{"id":67180,"date":"2026-10-20T09:51:45","date_gmt":"2026-10-20T06:51:45","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=67180"},"modified":"2026-10-20T09:51:45","modified_gmt":"2026-10-20T06:51:45","slug":"exponent-calculator","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/mathematics\/exponent-calculator\/","title":{"rendered":"Exponent 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 a Power or Find a Missing Value<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"67180\" data-favorite-title=\"Exponent\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/mathematics\/exponent-calculator\/\" data-favorite-excerpt=\"Calculate a base raised to an exponent, or find a missing base or exponent. Choose what to solve for, then enter the two known values.\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-algebra\">\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\/exponent-calculator\/\" method=\"POST\" class=\"calculator\" id=\"calculator-67180\" data-post=\"67180\"><fieldset class=\"fieldset-input is-1\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field\" id=\"input-1\"><label for=\"field-1\">Solve for<\/label><div class=\"grid grid-cols-1\"><select id=\"field-1\" name=\"solve_for\"><option value=\"power\" selected>Result (base raised to exponent)<\/option><option value=\"base\">Base<\/option><option value=\"exponent\">Exponent<\/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 has-term\" id=\"input-2\"><label for=\"field-2\">Base (a)<\/label><div class=\"term\">a<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"base_a\" id=\"field-2\" aria-describedby=\"calc-info-2\" step=\"any\" value=\"2\"\/><small id=\"calc-info-2\">Enter any real number. Hidden when solving for the base.<\/small><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-3\">Exponent (b)<\/label><div class=\"term\">b<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"exponent_b\" id=\"field-3\" aria-describedby=\"calc-info-3\" placeholder=\"e.g. 10, -2.5 or 2\/3\" step=\"any\" value=\"10\"\/><small id=\"calc-info-3\">Enter an integer, a decimal with up to 9 decimal places, or a fraction such as 2\/3. Hidden when solving for the exponent.<\/small><\/div><div class=\"field has-term\" id=\"input-4\"><label for=\"field-4\">Result (a^b)<\/label><div class=\"term\">a^b<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"result_ab\" id=\"field-4\" aria-describedby=\"calc-info-4\" step=\"any\" value=\"1024\"\/><small id=\"calc-info-4\">Used when solving for the base or exponent.<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"67180\">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> Exponent Results<\/h3><div class=\"result-box\"><div class=\"field-result is-column\" id=\"output-1\"><span class=\"field-title\"><span>Answer<\/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 is-column\" id=\"output-2\"><span class=\"field-title\"><span>Exact value<\/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 is-column\" id=\"output-3\"><span class=\"field-title\"><span>Scientific notation<\/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>Steps and special cases<\/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><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=\"67180\" 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>Exponent 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\\[r=a^b\\qquad a=r^{1\/b}\\qquad b=\\frac{\\ln(r)}{\\ln(a)}\\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(a\\) \u2014 the base<\/li>\n<li>\\(b\\) \u2014 the exponent<\/li>\n<li>\\(r\\) \u2014 the result, \\(a^b\\)<\/li>\n<\/ul>\n<p>The first equation calculates a power. The rearranged equations find a base or an exponent, subject to the real-number restrictions explained below; in particular, \\(b=\\ln(r)\/\\ln(a)\\) requires \\(a&gt;0\\), \\(a\\ne1\\), and \\(r&gt;0\\).<\/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>Exponent \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> using the default values, raise the base 2 to the exponent 10.<\/p>\n<p>\\[r=2^{10}=2\\times2\\times2\\times2\\times2\\times2\\times2\\times2\\times2\\times2=1024\\]<\/p>\n<p><strong>Result:<\/strong> \\(1024\\), or \\(1.024\\times10^3\\) in scientific notation. Powers are dimensionless unless the base has units; if it does, those units are raised to the same exponent.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to use the calculator<\/h2>\n<ol>\n<li>In <strong>Solve for<\/strong>, choose <strong>Result (base raised to exponent)<\/strong>, <strong>Base<\/strong>, or <strong>Exponent<\/strong>. The field for the unknown value is hidden.<\/li>\n<li>To calculate a power, enter <strong>Base (a)<\/strong> and <strong>Exponent (b)<\/strong>. The default entries, 2 and 10, give 1024.<\/li>\n<li>To find a base, enter <strong>Exponent (b)<\/strong> and <strong>Result (a^b)<\/strong>. To find an exponent, enter <strong>Base (a)<\/strong> and <strong>Result (a^b)<\/strong>.