{"id":65472,"date":"2026-09-29T12:27:00","date_gmt":"2026-09-29T09:27:00","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=65472"},"modified":"2026-09-29T15:19:11","modified_gmt":"2026-09-29T12:19:11","slug":"coefficient-of-variation-calculator","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/statistics\/coefficient-of-variation-calculator\/","title":{"rendered":"Coefficient of Variation Calculator"},"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\">Calculate the Coefficient of Variation<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"65472\" data-favorite-title=\"Coefficient of Variation\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/statistics\/coefficient-of-variation-calculator\/\" data-favorite-excerpt=\"Calculate the coefficient of variation (CV) from your own data set or from a known standard deviation and mean. Enter comma-, space- or line-separated numbers and get CV, SD, mean and an interpretation.\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-wpcalc-bell-curve\">\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\/statistics\/coefficient-of-variation-calculator\/\" method=\"POST\" class=\"calculator\" id=\"calculator-65472\" data-post=\"65472\"><fieldset class=\"fieldset-input is-1\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field\" id=\"input-1\"><label for=\"field-1\">Input method<\/label><div class=\"grid grid-cols-1\"><select id=\"field-1\" name=\"input_method\"><option value=\"dataset\" selected>Enter a data set<\/option><option value=\"direct\">Enter SD and mean directly<\/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><div class=\"field\" id=\"input-2\"><label for=\"field-2\">Data set<\/label><textarea id=\"field-2\" name=\"data_set\">12, 15, 14, 13, 16, 15, 14<\/textarea><\/div><div class=\"field has-term\" id=\"input-3\" hidden><label for=\"field-3\">Standard deviation<\/label><div class=\"term\">s<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"standard_deviation\" id=\"field-3\" aria-describedby=\"calc-info-3\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 5\" min=\"0\" value=\"5\"\/><small id=\"calc-info-3\">The standard deviation of your data. Must not be negative.<\/small><\/div><div class=\"field has-term\" id=\"input-4\" hidden><label for=\"field-4\">Mean<\/label><div class=\"term\">x\u0304<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"mean\" id=\"field-4\" aria-describedby=\"calc-info-4\" placeholder=\"e.g. 40\" step=\"any\" value=\"40\"\/><small id=\"calc-info-4\">The arithmetic mean of your data. Must not be zero (CV is undefined for a zero mean).<\/small><\/div><div class=\"field\" id=\"input-5\"><label for=\"field-5\">Standard deviation type<\/label><div class=\"grid grid-cols-1\"><select id=\"field-5\" name=\"standard_deviation_type\"><option value=\"sample\" selected>Sample (divide by n \u2212 1)<\/option><option value=\"population\">Population (divide by n)<\/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><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"65472\">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> Your Results<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Coefficient of variation<\/span><span class=\"result-term\">CV<\/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\" id=\"output-2\"><span class=\"field-title\"><span>Standard deviation<\/span><span class=\"result-term\">s<\/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 class=\"field-result\" id=\"output-3\"><span class=\"field-title\"><span>Mean<\/span><span class=\"result-term\">x\u0304<\/span><\/span><span class=\"field-value\" id=\"result-3\"><\/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\" id=\"output-4\"><span class=\"field-title\"><span>Count of values<\/span><span class=\"result-term\">n<\/span><\/span><span class=\"field-value\" id=\"result-4\"><\/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-5\"><span class=\"field-title\"><span>Interpretation &amp; details<\/span><\/span><span class=\"field-value\" id=\"result-5\"><\/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=\"65472\" 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>Coefficient of Variation 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\\[ CV = \\frac{s}{|\\bar{x}|} \\times 100\\% \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(s\\) \u2014 standard deviation of the data (sample or population)<\/li>\n<li>\\(\\bar{x}\\) \u2014 arithmetic mean of the data<\/li>\n<li>\\(|\\bar{x}|\\) \u2014 absolute value of the mean, so the CV is always non-negative<\/li>\n<\/ul>\n<p>The formula expresses the standard deviation as a percentage of the mean, which tells you how large the spread is relative to the typical value of the data.<\/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>Coefficient of Variation \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> seven measurements were recorded: 12, 15, 14, 13, 16, 15, 14.<\/p>\n<p>\\[ \\bar{x} = \\frac{12 + 15 + 14 + 13 + 16 + 15 + 14}{7} = \\frac{99}{7} \\approx 14.1429 \\]<\/p>\n<p>\\[ s = \\sqrt{\\frac{(12-14.1429)^2 + (15-14.1429)^2 + \\dots + (14-14.1429)^2}{7-1}} \\approx \\sqrt{\\frac{10.8571}{6}} \\approx 1.3452 \\]<\/p>\n<p>\\[ CV = \\frac{1.3452}{14.1429} \\times 100\\% \\approx 9.5117\\% \\]<\/p>\n<p><strong>Result:<\/strong> CV \u2248 9.51% \u2014 a low relative spread, since the values cluster tightly around the mean of about 14.14.