{"id":100091,"date":"2026-02-15T20:17:47","date_gmt":"2026-02-15T20:17:47","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100091"},"modified":"2026-07-12T03:59:47","modified_gmt":"2026-07-12T03:59:47","slug":"fatigue-life-calculator","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/id\/calculators\/fatigue-life-calculator\/","title":{"rendered":"S-N Log-Log Interpolation | Documented Curve Segment"},"content":{"rendered":"\r\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"S-N Log-Log Interpolation Calculator\",\"alternateName\":[\"Documented S-N Curve Interpolator\",\"Basquin Segment Interpolator\"],\"description\":\"Interpolate cycles within two documented points on one constant-amplitude S-N curve segment; extrapolation and design approval are not 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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}@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-fatigue-sn\"><header class=\"vc-header\"><p class=\"vc-header-eyebrow\">Documented curve segment required<\/p><h1 class=\"vc-header-title\">S\u2013N Log-Log Interpolation<\/h1><p class=\"vc-header-subtitle\">Interpolate cycles between two documented points from the same constant-amplitude S\u2013N curve. This tool does not create fatigue data from UTS, infer an endurance limit, extrapolate, or approve a design.<\/p><div class=\"vc-badges\"><span class=\"vc-badge\">Interpolation only<\/span><span class=\"vc-badge\">Same curve and stress ratio<\/span><span class=\"vc-badge\">Not an ISO compliance calculation<\/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-n1\">Point 1 cycles, N\u2081 <span class=\"vc-label-hint\">(lower cycle count)<\/span><\/label><input class=\"vc-input\" id=\"vc-n1\" inputmode=\"decimal\" type=\"text\"><\/div>\r\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-s1\">Point 1 stress, S\u2081 <span class=\"vc-label-hint\">(higher stress)<\/span><\/label><input class=\"vc-input\" id=\"vc-s1\" inputmode=\"decimal\" type=\"text\"><\/div>\r\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-n2\">Point 2 cycles, N\u2082 <span class=\"vc-label-hint\">(higher cycle count)<\/span><\/label><input class=\"vc-input\" id=\"vc-n2\" inputmode=\"decimal\" type=\"text\"><\/div>\r\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-s2\">Point 2 stress, S\u2082 <span class=\"vc-label-hint\">(lower stress)<\/span><\/label><input class=\"vc-input\" id=\"vc-s2\" inputmode=\"decimal\" type=\"text\"><\/div>\r\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-target\">Target stress, S<\/label><input class=\"vc-input\" id=\"vc-target\" inputmode=\"decimal\" type=\"text\"><\/div>\r\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-unit\">Common stress unit<\/label><select class=\"vc-select\" id=\"vc-unit\"><option value=\"\">Select\u2026<\/option><option value=\"MPa\">MPa<\/option><option value=\"ksi\">ksi<\/option><\/select><\/div>\r\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-quantity\">Documented stress quantity<\/label><select class=\"vc-select\" id=\"vc-quantity\"><option value=\"\">Select\u2026<\/option><option value=\"amplitude\">Stress amplitude<\/option><option value=\"range\">Stress range<\/option><option value=\"maximum\">Maximum stress<\/option><\/select><\/div>\r\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-ratio\">Curve stress ratio \/ mean-stress basis<\/label><input class=\"vc-input\" id=\"vc-ratio\" type=\"text\" maxlength=\"300\" placeholder=\"e.g. R = \u22121; no correction\"><\/div>\r\n<div class=\"vc-field vc-field-full\"><label class=\"vc-label\" for=\"vc-probability\">Curve probability \/ reliability basis<\/label><input class=\"vc-input\" id=\"vc-probability\" type=\"text\" maxlength=\"300\" placeholder=\"e.g. median fit; survival probability not stated\"><\/div>\r\n<div class=\"vc-field vc-field-full\"><label class=\"vc-label\" for=\"vc-source\">Exact curve \/ test report \/ dataset source<\/label><input class=\"vc-input\" id=\"vc-source\" type=\"text\" maxlength=\"500\"><\/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>Required compatibility:<\/strong> both points and the target must use the same material condition, specimen\/component definition, environment, loading mode, stress quantity, stress ratio or documented mean-stress treatment, failure\/runout definition, and probability basis. A published material name alone is not enough.