{"id":66820,"date":"2026-10-15T09:20:33","date_gmt":"2026-10-15T06:20:33","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=66820"},"modified":"2026-10-15T09:20:33","modified_gmt":"2026-10-15T06:20:33","slug":"factorial-calculator","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/mathematics\/factorial-calculator\/","title":{"rendered":"Factorial 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\">Find the Exact Factorial of a Nonnegative Integer<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"66820\" data-favorite-title=\"Factorial\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/mathematics\/factorial-calculator\/\" data-favorite-excerpt=\"Calculate the exact factorial n! of any nonnegative integer up to 10000, with every digit shown, plus the digit count, trailing zeros and scientific notation.\" 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\/factorial-calculator\/\" method=\"POST\" class=\"calculator\" id=\"calculator-66820\" data-post=\"66820\"><fieldset class=\"fieldset-input is-1\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">Nonnegative integer<\/label><div class=\"term\">n<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"nonnegative_integer\" id=\"field-1\" aria-describedby=\"calc-info-1\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" max=\"10000\" value=\"10\"\/><small id=\"calc-info-1\">Whole number from 0 to 10000; factorial grows extremely fast<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"66820\">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 is-column\" id=\"output-1\"><span class=\"field-title\"><span>Exact factorial<\/span><span class=\"result-term\">n!<\/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>Number of digits<\/span><span class=\"result-term\">d<\/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>Trailing zeros<\/span><span class=\"result-term\">z<\/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 is-column\" id=\"output-4\"><span class=\"field-title\"><span>Scientific notation (exact value)<\/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>How this result was calculated<\/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=\"66820\" 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>Factorial 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\\[ n! = \\prod_{k=1}^{n} k = 1 \\times 2 \\times 3 \\times \\dots \\times n \\,, \\qquad 0! = 1 \\]<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(n\\) \u2014 a nonnegative integer (0, 1, 2, 3, \u2026)<\/li>\n<li>\\(n!\\) \u2014 the factorial of \\(n\\), the product of all whole numbers from 1 up to \\(n\\)<\/li>\n<\/ul>\n<p>The factorial of a number is simply every whole number from 1 to that number multiplied together. The special case \\(0! = 1\\) is a definition that keeps counting and algebra formulas consistent.<\/p>\n<p>The number of trailing zeros of \\(n!\\) is given by Legendre's formula:<\/p>\n<p>\\[ z = \\left\\lfloor \\frac{n}{5} \\right\\rfloor + \\left\\lfloor \\frac{n}{25} \\right\\rfloor + \\left\\lfloor \\frac{n}{125} \\right\\rfloor + \\dots \\]\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>Factorial \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> find the factorial of 10, which is the calculator's default value.<\/p>\n<p>\\[ 10! = 1 \\times 2 \\times 3 \\times 4 \\times 5 \\times 6 \\times 7 \\times 8 \\times 9 \\times 10 \\]<\/p>\n<p>\\[ 10! = 3{,}628{,}800 \\]<\/p>\n<p><strong>Result:<\/strong> \\(10! = 3{,}628{,}800\\). It has 7 digits and 2 trailing zeros, and in scientific notation it equals \\(3.6288 \\times 10^{6}\\).<\/p>\n<p>\n\r\n<\/section>\n<h2>How to Use the Factorial Calculator<\/h2>\n<ol>\n<li>Type your number into the <strong>Nonnegative integer<\/strong> field (any whole number from 0 to 10000; the default is 10).<\/li>\n<li>Read the <strong>Exact factorial<\/strong> result \u2014 every digit is computed with arbitrary-precision arithmetic, so nothing is rounded.<\/li>\n<li>Check the <strong>Number of digits<\/strong> and <strong>Trailing zeros<\/strong> fields for a quick sense of the size of the answer.<\/li>\n<li>See the <strong>Scientific notation (exact value)<\/strong> line if the full number is too long to read comfortably.<\/li>\n<li>Review <strong>How this result was calculated<\/strong> for a short breakdown of the product and the trailing-zero count.<\/li>\n<\/ol>\n<h2>What Is a Factorial?