{"id":100255,"date":"2026-02-15T20:29:55","date_gmt":"2026-02-15T20:29:55","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100255"},"modified":"2026-07-15T19:03:33","modified_gmt":"2026-07-15T19:03:33","slug":"thermal-expansion-calculator","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/hi\/calculators\/thermal-expansion-calculator\/","title":{"rendered":"Source-Controlled Linear Thermal Expansion Calculator"},"content":{"rendered":"<p><script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Source-Controlled Linear Thermal Expansion Calculator\",\"description\":\"Calculate one-dimensional free thermal length change from a user-supplied mean linear expansion coefficient valid for the stated material condition and temperature interval.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/thermal-expansion-calculator\/\",\"applicationCategory\":\"EngineeringApplication\",\"operatingSystem\":\"Any\",\"isAccessibleForFree\":true,\"dateModified\":\"2026-07-15\",\"publisher\":{\"@type\":\"Organization\",\"name\":\"Vibromera\",\"url\":\"https:\/\/vibromera.eu\/\"}}<\/script><\/p>\n<style>\n#te-tool{--te-ink:#17212b;--te-muted:#53616f;--te-line:#cbd5df;--te-soft:#f4f7f9;--te-blue:#075985;--te-blue2:#e0f2fe;--te-red:#991b1b;--te-red2:#fef2f2;--te-green:#166534;max-width:980px;margin:24px auto;font-family:Inter,system-ui,-apple-system,\"Segoe UI\",sans-serif;color:var(--te-ink);line-height:1.55}#te-tool *{box-sizing:border-box}#te-tool h1,#te-tool h2,#te-tool h3{line-height:1.2;color:var(--te-ink)}#te-tool h1{font-size:clamp(1.65rem,4vw,2.35rem);margin:0 0 12px}#te-tool h2{font-size:1.28rem;margin:0 0 16px}#te-tool h3{font-size:1rem;margin:0 0 8px}#te-tool p{margin:0 0 12px}#te-tool 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auto}.te-result-grid{grid-template-columns:1fr}.te-card,.te-hero{border-radius:10px}.te-actions{display:grid}.te-btn{width:100%}}\n<\/style>\n<p><main id=\"te-tool\"><\/p>\n<header class=\"te-hero\">\n<div class=\"te-kicker\">Traceable free linear expansion<\/div>\n<h1>Linear Thermal Expansion Calculator<\/h1>\n<p class=\"te-lead\">Calculate one-dimensional free length change using a <strong>mean linear coefficient of thermal expansion supplied for the exact material condition and temperature interval<\/strong>. The tool does not invent a material coefficient or perform a piping-code stress analysis.<\/p>\n<div class=\"te-badges\"><span class=\"te-badge\">User-sourced mean CTE<\/span><span class=\"te-badge\">Exact unit paths<\/span><span class=\"te-badge\">No material presets<\/span><\/div>\n<\/header>\n<div class=\"te-alert\"><strong>Applicability boundary.<\/strong> This is a free, one-dimensional length-change calculation. It does not calculate restrained stress, support reactions, pressure effects, expansion joints, pipe-loop geometry, buckling, creep, plasticity, anisotropy or code compliance.<\/div>\n<form id=\"te-form\" class=\"te-card\" novalidate aria-labelledby=\"te-input-heading\">\n<h2 id=\"te-input-heading\">Inputs<\/h2>\n<div class=\"te-grid\">\n<div class=\"te-field\"><label for=\"te-length\">Original free length L\u2080 <span class=\"te-required\">*<\/span><\/label><input class=\"te-input\" id=\"te-length\" type=\"text\" inputmode=\"decimal\" maxlength=\"40\" autocomplete=\"off\" placeholder=\"For example: 6000\"><\/p>\n<div class=\"te-help\">Must be positive.