{"id":100151,"date":"2026-02-15T20:21:13","date_gmt":"2026-02-15T20:21:13","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100151"},"modified":"2026-02-15T20:21:13","modified_gmt":"2026-02-15T20:21:13","slug":"measurement-uncertainty","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/nb\/calculators\/measurement-uncertainty\/","title":{"rendered":"Kalkulator for m\u00e5leusikkerhet | ISO 17025 \/ GUM"},"content":{"rendered":"\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Measurement Uncertainty Calculator\",\"description\":\"Calculate combined and expanded measurement uncertainty per GUM \/ ISO 17025.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/measurement-uncertainty\/\",\"applicationCategory\":\"Engineering Calculator\",\"operatingSystem\":\"Any (Web Browser)\",\"offers\":{\"@type\":\"Offer\",\"price\":\"0\",\"priceCurrency\":\"EUR\"},\"creator\":{\"@type\":\"Organization\",\"name\":\"Vibromera\",\"url\":\"https:\/\/vibromera.eu\/\"},\"datePublished\":\"2024-01-01\",\"dateModified\":\"2025-02-14\",\"inLanguage\":\"en\",\"isAccessibleForFree\":true}<\/script>\n\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[\n{\"@type\":\"Question\",\"name\":\"What is measurement uncertainty?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Measurement uncertainty quantifies the doubt about a measurement result. It defines a range within which the true value is expected to lie with a stated probability (typically 95%). Required by ISO 17025 for all calibration and testing laboratories.\"}},\n{\"@type\":\"Question\",\"name\":\"What is the difference between Type A and Type B uncertainty?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Type A uncertainty is evaluated by statistical analysis of repeated measurements (standard deviation of the mean). Type B is evaluated by other means: manufacturer specifications, calibration certificates, experience, or published data.\"}},\n{\"@type\":\"Question\",\"name\":\"What is the coverage factor k?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"The coverage factor k multiplies the combined standard uncertainty to give expanded uncertainty. k=2 corresponds to approximately 95% confidence level (assuming normal distribution). k=3 gives about 99.7%.\"}},\n{\"@type\":\"Question\",\"name\":\"How do I combine uncertainty sources?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"For independent (uncorrelated) sources, the combined standard uncertainty is the root sum of squares (RSS): uc = \u221a(u1\u00b2 + u2\u00b2 + u3\u00b2 + ...). This is the law of propagation of uncertainty from GUM.\"}},\n{\"@type\":\"Question\",\"name\":\"What is GUM?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"GUM (Guide to the Expression of Uncertainty in Measurement) is the international guide for evaluating and expressing measurement uncertainty. Published by JCGM (Joint Committee for Guides in Metrology), it is the basis for ISO 17025 uncertainty requirements.\"}}\n]}<\/script>\n\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\":\"Measurement Uncertainty\",\"item\":\"https:\/\/vibromera.eu\/calculators\/measurement-uncertainty\/\"}]}<\/script>\n\n<link rel=\"preconnect\" href=\"https:\/\/fonts.googleapis.com\">\n\n<link rel=\"preconnect\" href=\"https:\/\/fonts.gstatic.com\" crossorigin>\n\n<link 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class=\"vc-calculator\" id=\"vc-uncertainty\">\n<header class=\"vc-header\">\n    <p class=\"vc-header-eyebrow\">Free Engineering Tool<\/p>\n    <h1 class=\"vc-header-title\">Measurement Uncertainty Calculator<\/h1>\n    <p class=\"vc-header-subtitle\">Calculate combined and expanded measurement uncertainty per GUM \/ ISO 17025. Enter up to 6 uncertainty sources with Type A or B classification.