<\/p><\/div><\/form>\r\n<div class=\"vc-results\" id=\"vc-results\"><div class=\"vc-results-head\"><h2 class=\"vc-results-title\">Interpolated point on this curve segment<\/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\">Interpolated cycles, N<\/div><div class=\"vc-rcard-value\" id=\"vc-r-n\">\u2014<\/div><\/div>\r\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Log-log slope, b<\/div><div class=\"vc-rcard-value\" id=\"vc-r-b\">\u2014<\/div><\/div>\r\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Segment coefficient, a<\/div><div class=\"vc-rcard-value\" id=\"vc-r-a\">\u2014<\/div><\/div>\r\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Position from point 1 to point 2<\/div><div class=\"vc-rcard-value\" id=\"vc-r-t\">\u2014<\/div><\/div>\r\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Method<\/div><div class=\"vc-rcard-value\" id=\"vc-r-method\">Log-log interpolation<\/div><\/div>\r\n<\/div><p id=\"vc-r-note\" style=\"margin:0;color:var(--vc-ink-secondary)\"><\/p><\/div><\/div>\r\n\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\">Formula, scope and standards context<\/span><\/span><\/button><div class=\"vc-section-body\"><div class=\"vc-section-inner vc-theory\">\r\n<p>For two positive points (N\u2081,S\u2081) and (N\u2082,S\u2082) on one straight segment in log-log coordinates, this calculator uses <strong>b=ln(S\u2082\/S\u2081)\/ln(N\u2082\/N\u2081)<\/strong>, <strong>a=S\u2081\/N\u2081<sup>b<\/sup><\/strong>, and <strong>N=(S\/a)<sup>1\/b<\/sup><\/strong>. Equivalently, ln N is linearly interpolated between ln N\u2081 and ln N\u2082. Cycle count is dimensionless; a has the selected stress unit. Using MPa or ksi consistently gives the same N and b.<\/p>\r\n<p>The calculator accepts only N\u2081&lt;N\u2082, S\u2081&gt;S\u2082 and S\u2082\u2264S\u2264S\u2081. Values outside the segment are rejected because extrapolation can cross a knee, runout region, different failure mechanism, or a regime where a different model is required. Equality with either endpoint returns that endpoint; no \u201cinfinite life\u201d is inferred.<\/p>\r\n<p><a href=\"https:\/\/www.iso.org\/standard\/67847.html\" target=\"_blank\" rel=\"noopener\">ISO 1099:2017, edition 3<\/a> is Published but at stage 90.92 (to be revised); <a href=\"https:\/\/www.iso.org\/standard\/85731.html\" target=\"_blank\" rel=\"noopener\">ISO\/FDIS 1099, edition 4<\/a> is under development. Its scope is axial, constant-amplitude, force-controlled fatigue testing of metallic specimens at ambient temperature and it obtains stress-versus-cycles information at specified stress ratios. It does not make a UTS-based generic curve or turn this interpolation into an ISO conformity result.<\/p>\r\n<p><a href=\"https:\/\/www.iso.org\/standard\/50242.html\" target=\"_blank\" rel=\"noopener\">ISO 12107:2012, edition 2<\/a> is Published and addresses statistical planning and analysis of metallic fatigue data; an <a href=\"https:\/\/www.iso.org\/standard\/85730.html\" target=\"_blank\" rel=\"noopener\">edition 3 work item<\/a> is under development. The licensed standard is required for its detailed procedures. This page neither performs the specified statistical analysis nor assigns a survival probability.<\/p>\r\n<p>NASA material describes a Basquin curve as a straight line in log-log form defined by fitted coefficients, and NASA\u2019s reliability handbook describes its constants as empirical and dependent on material and environment. A NIST fatigue study illustrates that fitted coefficients can carry substantial uncertainty and that mean stress changes the lifetime relation. Those sources support the restrictions here; they do not supply universal coefficients.<\/p>\r\n<div class=\"vc-warning-box\"><p style=\"margin:0\"><strong>Not included:<\/strong> mean-stress correction, variable-amplitude cycle counting or Palmgren\u2013Miner damage, low-cycle strain-life, multiaxial fatigue, crack-growth\/fracture mechanics, size\/surface\/notch\/environment corrections, runout treatment, confidence bounds, safety factors, inspection intervals, or design acceptance. Use a qualified fatigue analysis and applicable design code for consequential decisions.<\/p><\/div>\r\n<p>Sources: <a href=\"https:\/\/ntrs.nasa.gov\/api\/citations\/20160012240\/downloads\/20160012240.pdf?attachment=true\" target=\"_blank\" rel=\"noopener\">NASA\/NESC S\u2013N and spectral-fatigue paper<\/a>; <a href=\"https:\/\/ntrs.nasa.gov\/api\/citations\/19950009170\/downloads\/19950009170.pdf\" target=\"_blank\" rel=\"noopener\">NASA fatigue reliability handbook<\/a>; <a href=\"https:\/\/tsapps.nist.gov\/publication\/get_pdf.cfm?pub_id=50339\" target=\"_blank\" rel=\"noopener\">NIST fatigue-coefficient study<\/a>; ISO catalogue records linked above. Status checked 12 July 2026.