{"id":66828,"date":"2026-10-15T09:20:30","date_gmt":"2026-10-15T06:20:30","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=66828"},"modified":"2026-10-15T09:20:30","modified_gmt":"2026-10-15T06:20:30","slug":"triangle-area-calculator","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/mathematics\/triangle-area-calculator\/","title":{"rendered":"Triangle Area 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 Area of a Triangle<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"66828\" data-favorite-title=\"Triangle Area\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/mathematics\/triangle-area-calculator\/\" data-favorite-excerpt=\"Calculate the area of a triangle from three side lengths (Heron&#039;s formula) or from a base and height. Enter your known values, pick a unit, and get the area with step-by-step calculations.\" 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\/triangle-area-calculator\/\" method=\"POST\" class=\"calculator\" id=\"calculator-66828\" data-post=\"66828\"><fieldset class=\"fieldset-input is-2\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field is-single\" id=\"input-1\"><label for=\"field-1\">Known values<\/label><div class=\"grid grid-cols-1\"><select id=\"field-1\" name=\"known_values\"><option value=\"sss\" selected>Three side lengths (Heron&#039;s formula)<\/option><option value=\"bh\">Base and height<\/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\">Side 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=\"side_a\" id=\"field-2\" aria-describedby=\"calc-info-2\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0.0001\" value=\"3\"\/><small id=\"calc-info-2\">First side length.<\/small><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-3\">Side 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=\"side_b\" id=\"field-3\" aria-describedby=\"calc-info-3\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0.0001\" value=\"4\"\/><small id=\"calc-info-3\">Second side length.<\/small><\/div><div class=\"field has-term\" id=\"input-4\"><label for=\"field-4\">Side 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=\"side_c\" id=\"field-4\" aria-describedby=\"calc-info-4\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0.0001\" value=\"5\"\/><small id=\"calc-info-4\">Third side length.<\/small><\/div><div class=\"field has-term\" id=\"input-5\" hidden><label for=\"field-5\">Base<\/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=\"base\" id=\"field-5\" aria-describedby=\"calc-info-5\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0.0001\" value=\"10\"\/><small id=\"calc-info-5\">Length of the side the height is measured from.<\/small><\/div><div class=\"field has-term\" id=\"input-6\" hidden><label for=\"field-6\">Height<\/label><div class=\"term\">h<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"height\" id=\"field-6\" aria-describedby=\"calc-info-6\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0.0001\" value=\"6\"\/><small id=\"calc-info-6\">Perpendicular height to the base.<\/small><\/div><div class=\"field is-single\" id=\"input-7\"><label for=\"field-7\">Unit<\/label><div class=\"grid grid-cols-1\"><select id=\"field-7\" 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=\"66828\">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>Triangle Area<\/span><span class=\"result-term\">A<\/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>Semiperimeter<\/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 is-column\" id=\"output-3\"><span class=\"field-title\"><span>Calculation Steps<\/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><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=\"66828\" 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>Triangle Area 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\\[ A = \\frac{1}{2}\\, b\\, h \\]\n\\[ s = \\frac{a + b + c}{2}, \\qquad A = \\sqrt{s\\,(s-a)(s-b)(s-c)} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(A\\) \u2014 area of the triangle (in the chosen unit squared)<\/li>\n<li>\\(b\\) \u2014 base of the triangle (length of the side the height is measured from)<\/li>\n<li>\\(h\\) \u2014 height, the perpendicular distance from the base to the opposite vertex<\/li>\n<li>\\(a, b, c\\) \u2014 the three side lengths of the triangle<\/li>\n<li>\\(s\\) \u2014 semiperimeter, half of the perimeter<\/li>\n<\/ul>\n<p>The first formula is the classic base-height method: the area is half the product of a side and the perpendicular height dropped onto it. The second is Heron's formula, which finds the area from the three side lengths alone, without needing any angle or height.<\/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>Triangle Area \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> a triangle has sides \\(a = 3\\) cm, \\(b = 4\\) cm and \\(c = 5\\) cm (a right triangle). Find its area using Heron's formula.