<\/p>\n    <div class=\"vc-badges\"><span class=\"vc-badge\">ISO 17025<\/span><span class=\"vc-badge\">GUM<\/span><span class=\"vc-badge\">k=2 (95%)<\/span><\/div>\n<\/header>\n<div class=\"vc-card\">\n    <form class=\"vc-form\" id=\"vc-form\" autocomplete=\"off\">\n        <div class=\"vc-form-grid\">\n            <div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-value\">Measured Value<\/label><input class=\"vc-input\" type=\"number\" id=\"vc-value\" step=\"any\" placeholder=\"e.g. 10.035\" value=\"10.035\"><\/div>\n            <div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-unit\">Unit<\/label><input class=\"vc-input\" type=\"text\" id=\"vc-unit\" placeholder=\"e.g. mm\" value=\"mm\"><\/div>\n        <\/div>\n        <div id=\"vc-sources\">\n            <div class=\"vc-src-row\"><div class=\"vc-field\"><label class=\"vc-label\">Source<\/label><input class=\"vc-input vc-src-name\" value=\"Repeatability (Type A)\"><\/div><div class=\"vc-field\"><label class=\"vc-label\">Type<\/label><select class=\"vc-select vc-src-type\"><option value=\"A\" selected>A<\/option><option value=\"B-normal\">B (Normal)<\/option><option value=\"B-rect\">B (Rectangular)<\/option><\/select><\/div><div class=\"vc-field\"><label class=\"vc-label\">Value<\/label><input class=\"vc-input vc-src-val\" type=\"number\" step=\"any\" value=\"0.005\"><\/div><div class=\"vc-field\"><label class=\"vc-label\">Divisor<\/label><input class=\"vc-input vc-src-div\" type=\"number\" step=\"any\" value=\"1\" readonly><\/div><\/div>\n            <div class=\"vc-src-row\"><div class=\"vc-field\"><label class=\"vc-label\">Source<\/label><input class=\"vc-input vc-src-name\" value=\"Calibration cert (Type B)\"><\/div><div class=\"vc-field\"><label class=\"vc-label\">Type<\/label><select class=\"vc-select vc-src-type\"><option value=\"A\">A<\/option><option value=\"B-normal\" selected>B (Normal)<\/option><option value=\"B-rect\">B (Rectangular)<\/option><\/select><\/div><div class=\"vc-field\"><label class=\"vc-label\">Value<\/label><input class=\"vc-input vc-src-val\" type=\"number\" step=\"any\" value=\"0.010\"><\/div><div class=\"vc-field\"><label class=\"vc-label\">Divisor<\/label><input class=\"vc-input vc-src-div\" type=\"number\" step=\"any\" value=\"2\" readonly><\/div><\/div>\n            <div class=\"vc-src-row\"><div class=\"vc-field\"><label class=\"vc-label\">Source<\/label><input class=\"vc-input vc-src-name\" value=\"Resolution (Type B)\"><\/div><div class=\"vc-field\"><label class=\"vc-label\">Type<\/label><select class=\"vc-select vc-src-type\"><option value=\"A\">A<\/option><option value=\"B-normal\">B (Normal)<\/option><option value=\"B-rect\" selected>B (Rectangular)<\/option><\/select><\/div><div class=\"vc-field\"><label class=\"vc-label\">Value<\/label><input class=\"vc-input vc-src-val\" type=\"number\" step=\"any\" value=\"0.001\"><\/div><div class=\"vc-field\"><label class=\"vc-label\">Divisor<\/label><input class=\"vc-input vc-src-div\" type=\"number\" step=\"any\" value=\"1.732\" readonly><\/div><\/div>\n            <div class=\"vc-src-row\"><div class=\"vc-field\"><label class=\"vc-label\">Source<\/label><input class=\"vc-input vc-src-name\" value=\"Temperature effect (B)\"><\/div><div class=\"vc-field\"><label class=\"vc-label\">Type<\/label><select class=\"vc-select vc-src-type\"><option value=\"A\">A<\/option><option value=\"B-normal\">B (Normal)<\/option><option value=\"B-rect\" selected>B (Rectangular)<\/option><\/select><\/div><div