<\/li>\n<li>Read <strong>Answer<\/strong> for the requested value. Check <strong>Exact value<\/strong>, <strong>Scientific notation<\/strong>, and <strong>Steps and special cases<\/strong> for additional detail or an explanation of why an input has no unique real-number answer.<\/li>\n<\/ol>\n<p>The <strong>Exponent (b)<\/strong> field accepts an integer such as <code>10<\/code>, a decimal with at most nine places such as <code>-2.5<\/code>, or a fraction such as <code>2\/3<\/code>. Enter the fraction directly rather than a rounded decimal when its denominator matters: the calculator reduces the fraction before checking whether a negative base has a real result.<\/p>\n<h2>What an exponent means<\/h2>\n<p>An exponent describes a power of a base. For a positive integer exponent, \\(a^b\\) multiplies \\(a\\) by itself \\(b\\) times. A zero exponent gives \\(a^0=1\\) for any nonzero base. A negative exponent takes a reciprocal: \\(a^{-b}=1\/a^b\\), provided \\(a\\ne0\\). Thus \\(2^{-3}=1\/8\\), not \\(-8\\).<\/p>\n<p>A fractional exponent combines roots and powers. For integers \\(p\\) and nonzero \\(q\\), \\(a^{p\/q}=(\\sqrt[q]{a})^p\\) wherever that root is real. For example, \\(8^{2\/3}=(\\sqrt[3]{8})^2=4\\). The denominator determines the root; the numerator determines the power. For more direct root calculations, use the <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/nth-root\/\">Nth Root calculator<\/a>.<\/p>\n<p>Finding the exponent reverses the operation. If \\(a^b=r\\), taking logarithms gives \\(b=\\ln(r)\/\\ln(a)\\). For example, \\(2^b=1024\\) gives \\(b=10\\). This logarithm method works here only for a positive base other than 1 and a positive result. The <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/logarithm-calculator\/\">Logarithm calculator<\/a> can help with logarithms independently of a power equation.<\/p>\n<p>Finding the base can produce more than one answer. If \\(a^2=16\\), both \\(4\\) and \\(-4\\) work, so the answer is \\(\\pm4\\). The calculator accounts for both signs when the reduced exponent has an even numerator and an odd denominator. Otherwise, do not assume that applying a root always produces a negative as well as a positive real base.<\/p>\n<h2>Real-number limits and result displays<\/h2>\n<ul>\n<li><strong>Zero:<\/strong> The calculator treats \\(0^0\\) as undefined. Zero raised to a positive exponent is zero; zero raised to a negative exponent would require division by zero. A nonzero base raised to zero is 1, so solving \\(a^0=1\\) does not identify a unique base.<\/li>\n<li><strong>Negative bases:<\/strong> A reduced fractional exponent with an even denominator has no real result for a negative base. An odd denominator can give a real result: \\((-8)^{1\/3}=-2\\). To solve for an unknown exponent, this calculator uses real logarithms and therefore requires a positive base.<\/li>\n<li><strong>Base 1:<\/strong> Every real exponent makes \\(1^b=1\\). If the requested result is 1, the exponent is not unique; for any other result, no exponent works.<\/li>\n<li><strong>Output precision:<\/strong> <strong>Exact value<\/strong> is available for supported integer and rational powers of integer bases, subject to a 2,000-digit display limit. Other roots or logarithmic answers are numerical. <strong>Scientific notation<\/strong> makes very large or very small answers easier to read; the <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/scientific-notation-calculator\/\">Scientific Notation calculator<\/a> offers a separate way to work with that format.<\/li>\n<\/ul>\n<p>These results concern ordinary real-number powers, not modular arithmetic. If you need the remainder of an integer power after division by another integer, use the <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/modular-exponentiation-calculator\/\">Modular Exponentiation calculator<\/a> instead.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Calculate a base raised to an exponent, or find a missing base or exponent. Choose what to solve for, then enter the two known values.<\/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":[11],"class_list":["post-67180","post","type-post","status-publish","format-standard","hentry","category-mathematics","tag-algebra"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/67180","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=67180"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/67180\/revisions"}],"predecessor-version":[{"id":67193,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/67180\/revisions\/67193"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=67180"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=67180"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=67180"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}