<\/h2>\n<p>The factorial of a nonnegative integer \\(n\\), written \\(n!\\), is the product of all positive integers up to \\(n\\). So \\(5! = 1 \\times 2 \\times 3 \\times 4 \\times 5 = 120\\). The notation was introduced in the early 1800s, and it has become one of the most used symbols in mathematics because factorials appear everywhere: permutations and combinations, probability distributions such as the binomial and Poisson distributions, Taylor series for \\(e^x\\), and many counting problems.<\/p>\n<p>The most common interpretation is combinatorial: \\(n!\\) is the number of ways to arrange \\(n\\) distinct objects in a row. If you have 10 books, there are \\(10! = 3{,}628{,}800\\) different orders in which you can shelve them. This is why factorials show up in the <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/binomial-coefficient\/\">binomial coefficient<\/a> \\(\\binom{n}{k} = \\frac{n!}{k!(n-k)!}\\), which counts selections where order does not matter.<\/p>\n<p>Factorials grow faster than any exponential function. The first few values are small \u2014 \\(1! = 1\\), \\(5! = 120\\), \\(10! = 3{,}628{,}800\\) \u2014 but by \\(n = 20\\) the result already exceeds \\(2.4 \\times 10^{18}\\), and \\(70!\\) is larger than a googol. That explosive growth is exactly why this calculator uses arbitrary-precision arithmetic: ordinary floating-point numbers overflow around \\(170!\\), while here you get every last digit exactly, up to \\(10000!\\) (which has 35,660 digits).<\/p>\n<p>The extra outputs help you interpret huge results. The digit count tells you the order of magnitude, the scientific notation gives a compact exact form, and the trailing-zero count answers a classic question: how many times does \\(n!\\) end in zero? Every trailing zero comes from a factor of \\(10 = 2 \\times 5\\), and since factors of 5 are scarcer than factors of 2, the count is \\(z = \\lfloor n\/5 \\rfloor + \\lfloor n\/25 \\rfloor + \\lfloor n\/125 \\rfloor + \\dots\\), where the <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/floor-division\/\">floor (integer) division<\/a> drops the remainder at each step.<\/p>\n<h2>Assumptions, Limitations and Tips<\/h2>\n<ul>\n<li><strong>Nonnegative integers only.<\/strong> Factorials are not defined for negative integers, and inputs like 4.5 are rejected. For non-integer arguments mathematicians use the gamma function, where \\(\\Gamma(n+1) = n!\\).<\/li>\n<li><strong>Range 0 to 10000.<\/strong> The upper limit exists purely for performance; \\(10000!\\) is a 35,660-digit number, and results beyond that would take noticeably longer to compute and display.<\/li>\n<li><strong>Remember \\(0! = 1\\) and \\(1! = 1\\).<\/strong> These are definitions, not errors. Setting \\(0! = 1\\) keeps formulas like \\(\\binom{n}{0} = \\frac{n!}{0!\\,n!}\\) working correctly.<\/li>\n<li><strong>The result is exact, not an approximation.<\/strong> Many tools return \\(n!\\) as a rounded float (or fail past \\(170!\\)); here the full integer product is computed digit by digit.<\/li>\n<li><strong>Watch for overflow elsewhere.<\/strong> If you feed a factorial into a calculator using standard 64-bit arithmetic, values above \\(20!\\) will not fit, so keep this in mind when combining results \u2014 basic operations like <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/multiplication-calculator\/\">multiplication<\/a> or <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/division-calculator\/\">division<\/a> of large factorials are best done with ratio simplification instead of computing each factorial first.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Calculate the exact factorial n! of any nonnegative integer up to 10000, with every digit shown, plus the digit count, trailing zeros and scientific notation.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[7],"tags":[72],"class_list":["post-66820","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\/66820","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=66820"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66820\/revisions"}],"predecessor-version":[{"id":67139,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66820\/revisions\/67139"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=66820"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=66820"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=66820"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}