class=\"vc-field\"><label class=\"vc-label\">Value<\/label><input class=\"vc-input vc-src-val\" type=\"number\" step=\"any\" value=\"0.003\"><\/div><div class=\"vc-field\"><label class=\"vc-label\">Divisor<\/label><input class=\"vc-input vc-src-div\" type=\"number\" step=\"any\" value=\"1.732\" readonly><\/div><\/div>\n        <\/div>\n    <\/form>\n    <div class=\"vc-results\" id=\"vc-results\">\n        <div class=\"vc-results-head\"><h2 class=\"vc-results-title\">Results<\/h2><button type=\"button\" class=\"vc-copy-btn\" id=\"vc-copy-btn\"><svg width=\"14\" height=\"14\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><rect x=\"9\" y=\"9\" width=\"13\" height=\"13\" rx=\"2\"\/><path d=\"M5 15H4a2 2 0 01-2-2V4a2 2 0 012-2h9a2 2 0 012 2v1\"\/><\/svg> Copy<\/button><\/div>\n        <div class=\"vc-result-grid\">\n            <div class=\"vc-rcard vc-rcard-primary\"><div class=\"vc-rcard-label\">Result Expression<\/div><div class=\"vc-rcard-value\" id=\"vc-r-expr\">\u2014<\/div><\/div>\n            <div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Combined Standard Uncertainty (uc)<\/div><div class=\"vc-rcard-value\" id=\"vc-r-uc\">\u2014<\/div><\/div>\n            <div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Expanded Uncertainty U (k=2, 95%)<\/div><div class=\"vc-rcard-value\" id=\"vc-r-U\">\u2014<\/div><\/div>\n            <div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Coverage Factor k<\/div><div class=\"vc-rcard-value\" id=\"vc-r-k\">2<\/div><\/div>\n            <div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Relative Uncertainty<\/div><div class=\"vc-rcard-value\" id=\"vc-r-rel\">\u2014<\/div><\/div>\n        <\/div>\n    <\/div>\n<\/div>\n<div class=\"vc-section vc-open\" id=\"vc-sec-theory\">\n    <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\">Theory &amp; Formulas<\/span><\/span><svg class=\"vc-section-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg><\/button>\n    <div class=\"vc-section-body\"><div class=\"vc-section-inner vc-theory\">\n        <h3>Combined Standard Uncertainty<\/h3>\n        <div class=\"vc-formula-box\" id=\"vc-katex-1\"><\/div>\n        <h3>Expanded Uncertainty<\/h3>\n        <div class=\"vc-formula-box\" id=\"vc-katex-2\"><\/div>\n        <p>Where k = coverage factor (k=2 for ~95% confidence, k=3 for ~99.7%).<\/p>\n        <h3>Divisors by Distribution<\/h3>\n        <p><strong>Type A (statistical):<\/strong> divisor = 1 (value is already a standard uncertainty from s\/\u221an).<br>\n        <strong>Type B (Normal, from certificate U at k=2):<\/strong> divisor = 2.<br>\n        <strong>Type B (Rectangular, half-width a):<\/strong> divisor = \u221a3 \u2248 1.732.<\/p>\n    <\/div><\/div>\n<\/div>\n<div class=\"vc-section\" id=\"vc-sec-related\">\n    <button type=\"button\" class=\"vc-section-toggle\" aria-expanded=\"false\"><span class=\"vc-section-toggle-text\"><span class=\"vc-section-icon\">\ud83d\udd17<\/span><span class=\"vc-section-title\">Related Calculators<\/span><\/span><svg class=\"vc-section-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg><\/button>\n    <div class=\"vc-section-body\"><div class=\"vc-section-inner\"><div class=\"vc-related\">\n        <a class=\"vc-related-link\" href=\"\/calculators\/gage-rr-calculator\/\">Gage R&#038;R Calculator<\/a>\n        <a class=\"vc-related-link\" href=\"\/calculators\/aql-sampling-calculator\/\">AQL Sampling<\/a>\n    <\/div><\/div><\/div>\n<\/div>\n<div class=\"vc-section\" id=\"vc-sec-faq\">\n    <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><svg class=\"vc-section-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg><\/button>\n    <div class=\"vc-section-body\"><div class=\"vc-section-inner\"><div class=\"vc-faq-list\" id=\"vc-faq-list\"><\/div><\/div><\/div>\n<\/div>\n<div class=\"vc-promo\"><div 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Last updated: February 2025<\/p><div class=\"vc-footer-links\"><a href=\"\/calculators\/engineering-calculators\/\">All Calculators<\/a><a href=\"https:\/\/vibromera.eu\/contacts\/\">Contact<\/a><\/div><\/footer>\n<\/div>\n<script src=\"https:\/\/cdn.jsdelivr.net\/npm\/katex@0.16.11\/dist\/katex.min.js\"><\/script>\n<script>\n(function(){\n'use strict';\nfunction $(id){return document.getElementById(id)}\nfunction fmt(n,d){if(isNaN(n))return'\u2014';return n.toFixed(d===undefined?4:d)}\n\n\/\/ Update divisors when type changes\ndocument.querySelectorAll('.vc-src-type').forEach(function(sel){\n    sel.addEventListener('change',function(){\n        var div=this.closest('.vc-src-row').querySelector('.vc-src-div');\n        if(this.value==='A')div.value='1';\n        else if(this.value==='B-normal')div.value='2';\n        else div.value='1.732';\n        calculate();\n    });\n});\n\nfunction calculate(){\n    var val=parseFloat($('vc-value').value);\n    var unit=$('vc-unit').value||'';\n    var rows=document.querySelectorAll('.vc-src-row');\n    var sumSq=0,count=0;\n    rows.forEach(function(row){\n        var v=parseFloat(row.querySelector('.vc-src-val').value);\n        var d=parseFloat(row.querySelector('.vc-src-div').value)||1;\n        if(!isNaN(v)&&v>0){var ui=v\/d;sumSq+=ui*ui;count++}\n    });\n    if(count===0||isNaN(val)){$('vc-results').classList.remove('vc-visible');return}\n    var uc=Math.sqrt(sumSq);\n    var k=2;\n    var U=k*uc;\n    var rel=val!==0?(U\/Math.abs(val))*100:0;\n    $('vc-r-uc').innerHTML=fmt(uc)+' <span class=\"vc-rcard-unit\">'+unit+'<\/span>';\n    $('vc-r-U').innerHTML=fmt(U)+' <span class=\"vc-rcard-unit\">'+unit+'<\/span>';\n    $('vc-r-k').textContent='2 (95% confidence)';\n    $('vc-r-rel').innerHTML=fmt(rel,2)+' <span class=\"vc-rcard-unit\">%<\/span>';\n    $('vc-r-expr').innerHTML=fmt(val,3)+' \u00b1 '+fmt(U)+' <span class=\"vc-rcard-unit\">'+unit+' (k=2)<\/span>';\n    $('vc-results').classList.add('vc-visible');\n}\n\n$('vc-form').addEventListener('input',calculate);\n$('vc-form').addEventListener('change',calculate);\n\n$('vc-copy-btn').addEventListener('click',function(){var text='Measurement Uncertainty (GUM \/ ISO 17025)\\n\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\\nResult: '+$('vc-r-expr').textContent+'\\nuc: '+$('vc-r-uc').textContent+'\\nU (k=2): '+$('vc-r-U').textContent+'\\nRelative: '+$('vc-r-rel').textContent+'\\n\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\\nvibromera.eu\/calculators\/measurement-uncertainty\/';if(navigator.clipboard){navigator.clipboard.writeText(text).then(function(){var b=$('vc-copy-btn');b.classList.add('vc-copied');b.innerHTML='<svg width=\"14\" height=\"14\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><polyline points=\"20 6 9 17 4 12\"\/><\/svg> Copied!';setTimeout(function(){b.classList.remove('vc-copied');b.innerHTML='<svg width=\"14\" height=\"14\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><rect x=\"9\" y=\"9\" width=\"13\" height=\"13\" rx=\"2\"\/><path d=\"M5 15H4a2 2 0 01-2-2V4a2 2 0 012-2h9a2 2 0 012 2v1\"\/><\/svg> Copy'},2000)})}});\n\ndocument.querySelectorAll('.vc-section-toggle').forEach(function(btn){btn.addEventListener('click',function(){var s=this.closest('.vc-section');s.classList.toggle('vc-open');this.setAttribute('aria-expanded',s.classList.contains('vc-open'))})});\n\nvar faqData=[\n    {q:'What is measurement uncertainty?',a:'<p>Measurement uncertainty quantifies the <strong>doubt about a measurement result<\/strong>. It defines a range within which the true value lies with stated probability (typically 95%). Required by <strong>ISO 17025<\/strong> for all labs.