{"id":66736,"date":"2026-10-13T08:46:52","date_gmt":"2026-10-13T05:46:52","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=66736"},"modified":"2026-10-13T08:46:52","modified_gmt":"2026-10-13T05:46:52","slug":"compression-spring-rate","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/engineering\/compression-spring-rate\/","title":{"rendered":"Compression Spring Rate"},"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 Stiffness of a Helical Compression Spring<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"66736\" data-favorite-title=\"Compression Spring Rate\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/engineering\/compression-spring-rate\/\" data-favorite-excerpt=\"Calculate the spring rate (stiffness) of a helical compression spring from wire diameter, mean coil diameter, number of active coils and shear modulus. Optionally enter a load to get deflection and wire shear stress.\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-engineering\">\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\/compression-spring-rate\/\" method=\"POST\" class=\"calculator\" id=\"calculator-66736\" data-post=\"66736\"><fieldset class=\"fieldset-input is-1\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">Wire 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=\"wire_diameter_d\" id=\"field-1\" aria-describedby=\"calc-info-1\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 3\" min=\"0\" value=\"3\"\/><div class=\"grid grid-cols-1\"><select id=\"field-2\" name=\"unit\" aria-label=\"Unit\"><option value=\"mm\" selected>mm<\/option><option value=\"in\">in<\/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-1\">Diameter of the round wire the spring is wound from.<\/small><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-3\">Mean coil 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=\"mean_coil_diameter_d\" id=\"field-3\" aria-describedby=\"calc-info-3\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 25\" min=\"0\" value=\"25\"\/><div class=\"grid grid-cols-1\"><select id=\"field-4\" name=\"unit\" aria-label=\"Unit\"><option value=\"mm\" selected>mm<\/option><option value=\"in\">in<\/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-3\">Mean diameter of the coil, measured to the centre of the wire (outer diameter minus one wire diameter).<\/small><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-5\">Number of active coils (Na)<\/label><div class=\"term\">Na<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"number_of_active_coils_na\" id=\"field-5\" aria-describedby=\"calc-info-5\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 10\" min=\"0\" value=\"10\"\/><small id=\"calc-info-5\">Coils that actually deflect. For closed and ground ends: total coils \u2212 2; for closed unground ends: total coils \u2212 3; plain ends: all coils.<\/small><\/div><div class=\"field has-term\" id=\"input-4\"><label for=\"field-6\">Shear modulus (G)<\/label><div class=\"term\">G<\/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=\"shear_modulus_g\" id=\"field-6\" aria-describedby=\"calc-info-6\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 79.3\" min=\"0\" value=\"79.3\"\/><div class=\"grid grid-cols-1\"><select id=\"field-7\" name=\"unit\" aria-label=\"Unit\"><option value=\"gpa\" selected>GPa<\/option><option value=\"mpsi\">Mpsi (10\u2076 psi)<\/option><option value=\"psi\">psi<\/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-6\">Typical values: music wire (ASTM A228) \u2248 79.3 GPa (11.5 Mpsi), hard-drawn (A227) \u2248 77.2 GPa (11.2 Mpsi), stainless 302\/304 \u2248 69 GPa (10 Mpsi), chrome-silicon (A401) \u2248 77.2 GPa (11.2 Mpsi), phosphor bronze \u2248 41.2 GPa (6 Mpsi).<\/small><\/div><div class=\"field has-term\" id=\"input-5\"><label for=\"field-8\">Applied axial load (F) \u2014 optional<\/label><div class=\"term\">F<\/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=\"applied_axial_load_f_optional\" id=\"field-8\" aria-describedby=\"calc-info-8\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 250 (leave empty to skip)\" min=\"0\" value=\"250\"\/><div class=\"grid grid-cols-1\"><select id=\"field-9\" name=\"unit\" aria-label=\"Unit\"><option value=\"n\" selected>N<\/option><option value=\"lbf\">lbf<\/option><option value=\"kgf\">kgf<\/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-8\">If you enter a load, the calculator also estimates the deflection and the shear stress in the wire.