{"id":100183,"date":"2026-02-15T20:25:33","date_gmt":"2026-02-15T20:25:33","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100183"},"modified":"2026-07-13T02:15:54","modified_gmt":"2026-07-13T02:15:54","slug":"pipe-flexibility-calculator","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/ja\/calculators\/pipe-flexibility-calculator\/","title":{"rendered":"Documented Free Thermal Length-Change Arithmetic"},"content":{"rendered":"\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Documented Free Thermal Length-Change Arithmetic\",\"description\":\"Calculates signed free linear thermal strain and length change from a documented mean coefficient over a documented uniform temperature interval. It does not size expansion loops or perform a piping-code stress check.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/pipe-flexibility-calculator\/\",\"applicationCategory\":\"EngineeringApplication\",\"operatingSystem\":\"Any (Web Browser)\",\"offers\":{\"@type\":\"Offer\",\"price\":\"0\",\"priceCurrency\":\"EUR\"},\"creator\":{\"@type\":\"Organization\",\"name\":\"Vibromera\",\"url\":\"https:\/\/vibromera.eu\/\"},\"datePublished\":\"2025-01-01\",\"dateModified\":\"2026-07-13\",\"inLanguage\":\"en\",\"isAccessibleForFree\":true,\"featureList\":[\"Signed free thermal length change\",\"Mean-CTE source gate\",\"Celsius and Fahrenheit differences\",\"SI and inch-length conversion\",\"No loop or code-stress verdict\"],\"keywords\":\"free thermal expansion,linear thermal strain,mean coefficient of thermal expansion,pipe length change\"}<\/script>\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[{\"@type\":\"Question\",\"name\":\"Does this size an expansion loop?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"No. Loop geometry and piping flexibility require the full routing, restraints, supports, branches, component properties, load cases and applicable code procedure.\"}},{\"@type\":\"Question\",\"name\":\"Does free thermal expansion create the displayed piping stress?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"No stress is displayed. A freely expanding member has thermal strain and length change; restraint forces and stresses require a structural model.\"}},{\"@type\":\"Question\",\"name\":\"Which CTE should be entered?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Enter a documented mean or secant linear coefficient applicable to the exact material, condition and full temperature interval.\"}},{\"@type\":\"Question\",\"name\":\"Is this an EN 13480 or ASME B31.3 compliance check?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"No. The arithmetic is a preliminary imposed-movement input for a separate controlled code analysis.\"}}]}<\/script>\n<style>:root{--s:#fff;--sa:#f8f6f2;--i:#1a1a1a;--is:#5a5650;--im:#8a857e;--a:#a84a24;--al:#fdf0ea;--b:#d9d4cc;--bl:#e8e4dd;--y:#8a6500;--yl:#fef9e8;--r:#a12b2b;--f:'DM Sans',sans-serif;--m:'JetBrains Mono',monospace;--d:'Fraunces',serif}.vc-calculator{font-family:var(--f);font-size:15px;line-height:1.65;color:var(--i);max-width:960px;margin:auto;padding:20px 16px 40px}.vc-calculator *{box-sizing:border-box}.vc-header{text-align:center;padding:48px 20px 40px;border-bottom:3px solid var(--a)}.vc-header-eyebrow{font:500 11px var(--m);letter-spacing:.15em;text-transform:uppercase;color:var(--a)}.vc-header-title{font:800 clamp(24px,4vw,36px)\/1.15 var(--d);margin:10px 0 14px}.vc-header-subtitle{max-width:760px;margin:auto;color:var(--is)}.vc-badges{display:flex;gap:8px;justify-content:center;flex-wrap:wrap;margin-top:18px}.vc-badge{font:500 