<\/div>\n<\/div>\n<div class=\"te-field\"><label for=\"te-length-unit\">Length unit <span class=\"te-required\">*<\/span><\/label><select class=\"te-select\" id=\"te-length-unit\"><option value=\"\">Select<\/option><option value=\"mm\">millimetre (mm)<\/option><option value=\"m\">metre (m)<\/option><option value=\"in\">international inch (in)<\/option><\/select><\/div>\n<div class=\"te-field\"><label for=\"te-alpha\">Mean linear CTE \u03b1\u0304 <span class=\"te-required\">*<\/span><\/label><input class=\"te-input\" id=\"te-alpha\" type=\"text\" inputmode=\"decimal\" maxlength=\"40\" autocomplete=\"off\" placeholder=\"For example: 12\"><\/p>\n<div class=\"te-help\">\u00b5m\/(m\u00b7K), numerically equal to 10\u207b\u2076\/K. Signed values are allowed only when supported by the source.<\/div>\n<\/div>\n<div class=\"te-field\"><label for=\"te-temp-unit\">Temperature scale <span class=\"te-required\">*<\/span><\/label><select class=\"te-select\" id=\"te-temp-unit\"><option value=\"\">Select<\/option><option value=\"C\">degrees Celsius (\u00b0C)<\/option><option value=\"F\">degrees Fahrenheit (\u00b0F)<\/option><\/select><\/p>\n<div class=\"te-help\">Both endpoints must use the same scale.<\/div>\n<\/div>\n<div class=\"te-field\"><label for=\"te-t1\">Initial temperature T\u2081 <span class=\"te-required\">*<\/span><\/label><input class=\"te-input\" id=\"te-t1\" type=\"text\" inputmode=\"decimal\" maxlength=\"40\" autocomplete=\"off\" placeholder=\"For example: 20\"><\/div>\n<div class=\"te-field\"><label for=\"te-t2\">Final temperature T\u2082 <span class=\"te-required\">*<\/span><\/label><input class=\"te-input\" id=\"te-t2\" type=\"text\" inputmode=\"decimal\" maxlength=\"40\" autocomplete=\"off\" placeholder=\"For example: 100\"><\/div>\n<div class=\"te-field te-wide\"><label for=\"te-source\">CTE source and material condition <span class=\"te-required\">*<\/span><\/label><input class=\"te-input\" id=\"te-source\" type=\"text\" maxlength=\"300\" autocomplete=\"off\" placeholder=\"Document, table\/revision, alloy or grade, temper\/condition, and stated temperature range\"><\/p>\n<div class=\"te-help\">The calculator stores nothing; this text is echoed only into the result record.<\/div>\n<\/div><\/div>\n<p>    <label class=\"te-check\" for=\"te-confirm\"><input id=\"te-confirm\" type=\"checkbox\"><span>I confirmed that \u03b1\u0304 is a <strong>mean linear CTE applicable to this exact material direction\/condition and the full T\u2081\u2013T\u2082 interval<\/strong>, and that the member is free to change length.<\/span><\/label><\/p>\n<div class=\"te-actions\"><button class=\"te-btn te-primary\" type=\"submit\">Calculate free length change<\/button><button class=\"te-btn te-secondary\" id=\"te-reset\" type=\"button\">Clear<\/button><\/div>\n<div class=\"te-status\" id=\"te-status\" role=\"alert\" aria-live=\"polite\"><\/div>\n<\/p><\/form>\n<section class=\"te-card te-output\" id=\"te-output\" data-visible=\"false\" aria-labelledby=\"te-output-heading\">\n<h2 id=\"te-output-heading\">Calculated free length change<\/h2>\n<div class=\"te-result-grid\">\n<div class=\"te-result\"><span>Temperature change<\/span><output id=\"te-r-dt\">\u2014<\/output><\/div>\n<div class=\"te-result\"><span>Thermal strain<\/span><output id=\"te-r-strain\">\u2014<\/output><\/div>\n<div class=\"te-result\"><span>Length change<\/span><output id=\"te-r-dl\">\u2014<\/output><\/div>\n<div class=\"te-result\"><span>Final free length<\/span><output id=\"te-r-final\">\u2014<\/output><\/div>\n<\/p><\/div>\n<p class=\"te-note\" id=\"te-r-source\">\n<p class=\"te-note\">Arithmetic only: apply the uncertainty of L\u2080, both temperatures and the supplied mean CTE. A negative \u0394L means contraction along the stated direction.