<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"66736\">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> Spring Rate Results<\/h3><div class=\"result-box\"><div class=\"field-result is-column\" id=\"output-1\"><span class=\"field-title\"><span>Spring rate (k)<\/span><span class=\"result-term\">k<\/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>Deflection and wire stress under the applied load<\/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=\"66736\" 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>Compression Spring Rate 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\\[ k = \\frac{G\\, d^{4}}{8\\, N_a\\, D^{3}} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(k\\) \u2014 spring rate, or stiffness (N\/mm)<\/li>\n<li>\\(G\\) \u2014 shear modulus of the wire material (N\/mm\u00b2, i.e. MPa)<\/li>\n<li>\\(d\\) \u2014 wire diameter (mm)<\/li>\n<li>\\(N_a\\) \u2014 number of active coils<\/li>\n<li>\\(D\\) \u2014 mean coil diameter (mm)<\/li>\n<\/ul>\n<p>This formula applies to a close-coiled helical spring made of round wire, where the load is carried primarily by torsion of the wire. It shows that stiffness grows very rapidly with wire diameter (to the fourth power) and falls with the cube of the coil diameter and with the number of active coils.<\/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>Compression Spring Rate \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> a music-wire spring with a wire diameter of 3 mm, a mean coil diameter of 25 mm, 10 active coils and a shear modulus of 79.3 GPa (79,300 N\/mm\u00b2), loaded with 250 N.<\/p>\n<p>\\[ k = \\frac{79\\,300 \\times 3^{4}}{8 \\times 10 \\times 25^{3}} = \\frac{79\\,300 \\times 81}{1\\,250\\,000} \\approx 5.139 \\ \\text{N\/mm} \\]<br \/>\n\\[ f = \\frac{F}{k} = \\frac{250}{5.139} \\approx 48.65 \\ \\text{mm} \\]<br \/>\n\\[ \\tau = K_w \\, \\frac{8 F D}{\\pi d^{3}} = 1.176 \\times \\frac{8 \\times 250 \\times 25}{\\pi \\times 27} \\approx 693 \\ \\text{MPa} \\]<\/p>\n<p><strong>Result:<\/strong> the spring rate is k \u2248 5.139 N\/mm (29.34 lbf\/in). Under a 250 N load the spring deflects about 48.65 mm and the shear stress in the wire is roughly 693 MPa (\u2248 100 ksi).<\/p>\n<p>\n\r\n<\/section>\n<h2>How to Use the Calculator<\/h2>\n<ol>\n<li>Enter the <strong>Wire diameter (d)<\/strong> of the round wire and select mm or in.<\/li>\n<li>Enter the <strong>Mean coil diameter (D)<\/strong>, measured to the centre of the wire (outer diameter minus one wire diameter), with its unit.<\/li>\n<li>Enter the <strong>Number of active coils (Na)<\/strong>. For closed and ground ends subtract 2 from the total coils; for closed unground ends subtract 3; for plain ends count all coils.<\/li>\n<li>Enter the <strong>Shear modulus (G)<\/strong> of the wire material and pick its unit (GPa, Mpsi or psi). Typical values for common spring wires are listed in the field description.<\/li>\n<li>Optionally enter an <strong>Applied axial load (F)<\/strong> in N, lbf or kgf. The calculator then also reports the deflection (from Hooke's law, \\(f = F\/k\\)) and the shear stress in the wire, including the Wahl curvature correction factor.<\/li>\n<li>Read the spring rate in N\/mm, lbf\/in and N\/m in the results table, together with any warnings about the spring index or stress level.<\/li>\n<\/ol>\n<h2>What Is Spring Rate?<\/h2>\n<p>Spring rate, also called spring constant or stiffness, is the force required to compress (or extend) a spring by one unit of length. A spring with a rate of 5 N\/mm needs 5 newtons of force for every millimetre of compression \u2014 10 N compresses it 2 mm, 20 N compresses it 4 mm, and so on, as long as the spring stays in its elastic range. Spring rate is the single most important number describing a compression spring, because it determines how the spring will behave in a mechanism: how much force it exerts at a given displacement and how far it will sit under a given load.<\/p>\n<p>Although a compression spring looks like it is being squeezed, the wire itself is loaded almost entirely in torsion. Each cross-section of the wire twists slightly as the load is applied, and this twisting is what stores the energy. That is why the formula uses the shear modulus \\(G\\) rather than Young's modulus, and why it has the same \\(d^4 \/ D^3\\) character as a torsion formula \u2014 the same physics covered in more detail by our <a href=\"https:\/\/wpcalc.com\/en\/engineering\/shaft-torsion\/\">shaft torsion<\/a> calculator.