11px var(--m);padding:4px 10px;border:1px solid var(--b);border-radius:4px}.vc-card,.vc-section{background:var(--s);border:1px solid var(--b);border-radius:12px;overflow:hidden;margin-top:28px}.vc-form{padding:24px}.vc-grid{display:grid;grid-template-columns:1fr 1fr;gap:18px}.vc-field{display:flex;flex-direction:column}.vc-full{grid-column:1\/-1}.vc-label{font-size:12px;font-weight:600;letter-spacing:.04em;text-transform:uppercase;color:var(--is);margin-bottom:6px}.vc-hint{font-weight:400;text-transform:none;letter-spacing:0;color:var(--im)}.vc-input,.vc-select{width:100%;padding:10px 12px;border:1.5px solid var(--b);border-radius:6px;font:14px var(--f);background:var(--s)}.vc-check{display:flex;gap:10px;padding:12px;border:1px solid var(--bl);border-radius:6px;background:var(--sa);font-size:13px;color:var(--is)}.vc-check input{margin-top:4px}.vc-validation{min-height:22px;color:var(--r);font-size:13px;margin-top:10px}.vc-results{border-top:1px solid var(--bl);background:var(--sa);padding:0;max-height:0;overflow:hidden}.vc-results.vc-visible{max-height:1400px;padding:24px}.vc-result-grid{display:grid;grid-template-columns:repeat(2,1fr);gap:12px}.vc-rcard{background:var(--s);border:1px solid var(--bl);border-radius:8px;padding:16px}.vc-primary{grid-column:1\/-1;border:2px solid var(--a);background:var(--al)}.vc-rcard-label{font:500 10px var(--m);letter-spacing:.1em;text-transform:uppercase;color:var(--im)}.vc-rcard-value{font:600 19px var(--m);overflow-wrap:anywhere}.vc-primary .vc-rcard-value{font-size:24px;color:var(--a)}.vc-status{grid-column:1\/-1;padding:12px;background:var(--yl);border-left:3px solid var(--y);font-size:13px;color:var(--is)}.vc-section-toggle{width:100%;display:flex;justify-content:space-between;padding:18px 24px;border:0;background:transparent;cursor:pointer;text-align:left}.vc-section-title{font:700 18px var(--d)}.vc-section-body{max-height:0;overflow:hidden}.vc-section.vc-open .vc-section-body{max-height:15000px}.vc-section-inner{padding:0 24px 24px;border-top:1px solid var(--bl)}.vc-theory h3{font:700 17px var(--d);margin:24px 0 8px}.vc-theory p,.vc-theory li{font-size:14px;color:var(--is)}.vc-formula{padding:14px;border:2px solid var(--b);border-radius:6px;background:var(--sa);text-align:center;font:500 14px var(--m);margin:12px 0}.vc-warning{padding:14px;background:var(--yl);border-left:3px solid var(--y);color:var(--is)}.vc-faq-item{border:1px solid var(--bl);margin-top:8px}.vc-faq-q{width:100%;padding:14px;border:0;background:var(--sa);text-align:left;font-weight:600}.vc-faq-a{display:none;padding:14px;color:var(--is)}.vc-faq-item.vc-open .vc-faq-a{display:block}.vc-footer{text-align:center;padding:30px;color:var(--im);font-size:13px}@media(max-width:600px){.vc-grid,.vc-result-grid{grid-template-columns:1fr}.vc-full,.vc-primary,.vc-status{grid-column:1}}<\/style>\n<div class=\"vc-calculator\"><header class=\"vc-header\"><p class=\"vc-header-eyebrow\">Source-gated free-expansion arithmetic<\/p><h1 class=\"vc-header-title\">Documented Free Thermal Length-Change Arithmetic<\/h1><p class=\"vc-header-subtitle\">Calculate signed free linear thermal strain and length change using a documented mean coefficient for one material and uniform temperature interval. No expansion-loop geometry, restraint stress or code acceptance is invented.