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to Use the Calculator<\/h2>\n<ol>\n<li>Choose an <strong>Input method<\/strong>: \"Enter a data set\" to paste raw numbers, or \"Enter SD and mean directly\" if you already know those two statistics.<\/li>\n<li>If you chose the data set method, type your numbers into <strong>Data set<\/strong>. Separate them with commas, spaces, semicolons or line breaks; decimals and negative values are fine.<\/li>\n<li>If you chose direct input, fill in <strong>Standard deviation<\/strong> (a non-negative number) and <strong>Mean<\/strong> (any non-zero number).<\/li>\n<li>Pick the <strong>Standard deviation type<\/strong>: \"Sample (divide by n \u2212 1)\" when your data are a sample from a larger population, or \"Population (divide by n)\" when you have every possible observation.<\/li>\n<li>Read the <strong>Coefficient of variation<\/strong> in percent, along with the standard deviation, mean, count of values, and a short interpretation of the result.<\/li>\n<\/ol>\n<h2>What the Coefficient of Variation Means<\/h2>\n<p>The coefficient of variation (CV, also called relative standard deviation, RSD) is a measure of dispersion that expresses the standard deviation as a percentage of the mean. While the standard deviation alone tells you how spread out the data are in the original units, the CV tells you how big that spread is <em>compared with the size of the values themselves<\/em>. A standard deviation of 5 mm is huge for screw lengths but negligible for steel beams; the CV removes this ambiguity.<\/p>\n<p>Because CV is a ratio of two numbers in the same units, it is <strong>dimensionless<\/strong>. This is its main advantage: you can compare the variability of data sets measured in different units or on very different scales \u2014 for example, the consistency of a chemical assay (in mg\/L) against the reliability of a manufacturing process (in seconds). Lower CV means more consistency; higher CV means more relative scatter.<\/p>\n<p>As a rough rule of thumb used in many fields: a CV below 10% is usually considered low (tightly clustered data), 10\u201325% is moderate, 25\u201350% is high, and above 50% is very high. These thresholds are field-dependent \u2014 quality control labs often demand a CV under 5%, while ecological or economic data routinely exceed 30% \u2014 so always compare against the norms of your own discipline.<\/p>\n<p>For instance, entering a standard deviation of 5 and a mean of 40 in direct mode gives \\( CV = 5 \/ 40 \\times 100\\% = 12.5\\% \\), a moderate relative spread. Comparing this to the 9.51% from the example data set above is meaningful even if the two data sets were measured in completely different units.<\/p>\n<h2>Assumptions, Limitations and Tips<\/h2>\n<ul>\n<li><strong>Sample vs. population SD:<\/strong> the sample standard deviation divides by \\(n-1\\) and is slightly larger; the population version divides by \\(n\\). Use the same type for every data set you compare, otherwise the CVs are not comparable.<\/li>\n<li><strong>Zero or negative means:<\/strong> the CV is undefined when the mean is zero, and it is misleading when the mean is negative or close to zero relative to the spread \u2014 the ratio then explodes or flips sign without any change in the actual variability. This is why the calculator uses \\(|\\bar{x}|\\) and refuses a mean of exactly 0.<\/li>\n<li><strong>Ratio scale only:<\/strong> the CV is meaningful only for data with a true zero point (lengths, masses, times, concentrations). For interval-scale data such as temperatures in \u00b0C or \u00b0F, the zero point is arbitrary and the CV has no sound interpretation.<\/li>\n<li><strong>Outliers:<\/strong> a single extreme value inflates both the SD and the mean in different ways and can distort the CV. Inspect your data before trusting the result.<\/li>\n<li><strong>Small samples:<\/strong> with fewer than about 10 values, the sample CV is a noisy estimate; treat small-sample CVs as indicative rather than definitive.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Calculate the coefficient of variation (CV) from your own data set or from a known standard deviation and mean. Enter comma-, space- or line-separated numbers and get CV, SD, mean and an interpretation.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[74],"tags":[75],"class_list":["post-65472","post","type-post","status-publish","format-standard","hentry","category-statistics","tag-descriptive-statistics"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/65472","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=65472"}],"version-history":[{"count":3,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/65472\/revisions"}],"predecessor-version":[{"id":65681,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/65472\/revisions\/65681"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=65472"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=65472"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=65472"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}