<\/p>\r\n<\/div><\/div><\/div>\r\n<footer class=\"vc-footer\"><p>\u00a9 2024\u20132026 <a href=\"https:\/\/vibromera.eu\/\">Vibromera<\/a><\/p><p>Reference interpolation only; not a fatigue-life certification, design check or ISO test. Scientific review: July 2026.<\/p><\/footer><\/div>\r\n<script>(function(){'use strict';function $(i){return document.getElementById(i)}function pnum(s){s=s.trim().replace(',','.');return \/^[+]?(?:\\d+(?:\\.\\d*)?|\\.\\d+)(?:[eE][+-]?\\d+)?$\/.test(s)?Number(s):NaN}function clear(){['vc-r-n','vc-r-b','vc-r-a','vc-r-t'].forEach(function(id){$(id).textContent='\u2014'});$('vc-r-note').textContent='';$('vc-results').classList.remove('vc-visible')}function calc(){var ids=['vc-n1','vc-s1','vc-n2','vc-s2','vc-target','vc-unit','vc-quantity','vc-ratio','vc-probability','vc-source'],raw=ids.map(function(id){return $(id).value.trim()}),any=raw.some(Boolean);if(!raw.every(Boolean)){clear();$('vc-error').textContent=any?'Complete all ten fields using one documented curve segment.':'';return}var n1=pnum(raw[0]),s1=pnum(raw[1]),n2=pnum(raw[2]),s2=pnum(raw[3]),s=pnum(raw[4]);if(![n1,s1,n2,s2,s].every(function(v){return Number.isFinite(v)&&v>0})){clear();$('vc-error').textContent='Cycle counts and stresses must be strict, finite, positive numbers.';return}if(!(n1<n2)){clear();$('vc-error').textContent='Point order must satisfy N\u2081 < N\u2082.';return}if(!(s1>s2)){clear();$('vc-error').textContent='For this decreasing segment, stresses must satisfy S\u2081 > S\u2082.';return}if(s<s2||s>s1){clear();$('vc-error').textContent='Target stress is outside [S\u2082,S\u2081]; extrapolation is intentionally rejected.';return}var lnratio=Math.log(n2\/n1),b=Math.log(s2\/s1)\/lnratio,t=Math.log(s\/s1)\/Math.log(s2\/s1),lnn=Math.log(n1)+t*lnratio,n=Math.exp(lnn),a=Math.exp(Math.log(s1)-b*Math.log(n1));if(![b,t,n,a].every(Number.isFinite)||n<=0||a<=0){clear();$('vc-error').textContent='These values exceed the calculator\u2019s finite numerical range.';return}$('vc-error').textContent='';$('vc-r-n').textContent=n.toPrecision(12)+' cycles';$('vc-r-b').textContent=b.toPrecision(12);$('vc-r-a').textContent=a.toPrecision(12)+' '+raw[5];$('vc-r-t').textContent=(t*100).toFixed(6)+'%';$('vc-r-note').textContent='Source: '+raw[9]+' | '+raw[6]+' in '+raw[5]+' | '+raw[7]+' | '+raw[8]+' | No extrapolation or design verdict.';$('vc-results').classList.add('vc-visible');var u=new URL(location),keys=['n1','s1','n2','s2','target','unit','stress_quantity','stress_ratio_basis','probability_basis','source'];keys.forEach(function(k,i){u.searchParams.set(k,raw[i])});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 p=new URLSearchParams(location.search),keys=['n1','s1','n2','s2','target','unit','stress_quantity','stress_ratio_basis','probability_basis','source'],ids=['vc-n1','vc-s1','vc-n2','vc-s2','vc-target','vc-unit','vc-quantity','vc-ratio','vc-probability','vc-source'];keys.forEach(function(k,i){if(p.has(k))$(ids[i]).value=p.get(k)});calc()})();<\/script>\r\n","protected":false},"excerpt":{"rendered":"<p>Interpolate cycles only within two documented points on one constant-amplitude S-N curve segment;no extrapolation,material presets or design verdict.<\/p>","protected":false},"featured_media":0,"template":"","meta":{"ai_generated_summary":"","footnotes":""},"categories":[],"tags":[],"class_list":["post-100091","calculator","type-calculator","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/vibromera.eu\/id\/wp-json\/wp\/v2\/calculator\/100091","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vibromera.eu\/id\/wp-json\/wp\/v2\/calculator"}],"about":[{"href":"https:\/\/vibromera.eu\/id\/wp-json\/wp\/v2\/types\/calculator"}],"version-history":[{"count":2,"href":"https:\/\/vibromera.eu\/id\/wp-json\/wp\/v2\/calculator\/100091\/revisions"}],"predecessor-version":[{"id":102392,"href":"https:\/\/vibromera.eu\/id\/wp-json\/wp\/v2\/calculator\/100091\/revisions\/102392"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/id\/wp-json\/wp\/v2\/media?parent=100091"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/id\/wp-json\/wp\/v2\/categories?post=100091"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/id\/wp-json\/wp\/v2\/tags?post=100091"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}