":"https:\/\/vibromera.eu\/it\/wp-json\/wp\/v2\/calculator\/100062\/revisions\/102352"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/it\/wp-json\/wp\/v2\/media?parent=100062"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/it\/wp-json\/wp\/v2\/categories?post=100062"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/it\/wp-json\/wp\/v2\/tags?post=100062"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}