<\/p>\n<p>\\[ s = \\frac{3 + 4 + 5}{2} = 6 \\text{ cm} \\]&lt;\/n<\/p>\n<p>\\[ A = \\sqrt{6 \\times (6-3) \\times (6-4) \\times (6-5)} = \\sqrt{6 \\times 3 \\times 2 \\times 1} = \\sqrt{36} = 6 \\text{ cm}^2 \\]<\/p>\n<p><strong>Result:<\/strong> the area is 6 cm\u00b2. As a check, the base-height formula with legs 3 and 4 gives \\(\\tfrac{1}{2} \\times 3 \\times 4 = 6\\) cm\u00b2 \u2014 the same answer.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to use the calculator<\/h2>\n<ol>\n<li>Open the <strong>Known values<\/strong> dropdown and choose <em>Three side lengths (Heron's formula)<\/em> or <em>Base and height<\/em>, depending on what you know about your triangle.<\/li>\n<li>If you chose three side lengths, enter <strong>Side a<\/strong>, <strong>Side b<\/strong> and <strong>Side c<\/strong>. If you chose base and height, enter <strong>Base<\/strong> and <strong>Height<\/strong> instead.<\/li>\n<li>Pick the <strong>Unit<\/strong> (cm, m, in or ft). It applies to all lengths you enter and to the result.<\/li>\n<li>Read the <strong>Triangle Area<\/strong> in square units. For the side-length method you also get the <strong>Semiperimeter<\/strong>, and the <strong>Calculation Steps<\/strong> panel shows exactly how the answer was found.<\/li>\n<\/ol>\n<h2>What is the area of a triangle?<\/h2>\n<p>The area of a triangle is the amount of surface enclosed by its three sides, measured in square units (cm\u00b2, m\u00b2, in\u00b2, ft\u00b2). Two equivalent formulas cover almost every practical situation. If you can measure one side together with the perpendicular height dropped onto that side, use \\(A = \\tfrac{1}{2}bh\\). If you only know the three side lengths \u2014 common in surveying, land measurement and geometry problems \u2014 Heron's formula gives the area directly.<\/p>\n<p>Heron's formula, attributed to Heron (Hero) of Alexandria in the 1st century AD, first computes the semiperimeter \\(s\\), which is simply half the perimeter. The area is then the square root of the product \\(s(s-a)(s-b)(s-c)\\). The result is always the same no matter which side you label \\(a\\), \\(b\\) or \\(c\\).<\/p>\n<p>Interpreting the result is straightforward: the number tells you how many unit squares would fit inside the triangle. For instance, an area of 6 cm\u00b2 means six 1 cm \u00d7 1 cm squares would cover the triangle exactly. Keep in mind that the height in the base-height formula must be <em>perpendicular<\/em> to the base \u2014 a slanted side length is not a height unless the triangle is right-angled and the leg is used as the base.<\/p>\n<h2>Assumptions, limitations and tips<\/h2>\n<ul>\n<li><strong>Triangle inequality:<\/strong> the three sides must satisfy \\(a + b &gt; c\\), \\(a + c &gt; b\\) and \\(b + c &gt; a\\). If any side is as long as or longer than the sum of the other two, no triangle exists and the calculator shows an error.<\/li>\n<li><strong>Positive values only:<\/strong> all lengths must be greater than zero. The calculator rejects zero or negative inputs.<\/li>\n<li><strong>Same unit for everything:<\/strong> enter all lengths in the same unit; the area comes out in that unit squared. For a result in m\u00b2, enter sides in metres, not centimetres.<\/li>\n<li><strong>Height must be perpendicular:<\/strong> when using the base-height method, the height is the shortest distance from the base to the opposite vertex, not the length of a slanted side.<\/li>\n<li><strong>Units don't mix with exact values:<\/strong> because of rounding, very \"thin\" triangles (one side barely shorter than the sum of the other two) can give extremely small areas that are sensitive to input precision \u2014 measure carefully in such cases.<\/li>\n<\/ul>\n<h2>Related calculations<\/h2>\n<p>Once you have the sides of a triangle, you may also want the <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/average-calculator\/\">average of the three sides<\/a> (which relates directly to the semiperimeter), or to scale your measurements with the <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/multiplication-calculator\/\">multiplication calculator<\/a>. If your triangle work involves the quadratic formula, our <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/nth-root\/\">nth root calculator<\/a> helps with taking roots of any degree.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Calculate the area of a triangle from three side lengths (Heron's formula) or from a base and height. Enter your known values, pick a unit, and get the area with step-by-step calculations.<\/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":[23],"class_list":["post-66828","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\/66828","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=66828"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66828\/revisions"}],"predecessor-version":[{"id":67133,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66828\/revisions\/67133"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=66828"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=66828"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=66828"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}