<\/p>\n<\/section>\n<section class=\"te-card\" aria-labelledby=\"te-method-heading\">\n<h2 id=\"te-method-heading\">Definition, formula and unit treatment<\/h2>\n<div class=\"te-formula\">Mean linear CTE over T\u2081\u2192T\u2082: \u03b1\u0304 = \u0394L \/ (L\u2080 \u00b7 \u0394T)<br \/>Therefore: \u0394L = L\u2080 \u00b7 (\u03b1\u0304 \u00d7 10\u207b\u2076 K\u207b\u00b9) \u00b7 \u0394T<br \/>Final free length: L\u2082 = L\u2080 + \u0394L<\/div>\n<p>The equation is the rearranged definition of the <em>mean<\/em> coefficient over the stated interval. It is not an ISO pipe-design formula. For Celsius endpoints, \u0394T in kelvins equals T\u2082\u2212T\u2081. For Fahrenheit endpoints, \u0394T in kelvins equals (T\u2082\u2212T\u2081)\u00d75\/9. The international inch is exactly 25.4 mm.<\/p>\n<div class=\"te-boundary\">\n<div>\n<h3>Required evidence<\/h3>\n<ul>\n<li>Exact material and condition.<\/li>\n<li>Direction if anisotropic.<\/li>\n<li>Mean CTE source and interval.<\/li>\n<\/ul>\n<\/div>\n<div>\n<h3>Rejected<\/h3>\n<ul>\n<li>Temperatures below absolute zero.<\/li>\n<li>Zero\/negative original length.<\/li>\n<li>Exponent, grouping or unit suffix.<\/li>\n<li>A result with non-positive final length.<\/li>\n<\/ul>\n<\/div>\n<div>\n<h3>Not calculated<\/h3>\n<ul>\n<li>Stress, force or yield margin.<\/li>\n<li>Volumetric\/fluid expansion.<\/li>\n<li>Pipe loops or expansion joints.<\/li>\n<li>Any code acceptance decision.<\/li>\n<\/ul>\n<\/div><\/div>\n<div class=\"te-info\"><strong>Why there is no generic material table.<\/strong> NIST cautions that a handbook label such as \u201csteel\u201d may not identify the actual alloy and that reference values are averages over a stated temperature range. NIST copper data also show CTE changing materially with temperature. Use a controlled manufacturer, material-standard or measured source for the actual condition.<\/div>\n<\/section>\n<section class=\"te-card\" aria-labelledby=\"te-source-heading\">\n<h2 id=\"te-source-heading\">Primary sources and standards boundary<\/h2>\n<ul class=\"te-source-list\">\n<li><a href=\"https:\/\/store.astm.org\/standards\/e228\" rel=\"noopener\" target=\"_blank\">ASTM E228-22, Standard Test Method for Linear Thermal Expansion of Solid Materials With a Push-Rod Dilatometer<\/a> \u2014 active. ASTM states that accurate expansion determination requires a calibrated dilatometer and accurate length and temperature measurements. This calculator does not implement that test method.<\/li>\n<li><a href=\"https:\/\/www.iso.org\/standard\/81835.html\" rel=\"noopener\" target=\"_blank\">ISO 11359-2:2021, Plastics \u2014 Thermomechanical analysis \u2014 Part 2<\/a> \u2014 Edition 2, published, stage 90.60 after systematic review. Its public scope is a TMA method for solid-state plastics; it is not a universal material-property table.<\/li>\n<li><a href=\"https:\/\/emtoolbox.nist.gov\/faq\/faq.asp\" rel=\"noopener\" target=\"_blank\">NIST Engineering Metrology Toolbox FAQ<\/a> \u2014 explains why an actual manufacturer\/material source and its temperature range are needed instead of an unidentified handbook coefficient.<\/li>\n<li><a href=\"https:\/\/itl.nist.gov\/div898\/handbook\/pmd\/section6\/pmd641.htm\" rel=\"noopener\" target=\"_blank\">NIST\/SEMATECH e-Handbook, Thermal Expansion of Copper case study<\/a> \u2014 provides measured CTE as a function of temperature, demonstrating that a single coefficient is not generally universal.<\/li>\n<li><a href=\"https:\/\/www.bipm.org\/documents\/20126\/41483022\/SI-Brochure-9-EN.pdf\" rel=\"noopener\" target=\"_blank\">BIPM SI Brochure, 9th edition, version 4.01 (2026)<\/a>, page 129 \u2014 distinguishes temperature values from temperature differences and states the kelvin\/degree-Celsius interval relation.<\/li>\n<li><a href=\"https:\/\/www.nist.gov\/pml\/special-publication-811\/nist-guide-si-appendix-b-conversion-factors\/nist-guide-si-appendix-b8\" rel=\"noopener\" target=\"_blank\">NIST SP 811, Appendix B.8<\/a> \u2014 exact temperature-interval and international-inch conversion factors.