<\/p>\n<p>The strong dependence on dimensions matters in practice. Doubling the wire diameter makes the spring 16 times stiffer; doubling the coil diameter makes it 8 times softer; doubling the number of coils makes it twice as soft. This is why spring manufacturers quote wire and coil diameters to very tight tolerances \u2014 small dimensional errors produce noticeable rate changes. If you are checking whether a spring is strong enough as a component, the wire stress result also serves as a quick sanity check, similar in spirit to verifying <a href=\"https:\/\/wpcalc.com\/en\/engineering\/beam-section-modulus\/\">section modulus<\/a> in beam design.<\/p>\n<h2>Interpreting the Results<\/h2>\n<p>The main result, \\(k\\), is given in N\/mm and lbf\/in. If you entered a load, the deflection \\(f = F\/k\\) tells you how far the spring shortens under that load, and the shear stress tells you whether the wire is working comfortably within its material limits. For common spring steels, keep the corrected shear stress well below about 45\u201350 % of the wire's tensile strength for static loads, and lower still for cyclic service. The calculator flags results that approach roughly 1000 MPa, a typical threshold for common spring wires.<\/p>\n<p>The calculator also reports the spring index \\(C = D\/d\\). Values between about 4 and 12 are considered manufacturable and well-behaved: below 4 the coiling stresses are severe and the spring is hard to wind; above 15 the coil is flimsy and may buckle, tangle or behave inconsistently. The example spring above has \\(C = 25\/3 \\approx 8.3\\), squarely in the good range.<\/p>\n<h2>Assumptions and Practical Tips<\/h2>\n<ul>\n<li><strong>Close-coiled round wire:<\/strong> the formula assumes a helical spring of round wire with closely spaced coils, loaded axially, with negligible direct shear and bending effects.<\/li>\n<li><strong>Linear elastic behaviour:<\/strong> the rate is constant only until the wire yields or the coils reach solid height. Once coils touch, the effective rate rises sharply.<\/li>\n<li><strong>Count active coils correctly:<\/strong> end coils that are closed (touching) barely deflect. Using the total coil count instead of the active count is the most common source of error \u2014 it can underestimate the rate by 20\u201330 % on short springs.<\/li>\n<li><strong>Check deflection against available travel:<\/strong> the calculated deflection must fit between the free length and the solid height of the spring; otherwise the spring bottoms out.<\/li>\n<li><strong>Use the right shear modulus:<\/strong> stainless steel and non-ferrous wires are noticeably softer than music wire (\u2248 69 GPa vs \u2248 79.3 GPa), which lowers the rate accordingly.<\/li>\n<li><strong>Temperature and service:<\/strong> at elevated temperatures springs relax and lose force over time; the calculated rate applies to the wire at room temperature.<\/li>\n<\/ul>\n<p>When sizing the wire for a given load, remember that stress rises with \\(1\/d^3\\) while rate rises with \\(d^4\\), so there is a direct trade-off between stiffness and stress \u2014 a thicker wire gives a stiffer, lower-stressed spring but a much higher force for the same travel. For pressure-containing parts a similar wall-thickness logic applies, as covered in our <a href=\"https:\/\/wpcalc.com\/en\/engineering\/pipe-wall-thickness\/\">pipe wall thickness<\/a> calculator.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Calculate the spring rate (stiffness) of a helical compression spring from wire diameter, mean coil diameter, number of active coils and shear modulus. Optionally enter a load to get deflection and wire shear stress.<\/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":[95],"class_list":["post-66736","post","type-post","status-publish","format-standard","hentry","category-engineering","tag-springs"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66736","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=66736"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66736\/revisions"}],"predecessor-version":[{"id":66737,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66736\/revisions\/66737"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=66736"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=66736"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=66736"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}