{"id":65085,"date":"2025-08-01T08:10:56","date_gmt":"2025-08-01T05:10:56","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=65085"},"modified":"2026-09-30T20:34:13","modified_gmt":"2026-09-30T17:34:13","slug":"geometric-mean","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/mathematics\/geometric-mean\/","title":{"rendered":"Geometric Mean 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 Geometric Average of Numbers<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"65085\" data-favorite-title=\"Geometric Mean\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/mathematics\/geometric-mean\/\" data-favorite-excerpt=\"Calculate the geometric mean of any set of positive numbers. Enter how many values you have, type them in, and get the n-th root of their product instantly \u2014 ideal for growth rates, ratios, and returns.\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-arithmetic\">\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\/mathematics\/geometric-mean\/\" method=\"POST\" class=\"calculator\" id=\"calculator-65085\" data-post=\"65085\"><fieldset class=\"fieldset-input\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field is-single\" id=\"input-1\"><label for=\"field-1\">Number of values<\/label><input type=\"text\" name=\"number_of_values\" id=\"field-1\" aria-describedby=\"calc-info-1\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"2\" value=\"2\"\/><small id=\"calc-info-1\">Enter how many values to calculate the geometric mean for<\/small><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-2\">Number 1<\/label><div class=\"term\">n\u2081<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"number_1\" id=\"field-2\" step=\"any\" value=\"10\"\/><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-3\">Number 2<\/label><div class=\"term\">n\u2082<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"number_2\" id=\"field-3\" step=\"any\" value=\"20\"\/><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"65085\">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>Average<\/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><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=\"65085\" 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>Geometric Mean 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\\[ GM = \\sqrt[n]{x_1 \\cdot x_2 \\cdot \\cdots \\cdot x_n} = \\left( \\prod_{i=1}^{n} x_i \\right)^{1\/n} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(x_1, x_2, \\ldots, x_n\\) \u2014 the individual values (all must be positive and non-zero)<\/li>\n<li>\\(n\\) \u2014 the number of values<\/li>\n<li>\\(GM\\) \u2014 the geometric mean<\/li>\n<\/ul>\n<p>The formula multiplies all \\(n\\) values together and takes the \\(n\\)-th root of the product. An equivalent form often used with logarithms is \\( GM = \\exp\\!\\left( \\frac{1}{n} \\sum_{i=1}^{n} \\ln x_i \\right) \\), which is how spreadsheets compute it for large data sets.<\/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>Geometric Mean \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> find the geometric mean of 10 and 20 (the calculator's default values).<\/p>\n<p>\\[ GM = \\sqrt[2]{10 \\times 20} = \\sqrt{200} \\approx 14.14 \\]<\/p>\n<p><strong>Result:<\/strong> the geometric mean is <strong>14.14<\/strong>. Note that the arithmetic mean of the same numbers is 15 \u2014 the geometric mean is always less than or equal to it.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to use the calculator<\/h2>\n<ol>\n<li>Enter the <strong>Number of values<\/strong> you want to average (minimum 2). Additional input fields appear automatically.<\/li>\n<li>Type your numbers into the fields <strong>Number 1<\/strong>, <strong>Number 2<\/strong>, and so on. Every value must be positive and non-zero.<\/li>\n<li>Read the <strong>Average<\/strong> field \u2014 it shows the geometric mean of all entered values.<\/li>\n<li>Use the reset button to clear the form and start over with a new data set.<\/li>\n<\/ol>\n<h2>What is the geometric mean?<\/h2>\n<p>The geometric mean is a measure of central tendency based on multiplication rather than addition. Instead of adding the values and dividing by their count (as the <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/average-calculator\/\">arithmetic mean<\/a> does), it multiplies the values together and takes the n-th root of the product. It answers the question: <em>if all values were equal, what single value would produce the same product?<\/em><\/p>\n<p>Because it works multiplicatively, the geometric mean is the correct average for quantities that compound: growth rates, interest rates, percentage changes, ratios, and index numbers. For example, if an investment grows by 10% one year and 20% the next, the equivalent constant annual growth rate is the geometric mean of the growth factors \\(1.10 \\times 1.20\\), not the arithmetic mean of the percentages.<\/p>\n<p>The geometric mean is always less than or equal to the arithmetic mean, and the gap widens as the data becomes more spread out. It also dampens the effect of a single extreme value: one very large number inflates an arithmetic mean dramatically, but pulls the geometric mean up far less. This makes it a standard tool in finance (portfolio returns over multiple periods), biology (population growth rates, bacterial cultures), and geometry (the altitude of a right triangle is the geometric mean of the segments it creates on the hypotenuse).<\/p>\n<h2>Geometric vs. arithmetic vs. other means<\/h2>\n<table>\n<thead>\n<tr>\n<th>Mean<\/th>\n<th>Best for<\/th>\n<th>Example (2, 8)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Arithmetic<\/td>\n<td>Additive data: sums, counts, temperatures<\/td>\n<td>5<\/td>\n<\/tr>\n<tr>\n<td>Geometric<\/td>\n<td>Multiplicative data: rates, ratios, growth<\/td>\n<td>4<\/td>\n<\/tr>\n<tr>\n<td>Harmonic<\/td>\n<td>Rates over fixed distances: speeds<\/td>\n<td>3.2<\/td>\n<\/tr>\n<tr>\n<td>Quadratic (RMS)<\/td>\n<td>Varying quantities: error, voltage<\/td>\n<td>5.83<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>If your data involves weights, use the <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/weighted-mean\/\">Weighted Mean calculator<\/a>; for rates and speeds, see the <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/harmonic-mean\/\">Harmonic Mean<\/a> or <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/quadratic-mean-calculator-root-mean-square\/\">Quadratic Mean (RMS)<\/a> calculators.<\/p>\n<h2>Limitations and practical tips<\/h2>\n<ul>\n<li><strong>All values must be positive.<\/strong> The geometric mean is undefined for zero and negative numbers \u2014 the calculator will show an error if you enter one. If your data contains negative percentage changes, convert them to growth factors first (e.g. \u22125% becomes 0.95).<\/li>\n<li><strong>Use it only for multiplicative data.<\/strong> For quantities that add up \u2014 prices, heights, test scores \u2014 the arithmetic mean is the appropriate choice.<\/li>\n<li><strong>Convert percentages correctly.<\/strong> Never average the percentages directly. A 10% loss followed by a 10% gain is not break-even: the geometric mean of 0.90 and 1.10 is \u2248 0.995, a small net loss.<\/li>\n<li><strong>Large data sets.<\/strong> The product of many values can overflow simple arithmetic; in such cases the logarithmic form of the formula is used, which is also handy for manual checks with the <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/nth-root\/\">Nth Root<\/a> calculator.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Calculate the geometric mean of any set of positive numbers. Enter how many values you have, type them in, and get the n-th root of their product instantly \u2014 ideal for growth rates, ratios, and returns.<\/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":[7],"tags":[72],"class_list":["post-65085","post","type-post","status-publish","format-standard","hentry","category-mathematics","tag-arithmetic-calculators"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/65085","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=65085"}],"version-history":[{"count":3,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/65085\/revisions"}],"predecessor-version":[{"id":66247,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/65085\/revisions\/66247"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=65085"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=65085"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=65085"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}