<\/li>\n<\/ul>\n<p><strong>Classification:<\/strong> general engineering calculation from a user-controlled mean coefficient. It is not a conformity assessment, material database, stress analysis or implementation of ASTM E228 or ISO 11359-2.<\/p>\n<\/section>\n<p><\/main><\/p>\n<p><script>\n(function(){\n  'use strict';\n  function byId(id){return document.getElementById(id);}\n  function parsePlain(raw){var t=String(raw).trim();if(t.length<1||t.length>40||!(\/^[+-]?(?:\\d+(?:[.,]\\d*)?|[.,]\\d+)$\/).test(t))throw new Error('format');var n=Number(t.replace(',','.'));if(!Number.isFinite(n))throw new Error('format');return Object.is(n,-0)?0:n;}\n  function cleanSource(raw){var t=String(raw).trim();if(t.length<3||t.length>300||\/[\\u0000-\\u001f\\u007f]\/.test(t))throw new Error('source');return t;}\n  function toMeters(value,unit){if(!(value>0))throw new Error('length');if(unit!=='mm'&&unit!=='m'&&unit!=='in')throw new Error('length-unit');var m=unit==='mm'?value\/1000:unit==='m'?value:value*0.0254;if(!Number.isFinite(m)||m<=0||m>1e12)throw new Error('length-range');return m;}\n  function endpointKelvin(value,scale){if(scale!=='C'&&scale!=='F')throw new Error('temperature-unit');var k=scale==='C'?value+273.15:(value+459.67)*5\/9;if(!Number.isFinite(k))throw new Error('temperature-range');if(k<0&&k>-1e-12)k=0;if(k<0)throw new Error('below');if(k>1e9)throw new Error('temperature-range');return k;}\n  function deltaK(t1,t2,scale){var k1=endpointKelvin(t1,scale),k2=endpointKelvin(t2,scale);return k2-k1;}\n  function calculate(length,unit,alpha,t1,t2,scale){var l0=toMeters(length,unit);if(!Number.isFinite(alpha)||Math.abs(alpha)>1e6)throw new Error('alpha');var dt=deltaK(t1,t2,scale),strain=alpha*1e-6*dt,dl=l0*strain,finalLength=l0+dl;if(!Number.isFinite(strain)||!Number.isFinite(dl)||!Number.isFinite(finalLength))throw new Error('result');if(finalLength<=0)throw new Error('final');return Object.freeze({l0_m:l0,dt_K:dt,strain:strain,dl_m:dl,final_m:finalLength});}\n  function fmt(n){if(Object.is(n,-0)||Math.abs(n)<1e-15)n=0;var a=Math.abs(n);if(a!==0&&(a>=1e12||a<1e-9))return n.toExponential(11).replace(\/\\.?0+e\/,'e');return new Intl.NumberFormat('en-US',{maximumSignificantDigits:12,useGrouping:false}).format(n);}\n  function displayLength(m,unit){var value=unit==='mm'?m*1000:unit==='m'?m:m\/0.0254;return fmt(value)+' '+unit;}\n  function clearResults(){byId('te-output').dataset.visible='false';['dt','strain','dl','final'].forEach(function(x){byId('te-r-'+x).textContent='\u2014';});byId('te-r-source').textContent='';}\n  function fail(message,field){clearResults();var s=byId('te-status');s.dataset.kind='error';s.textContent=message;if(field)field.focus();}\n  byId('te-form').addEventListener('submit',function(ev){\n    ev.preventDefault();var length,alpha,t1,t2,source,result,unit=byId('te-length-unit').value,scale=byId('te-temp-unit').value;\n    try{length=parsePlain(byId('te-length').value);}catch(e){fail('Enter the original length as one signed plain decimal.',byId('te-length'));return;}\n    try{alpha=parsePlain(byId('te-alpha').value);}catch(e){fail('Enter the mean linear CTE as one signed plain decimal.',byId('te-alpha'));return;}\n    try{t1=parsePlain(byId('te-t1').value);}catch(e){fail('Enter the initial temperature as one signed plain decimal.',byId('te-t1'));return;}\n    try{t2=parsePlain(byId('te-t2').value);}catch(e){fail('Enter the final temperature as one signed plain decimal.',byId('te-t2'));return;}\n    try{source=cleanSource(byId('te-source').value);}catch(e){fail('Identify