<\/p><div class=\"vc-badges\"><span class=\"vc-badge\">No material presets<\/span><span class=\"vc-badge\">No loop sizing<\/span><span class=\"vc-badge\">No stress OK\/OVER<\/span><\/div><\/header><div class=\"vc-card\"><form class=\"vc-form\" id=\"vc-form\" autocomplete=\"off\" novalidate><div class=\"vc-grid\"><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-length\">Reference free length L\u2080<\/label><input class=\"vc-input\" id=\"vc-length\" inputmode=\"decimal\"><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-length-unit\">Length unit<\/label><select class=\"vc-select\" id=\"vc-length-unit\"><option value=\"m\">m<\/option><option value=\"ft\">ft<\/option><option value=\"mm\">mm<\/option><option value=\"in\">in<\/option><\/select><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-t1\">Initial\/reference temperature T\u2081<\/label><input class=\"vc-input\" id=\"vc-t1\" inputmode=\"decimal\"><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-t2\">Final temperature T\u2082<\/label><input class=\"vc-input\" id=\"vc-t2\" inputmode=\"decimal\"><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-temp-unit\">Temperature unit<\/label><select class=\"vc-select\" id=\"vc-temp-unit\"><option value=\"c\">\u00b0C<\/option><option value=\"f\">\u00b0F<\/option><\/select><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-alpha\">Documented mean linear CTE \u03b1\u0304<\/label><input class=\"vc-input\" id=\"vc-alpha\" inputmode=\"decimal\"><\/div><div class=\"vc-field vc-full\"><label class=\"vc-label\" for=\"vc-alpha-unit\">CTE unit<\/label><select class=\"vc-select\" id=\"vc-alpha-unit\"><option value=\"um_mk\">\u03bcm\/(m\u00b7K) = 10\u207b\u2076\/K<\/option><option value=\"uin_inf\">\u03bcin\/(in\u00b7\u00b0F) = 10\u207b\u2076\/\u00b0F<\/option><\/select><\/div><div class=\"vc-field vc-full\"><label class=\"vc-label\" for=\"vc-source\">Material, condition and coefficient source<\/label><input class=\"vc-input\" id=\"vc-source\" type=\"text\" placeholder=\"material specification\/heat\/condition; coefficient type and source; covered T1\u2013T2 interval; revision\/date\"><\/div><div class=\"vc-field vc-full\"><label class=\"vc-check\" for=\"vc-gate\"><input id=\"vc-gate\" type=\"checkbox\"><span>L\u2080 is the free reference length at T\u2081. The entered mean\/secant linear CTE applies to the exact material, condition and complete T\u2081\u2013T\u2082 interval. Temperature is treated as uniform along the length and the small-strain linear free-expansion approximation is applicable. Restraints, supports, branches, joints, gradients and code load combinations are evaluated separately.<\/span><\/label><\/div><\/div><div class=\"vc-validation\" id=\"vc-validation\" role=\"status\" aria-live=\"polite\"><\/div><\/form><div class=\"vc-results\" id=\"vc-results\"><div class=\"vc-result-grid\"><div class=\"vc-rcard vc-primary\"><div class=\"vc-rcard-label\">Signed free length change \u0394L<\/div><div class=\"vc-rcard-value\" id=\"vc-r-delta\">\u2014<\/div><\/div><div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Temperature difference T\u2082\u2212T\u2081<\/div><div class=\"vc-rcard-value\" id=\"vc-r-dt\">\u2014<\/div><\/div><div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Free thermal strain \u03b5th<\/div><div class=\"vc-rcard-value\" id=\"vc-r-strain\">\u2014<\/div><\/div><div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Calculated free final length<\/div><div class=\"vc-rcard-value\" id=\"vc-r-final\">\u2014<\/div><\/div><div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Entered mean-CTE basis<\/div><div class=\"vc-rcard-value\" id=\"vc-r-alpha\">\u2014<\/div><\/div><div class=\"vc-status\" id=\"vc-r-note\">Free length-change arithmetic only.