{"id":66827,"date":"2026-10-15T09:20:30","date_gmt":"2026-10-15T06:20:30","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=66827"},"modified":"2026-10-23T17:12:19","modified_gmt":"2026-10-23T14:12:19","slug":"pythagorean-theorem-calculator","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/mathematics\/pythagorean-theorem-calculator\/","title":{"rendered":"Hypotenuse Calculator \u2013 Pythagorean Theorem"},"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 Missing Side of a Right Triangle<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"66827\" data-favorite-title=\"Pythagorean Theorem\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/mathematics\/pythagorean-theorem-calculator\/\" data-favorite-excerpt=\"Enter any two sides of a right triangle (legs a and b, or the hypotenuse c) and this calculator instantly finds the missing side, plus the area and perimeter.\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-geometry\">\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\/pythagorean-theorem-calculator\/\" method=\"POST\" class=\"calculator\" id=\"calculator-66827\" data-post=\"66827\"><fieldset class=\"fieldset-input is-3\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">Leg 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=\"text\" name=\"leg_a\" id=\"field-1\" aria-describedby=\"calc-info-1\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0.0001\" value=\"3\"\/><small id=\"calc-info-1\">One of the two shorter sides. Leave empty if this is the side you are looking for.<\/small><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-2\">Leg 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=\"leg_b\" id=\"field-2\" aria-describedby=\"calc-info-2\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0.0001\" value=\"4\"\/><small id=\"calc-info-2\">The other short side. Leave empty if this is the side you are looking for.<\/small><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-3\">Hypotenuse c<\/label><div class=\"term\">c<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"hypotenuse_c\" id=\"field-3\" aria-describedby=\"calc-info-3\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0.0001\"\/><small id=\"calc-info-3\">The longest side, opposite the right angle. Leave empty if this is the side you are looking for.<\/small><\/div><div class=\"field\" id=\"input-4\"><label for=\"field-4\">Unit<\/label><div class=\"grid grid-cols-1\"><select id=\"field-4\" name=\"unit\"><option value=\"cm\" selected>cm<\/option><option value=\"m\">m<\/option><option value=\"in\">in<\/option><option value=\"ft\">ft<\/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=\"66827\">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 Triangle<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Missing Side<\/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>Triangle Area<\/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>Perimeter<\/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>Calculation Steps<\/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=\"66827\" 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>Pythagorean Theorem 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\">\\[ a^2 + b^2 = c^2 \\\\ c = \\sqrt{a^2 + b^2} \\\\ b = \\sqrt{c^2 - a^2} \\\\ a = \\sqrt{c^2 - b^2} \\]<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(a\\) \u2014 first leg of the right triangle (one of the two sides that form the right angle)<\/li>\n<li>\\(b\\) \u2014 second leg of the right triangle<\/li>\n<li>\\(c\\) \u2014 hypotenuse, the side opposite the right angle and always the longest side<\/li>\n<\/ul>\n<p>The first equation is the Pythagorean theorem itself: in any right triangle, the square of the hypotenuse equals the sum of the squares of the two legs. The other three equations are simply rearranged to solve for whichever side is missing.<\/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>Pythagorean Theorem \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> a right triangle has leg \\(a = 3\\) cm and leg \\(b = 4\\) cm. Find the hypotenuse.<\/p>\n<p>\\[ c = \\sqrt{a^2 + b^2} = \\sqrt{3^2 + 4^2} = \\sqrt{9 + 16} = \\sqrt{25} = 5 \\]<\/p>\n<p><strong>Result:<\/strong> the hypotenuse is \\(c = 5\\) cm. The calculator also reports the area \\(\\frac{1}{2} \\cdot 3 \\cdot 4 = 6\\) cm\u00b2 and the perimeter \\(3 + 4 + 5 = 12\\) cm.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to Use the Calculator<\/h2>\n<ol>\n<li>Enter the known sides into the fields <strong>Leg a<\/strong>, <strong>Leg b<\/strong> and <strong>Hypotenuse c<\/strong>. Leave exactly one of the three fields empty \u2014 that is the side the calculator will find.