the controlled CTE source and material condition in 3\u2013300 characters.',byId('te-source'));return;}\n    if(!byId('te-confirm').checked){fail('Confirm the mean-CTE applicability and free-expansion conditions.',byId('te-confirm'));return;}\n    try{result=calculate(length,unit,alpha,t1,t2,scale);}catch(e){var messages={length:'Original length must be greater than zero.','length-range':'Original length is outside the documented computational range.','length-unit':'Select the original length unit.',alpha:'The CTE magnitude must not exceed 1000000 \u00b5m\/(m\u00b7K).','temperature-unit':'Select the temperature scale.','temperature-range':'A temperature endpoint is outside the documented computational range.',below:'A temperature endpoint is below absolute zero.',final:'The supplied data produce a non-positive final length; the mean-CTE model is not applicable.',result:'The supplied values do not produce a finite result.'};fail(messages[e.message]||messages.result,e.message==='length-unit'?byId('te-length-unit'):e.message==='temperature-unit'?byId('te-temp-unit'):e.message==='alpha'?byId('te-alpha'):e.message==='below'||e.message==='temperature-range'?byId('te-t1'):byId('te-length'));return;}\n    byId('te-r-dt').textContent=fmt(result.dt_K)+' K';byId('te-r-strain').textContent=fmt(result.strain)+' ('+fmt(result.strain*1e6)+' \u00b5m\/m)';byId('te-r-dl').textContent=fmt(result.dl_m*1000)+' mm ('+fmt(result.dl_m*1e6)+' \u00b5m; '+fmt(result.dl_m\/0.0254)+' in)';byId('te-r-final').textContent=displayLength(result.final_m,unit);byId('te-r-source').textContent='CTE source\/condition recorded by user: '+source;byId('te-output').dataset.visible='true';var s=byId('te-status');s.dataset.kind='ok';s.textContent=result.dl_m>0?'Free expansion calculated.':result.dl_m<0?'Free contraction calculated.':'No free length change for the supplied data.';byId('te-output').scrollIntoView({behavior:'smooth',block:'start'});\n  });\n  byId('te-reset').addEventListener('click',function(){byId('te-form').reset();clearResults();var s=byId('te-status');s.textContent='';s.dataset.kind='';byId('te-length').focus();});\n  window.C100255Test=Object.freeze({parsePlain:parsePlain,cleanSource:cleanSource,toMeters:toMeters,endpointKelvin:endpointKelvin,deltaK:deltaK,calculate:calculate});clearResults();\n})();\n<\/script><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Calculate free one-dimensional length change from a documented mean linear CTE valid for the stated material condition and temperature interval.<\/p>","protected":false},"featured_media":0,"template":"","meta":{"ai_generated_summary":"","footnotes":""},"categories":[],"tags":[],"class_list":["post-100255","calculator","type-calculator","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/vibromera.eu\/hi\/wp-json\/wp\/v2\/calculator\/100255","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vibromera.eu\/hi\/wp-json\/wp\/v2\/calculator"}],"about":[{"href":"https:\/\/vibromera.eu\/hi\/wp-json\/wp\/v2\/types\/calculator"}],"version-history":[{"count":4,"href":"https:\/\/vibromera.eu\/hi\/wp-json\/wp\/v2\/calculator\/100255\/revisions"}],"predecessor-version":[{"id":102599,"href":"https:\/\/vibromera.eu\/hi\/wp-json\/wp\/v2\/calculator\/100255\/revisions\/102599"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/hi\/wp-json\/wp\/v2\/media?parent=100255"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/hi\/wp-json\/wp\/v2\/categories?post=100255"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/hi\/wp-json\/wp\/v2\/tags?post=100255"}],"curies":[{"name":"\u0921\u092c\u094d\u0932\u094d\u092f\u0942\u092a\u0940","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}