<\/div><\/div><\/div><\/div>\n<div class=\"vc-section vc-open\"><button class=\"vc-section-toggle\" type=\"button\" aria-expanded=\"true\"><span class=\"vc-section-title\">Equation and piping-code boundary<\/span><span>\u2304<\/span><\/button><div class=\"vc-section-body\"><div class=\"vc-section-inner vc-theory\"><div class=\"vc-formula\">\u0394T=T\u2082\u2212T\u2081;&nbsp; \u03b5th=\u03b1\u0304\u0394T;&nbsp; \u0394L=L\u2080\u03b5th;&nbsp; Lfree,2=L\u2080+\u0394L<\/div><p>\u03b1\u0304 is a documented mean\/secant linear coefficient over the complete interval, not a universal room-temperature material label. The relation is a small-strain free-expansion approximation and general mechanics arithmetic; it is not an EN 13480 or ASME B31.3 flexibility equation.<\/p><h3>Units and sign<\/h3><p>A kelvin and degree Celsius have equal interval size. A Fahrenheit interval is5\/9 of a kelvin interval. One international inch is0.0254m exactly and one international foot is0.3048m exactly. Positive \u0394L is elongation; negative \u0394L is contraction. Equal temperatures correctly return zero.<\/p><h3>Why no stress or loop result?<\/h3><p>Thermal strain becomes stress only through compatibility and restraint. Actual piping response depends on the complete three-dimensional routing, restraint stiffness and gaps, supports, branches, fittings, stress-intensification\/flexibility factors, material properties versus temperature, pressure\/weight\/occasional loads, cycles and the applicable acceptance procedure. A fully restrained uniaxial textbook expression is not a general piping stress result, and one guided-cantilever leg does not define an expansion loop.<\/p><h3>Current code scope<\/h3><p>EN13480-3:2024 is the current design-and-calculation part for industrial metallic piping systems including supports. ASME B31.3-2024 covers process-piping materials\/components,design,fabrication,assembly,erection,examination,inspection and testing. Neither public scope record validates a one-line loop or stress-pass formula.<\/p><div class=\"vc-warning\"><strong>NEEDS_LICENSED_SOURCE:<\/strong> exact flexibility,displacement-stress-range,stress-intensification,allowable-range,cycle,load-combination and acceptance rules from the selected current code edition. No compliance conclusion is emitted here.<\/div><h3>Not calculated<\/h3><ul><li>Expansion-loop leg\/width,guide or anchor geometry.<\/li><li>Restraint force,thermal stress,code stress range or fatigue utilization.<\/li><li>Pressure\/weight\/occasional loads,nozzle loads,support reactions or equipment movement.<\/li><li>Temperature gradients,creep,plasticity,phase changes,composite\/anisotropic response or transient temperature fields.<\/li><\/ul><h3>Sources<\/h3><p><a href=\"https:\/\/www.metallurgy.nist.gov\/mechanical_properties\/solder_paper.html\" target=\"_blank\" rel=\"noopener\">NIST definition and temperature dependence of linear CTE<\/a>; <a href=\"https:\/\/mechref.engr.illinois.edu\/sol\/axial.html\" target=\"_blank\" rel=\"noopener\">University of Illinois thermal strain and free elongation<\/a>; <a href=\"https:\/\/www.nen.nl\/en\/nen-en-13480-3-2024-en-327380\" target=\"_blank\" rel=\"noopener\">EN13480-3:2024 official national-body record<\/a>; <a href=\"https:\/\/www.asme.org\/codes-standards\/find-codes-standards\/b31-3-process-piping\/2024\" target=\"_blank\" rel=\"noopener\">ASME B31.3-2024 official record<\/a>.