<\/li>\n<li>Pick the <strong>Unit<\/strong> (cm, m, in or ft) that applies to all sides and results.<\/li>\n<li>Read the <strong>Missing Side<\/strong> value, along with the <strong>Triangle Area<\/strong>, <strong>Perimeter<\/strong> and step-by-step solution.<\/li>\n<\/ol>\n<p>If you give the two legs, the calculator solves for the hypotenuse. If you give the hypotenuse and one leg, it solves for the other leg and checks that the hypotenuse is actually longer than the leg you entered.<\/p>\n<h2>What Is the Pythagorean Theorem?<\/h2>\n<p>The Pythagorean theorem states that in a right triangle \u2014 a triangle with one 90\u00b0 angle \u2014 the square of the hypotenuse equals the sum of the squares of the two legs. It is one of the oldest and most used results in geometry, attributed to the Greek mathematician Pythagoras around 500 BC, although versions of it were known earlier in Babylon and Egypt.<\/p>\n<p>The theorem only holds for right triangles, and the hypotenuse is always the side opposite the right angle. This gives a quick way to check whether a triangle is right-angled: if the three sides satisfy \\(a^2 + b^2 = c^2\\), the angle between legs \\(a\\) and \\(b\\) must be 90\u00b0. Carpenters and builders use exactly this test, often with the 3-4-5 triangle, to lay out square corners.<\/p>\n<p>Beyond geometry, the theorem is the foundation of the distance formula in coordinate geometry: the distance between two points is the hypotenuse of a right triangle whose legs are the differences in their coordinates. The same idea \u2014 combining quantities by squaring, adding and taking the square root \u2014 appears in the <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/quadratic-mean-calculator-root-mean-square\/\">quadratic mean (root mean square)<\/a>, which is how effective voltage and other averaged quantities are computed.<\/p>\n<h2>Common Pythagorean Triples<\/h2>\n<p>A Pythagorean triple is a set of three whole numbers that satisfies the theorem. Because the sides are integers, these triangles are handy for quick checks and construction layouts.<\/p>\n<table>\n<thead>\n<tr>\n<th>Leg a<\/th>\n<th>Leg b<\/th>\n<th>Hypotenuse c<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>3<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<\/tr>\n<tr>\n<td>5<\/td>\n<td>12<\/td>\n<td>13<\/td>\n<\/tr>\n<tr>\n<td>8<\/td>\n<td>15<\/td>\n<td>17<\/td>\n<\/tr>\n<tr>\n<td>7<\/td>\n<td>24<\/td>\n<td>25<\/td>\n<\/tr>\n<tr>\n<td>9<\/td>\n<td>40<\/td>\n<td>41<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Any multiple of a triple is also a triple: 6-8-10 and 9-12-15 are just the 3-4-5 triangle scaled up.<\/p>\n<h2>Limitations and Tips<\/h2>\n<ul>\n<li><strong>Right triangles only.<\/strong> The formula does not work for obtuse or acute triangles; for those you need the law of cosines.<\/li>\n<li><strong>The hypotenuse must be the longest side.<\/strong> If you enter a hypotenuse that is shorter than or equal to a given leg, the calculator returns an error, because no right triangle can have those measurements.<\/li>\n<li><strong>Use the same unit for all sides.<\/strong> Convert everything to a single unit (the one you pick in the <strong>Unit<\/strong> field) before entering the values.<\/li>\n<li><strong>Results are rounded to three decimals.<\/strong> The missing side often involves a square root; if you need the root of a specific number directly, the <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/nth-root\/\">Nth Root calculator<\/a> can compute it.<\/li>\n<li><strong>Sanity-check your input.<\/strong> The hypotenuse should always be greater than either leg but less than their sum \u2014 otherwise the values cannot form a triangle at all.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Enter any two sides of a right triangle (legs a and b, or the hypotenuse c) and this calculator instantly finds the missing side, plus the area and perimeter.<\/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":[23],"class_list":["post-66827","post","type-post","status-publish","format-standard","hentry","category-mathematics","tag-geometry"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66827","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=66827"}],"version-history":[{"count":2,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66827\/revisions"}],"predecessor-version":[{"id":67522,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66827\/revisions\/67522"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=66827"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=66827"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=66827"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}