<\/p>'},\n    {q:'Type A vs Type B uncertainty?',a:'<p><strong>Type A<\/strong> = evaluated by statistical analysis (repeated measurements \u2192 standard deviation of mean). <strong>Type B<\/strong> = evaluated from other info: calibration certificates, specifications, published data, experience.<\/p>'},\n    {q:'What is coverage factor k?',a:'<p>k multiplies combined standard uncertainty to give expanded uncertainty. <strong>k=2<\/strong> \u2248 95% confidence. <strong>k=3<\/strong> \u2248 99.7%. k=2 is the default for most calibrations.<\/p>'},\n    {q:'How do I combine sources?',a:'<p>For independent sources: <strong>RSS (root sum of squares)<\/strong>: uc = \u221a(u\u2081\u00b2 + u\u2082\u00b2 + u\u2083\u00b2 + ...). Each source value is first divided by its divisor to get standard uncertainty.<\/p>'},\n    {q:'What is GUM?',a:'<p><strong>GUM<\/strong> (Guide to the Expression of Uncertainty in Measurement) is the international guide published by JCGM. It is the basis for ISO 17025 uncertainty requirements and provides the framework for evaluating and expressing measurement uncertainty.<\/p>'}\n];\nvar fl=$('vc-faq-list');faqData.forEach(function(f){fl.innerHTML+='<div class=\"vc-faq-item\"><button type=\"button\" class=\"vc-faq-q\"><span>'+f.q+'<\/span><svg class=\"vc-faq-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg><\/button><div class=\"vc-faq-a\"><div class=\"vc-faq-a-inner\">'+f.a+'<\/div><\/div><\/div>'});\nfl.addEventListener('click',function(e){var b=e.target.closest('.vc-faq-q');if(b)b.closest('.vc-faq-item').classList.toggle('vc-open')});\n\nfunction init(){\n    try{\n        katex.render('u_c = \\\\sqrt{u_1^2 + u_2^2 + u_3^2 + \\\\cdots + u_n^2}',$('vc-katex-1'),{displayMode:true,throwOnError:false});\n        katex.render('U = k \\\\times u_c \\\\quad (k=2 \\\\text{ for } \\\\approx 95\\\\%)',$('vc-katex-2'),{displayMode:true,throwOnError:false});\n    }catch(e){}\n    calculate();\n}\nif(document.readyState==='loading')document.addEventListener('DOMContentLoaded',init);else init();\n})();\n<\/script>\n","protected":false},"excerpt":{"rendered":"<p>Gratis kalkulator for m\u00e5leusikkerhet i henhold til ISO 17025 \/ GUM. Skriv inn usikkerhetskilder (Type A og B), beregn kombinert og utvidet usikkerhet med dekningsfaktor k=2 (95%).<\/p>","protected":false},"featured_media":0,"template":"","meta":{"ai_generated_summary":"","footnotes":""},"categories":[],"tags":[],"class_list":["post-100151","calculator","type-calculator","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/vibromera.eu\/nb\/wp-json\/wp\/v2\/calculator\/100151","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vibromera.eu\/nb\/wp-json\/wp\/v2\/calculator"}],"about":[{"href":"https:\/\/vibromera.eu\/nb\/wp-json\/wp\/v2\/types\/calculator"}],"version-history":[{"count":1,"href":"https:\/\/vibromera.eu\/nb\/wp-json\/wp\/v2\/calculator\/100151\/revisions"}],"predecessor-version":[{"id":100466,"href":"https:\/\/vibromera.eu\/nb\/wp-json\/wp\/v2\/calculator\/100151\/revisions\/100466"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/nb\/wp-json\/wp\/v2\/media?parent=100151"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/nb\/wp-json\/wp\/v2\/categories?post=100151"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/nb\/wp-json\/wp\/v2\/tags?post=100151"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}