<\/p><\/div><\/div><\/div><div class=\"vc-section\"><button class=\"vc-section-toggle\" type=\"button\" aria-expanded=\"false\"><span class=\"vc-section-title\">Frequently asked questions<\/span><span>\u2304<\/span><\/button><div class=\"vc-section-body\"><div class=\"vc-section-inner\"><div id=\"vc-faq-list\"><\/div><\/div><\/div><\/div><footer class=\"vc-footer\">\u00a9 2024\u20132026 Vibromera \u2014 reviewed 13 July 2026<\/footer><\/div>\n<script>(function(){'use strict';function $(id){return document.getElementById(id)}function read(raw){var t=String(raw||'').trim();if(!t||(t.includes(',')&&t.includes('.')))return null;t=t.replace(',','.');if(!\/^[+-]?(?:\\d+(?:\\.\\d*)?|\\.\\d+)$\/.test(t))return null;var v=Number(t);return Number.isFinite(v)?v:null}function fmt(v){if(v===0)return'0';if(Math.abs(v)>=1e9||Math.abs(v)<1e-6)return v.toExponential(6);return Number(v.toPrecision(10)).toString()}function lengthSI(v,u){return v*({m:1,ft:.3048,mm:.001,in:.0254})[u]}function hide(m){$('vc-results').classList.remove('vc-visible');$('vc-validation').textContent=m||''}function calc(){if(!$('vc-source').value.trim())return hide('Enter the controlled material and coefficient source.');if(!$('vc-gate').checked)return hide('Confirm the free-expansion model and separate piping-analysis conditions.');var L0r=read($('vc-length').value),T1=read($('vc-t1').value),T2=read($('vc-t2').value),ar=read($('vc-alpha').value);if(L0r===null||L0r<=0||T1===null||T2===null||ar===null)return hide('Enter a positive length and complete finite temperatures\/CTE using a decimal point or comma.');var L0=lengthSI(L0r,$('vc-length-unit').value),dT=(T2-T1)*($('vc-temp-unit').value==='f'?5\/9:1),alpha=ar*1e-6*($('vc-alpha-unit').value==='uin_inf'?9\/5:1),strain=alpha*dT,dL=L0*strain,L2=L0+dL;if(![L0,dT,alpha,strain,dL,L2].every(Number.isFinite)||L2<=0)return hide('The stated linear model gives a non-positive or non-finite final length;verify inputs and applicability.');$('vc-r-delta').textContent=(dL>0?'+':'')+fmt(dL*1000)+' mm | '+(dL>0?'+':'')+fmt(dL\/.0254)+' in';$('vc-r-dt').textContent=(dT>0?'+':'')+fmt(dT)+' K | '+(dT>0?'+':'')+fmt(dT*9\/5)+' \u00b0F interval';$('vc-r-strain').textContent=(strain>0?'+':'')+fmt(strain)+' | '+(strain>0?'+':'')+fmt(strain*1e6)+' \u03bcstrain';$('vc-r-final').textContent=fmt(L2)+' m | '+fmt(L2\/.3048)+' ft';$('vc-r-alpha').textContent=fmt(alpha*1e6)+' \u03bcm\/(m\u00b7K) | '+fmt(alpha*1e6*5\/9)+' \u03bcin\/(in\u00b7\u00b0F)';$('vc-r-note').textContent=dL>0?'Free elongation only.No restraint stress,loop geometry or code acceptance is 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establishes that value as an applicable mean\/secant coefficient for the complete interval.'],['Why is contraction negative?','The signed result preserves T2\u2212T1.A lower final temperature normally gives negative free length change for positive CTE.']];var l=$('vc-faq-list');faq.forEach(function(x){var w=document.createElement('div');w.className='vc-faq-item';var b=document.createElement('button');b.type='button';b.className='vc-faq-q';b.textContent=x[0];var a=document.createElement('div');a.className='vc-faq-a';a.textContent=x[1];w.appendChild(b);w.appendChild(a);l.appendChild(w)});l.addEventListener('click',function(e){var b=e.target.closest('.vc-faq-q');if(b)b.closest('.vc-faq-item').classList.toggle('vc-open')});hide('')})();<\/script>\n","protected":false},"excerpt":{"rendered":"<p>Calculate signed free linear thermal strain and length change from a documented mean CTE without inventing loop geometry,restraint stress or piping-code 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