{"id":66844,"date":"2026-10-15T09:20:25","date_gmt":"2026-10-15T06:20:25","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=66844"},"modified":"2026-10-15T09:20:25","modified_gmt":"2026-10-15T06:20:25","slug":"regular-polygon-area-calculator","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/mathematics\/regular-polygon-area-calculator\/","title":{"rendered":"Regular Polygon 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 Regular Polygon<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"66844\" data-favorite-title=\"Regular Polygon Area\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/mathematics\/regular-polygon-area-calculator\/\" data-favorite-excerpt=\"Calculate the area of any regular polygon from its side length, apothem, or circumradius. Enter the number of sides and one known dimension to get the area, perimeter, and angles.\" 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\/regular-polygon-area-calculator\/\" method=\"POST\" class=\"calculator\" id=\"calculator-66844\" data-post=\"66844\"><fieldset class=\"fieldset-input is-2\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">Number of sides (n)<\/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=\"number_of_sides_n\" id=\"field-1\" aria-describedby=\"calc-info-1\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"6\" min=\"3\" max=\"10000\" value=\"6\"\/><small id=\"calc-info-1\">Whole number of equal sides, 3 or more.<\/small><\/div><div class=\"field\" id=\"input-2\"><label for=\"field-2\">Known quantity<\/label><div class=\"grid grid-cols-1\"><select id=\"field-2\" name=\"known_quantity\"><option value=\"side\" selected>Side length (s)<\/option><option value=\"apothem\">Apothem (a)<\/option><option value=\"circumradius\">Circumradius (R)<\/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-3\"><label for=\"field-3\">Side length (s)<\/label><div class=\"term\">s<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"side_length_s\" id=\"field-3\" aria-describedby=\"calc-info-3\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"10\" min=\"0\" value=\"10\"\/><div class=\"grid grid-cols-1\"><select id=\"field-4\" name=\"unit\" aria-label=\"Unit\"><option value=\"m\">m<\/option><option value=\"cm\" selected>cm<\/option><option value=\"mm\">mm<\/option><option value=\"ft\">ft<\/option><option value=\"in\">in<\/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><small id=\"calc-info-3\">Length of one side of the polygon.<\/small><\/div><div class=\"field has-term\" id=\"input-4\" hidden><label for=\"field-5\">Apothem (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><div class=\"field-group\"><input type=\"text\" name=\"apothem_a\" id=\"field-5\" aria-describedby=\"calc-info-5\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"8.66\" min=\"0\" value=\"8.66\"\/><div class=\"grid grid-cols-1\"><select id=\"field-6\" name=\"unit\" aria-label=\"Unit\"><option value=\"m\">m<\/option><option value=\"cm\" selected>cm<\/option><option value=\"mm\">mm<\/option><option value=\"ft\">ft<\/option><option value=\"in\">in<\/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><small id=\"calc-info-5\">Distance from the center to the middle of a side (inradius).<\/small><\/div><div class=\"field has-term\" id=\"input-5\" hidden><label for=\"field-7\">Circumradius (R)<\/label><div class=\"term\">R<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"circumradius_r\" id=\"field-7\" aria-describedby=\"calc-info-7\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"10\" min=\"0\" value=\"10\"\/><div class=\"grid grid-cols-1\"><select id=\"field-8\" name=\"unit\" aria-label=\"Unit\"><option value=\"m\">m<\/option><option value=\"cm\" selected>cm<\/option><option value=\"mm\">mm<\/option><option value=\"ft\">ft<\/option><option value=\"in\">in<\/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><small id=\"calc-info-7\">Distance from the center to a vertex (radius of the circumscribed circle).<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"66844\">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 Polygon<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>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>Perimeter<\/span><span class=\"result-term\">P<\/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>Side length<\/span><span class=\"result-term\">s<\/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\" id=\"output-4\"><span class=\"field-title\"><span>Apothem<\/span><span class=\"result-term\">a<\/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\" id=\"output-5\"><span class=\"field-title\"><span>Circumradius<\/span><span class=\"result-term\">R<\/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 class=\"field-result\" id=\"output-6\"><span class=\"field-title\"><span>Interior angle<\/span><span class=\"result-term\">\u03b1<\/span><\/span><span class=\"field-value\" id=\"result-6\"><\/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-7\"><span class=\"field-title\"><span>Calculation steps<\/span><\/span><span class=\"field-value\" id=\"result-7\"><\/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=\"66844\" 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>Regular Polygon Area<\/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{n\\,s^2}{4\\tan(\\pi\/n)} = \\frac{1}{2}\\,P\\,a = \\frac{1}{2}\\,n\\,R^2\\sin\\!\\left(\\frac{2\\pi}{n}\\right) \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(n\\) \u2014 number of sides (\\(n \\ge 3\\))<\/li>\n<li>\\(s\\) \u2014 length of one side<\/li>\n<li>\\(a\\) \u2014 apothem (distance from the center to the midpoint of a side, i.e. the inradius)<\/li>\n<li>\\(R\\) \u2014 circumradius (distance from the center to a vertex)<\/li>\n<li>\\(P = n \\cdot s\\) \u2014 perimeter<\/li>\n<li>\\(\\pi \\approx 3.14159\\)<\/li>\n<\/ul>\n<p>All three expressions give the same area; you use whichever matches the dimension you know. The middle form, \\(A = \\tfrac{1}{2}Pa\\), is the classic result obtained by splitting the polygon into \\(n\\) identical triangles, each with base \\(s\\) and height \\(a\\).<\/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>Regular Polygon Area \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> a regular hexagon with a side length of 10 cm.<\/p>\n<p>\\[ a = \\frac{s}{2\\tan(\\pi\/n)} = \\frac{10}{2\\tan(\\pi\/6)} = \\frac{10}{2 \\cdot 0.5774} \\approx 8.660 \\text{ cm} \\]<\/p>\n<p>\\[ P = n \\cdot s = 6 \\cdot 10 = 60 \\text{ cm} \\]<\/p>\n<p>\\[ A = \\tfrac{1}{2}\\,P\\,a = \\tfrac{1}{2} \\cdot 60 \\cdot 8.660 \\approx 259.81 \\text{ cm}^2 \\]<\/p>\n<p><strong>Result:<\/strong> the area is approximately <strong>259.81 cm\u00b2<\/strong>. The calculator also reports the circumradius \\(R = 10\\) cm and an interior angle of 120\u00b0.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to Use the Calculator<\/h2>\n<ol>\n<li>Enter the <strong>Number of sides (n)<\/strong> \u2014 any whole number from 3 (triangle) up to 10,000.<\/li>\n<li>Choose the dimension you know in the <strong>Known quantity<\/strong> dropdown: <em>Side length (s)<\/em>, <em>Apothem (a)<\/em>, or <em>Circumradius (R)<\/em>. Only the matching input field stays visible.<\/li>\n<li>Type the value in the field that appears \u2014 <strong>Side length (s)<\/strong>, <strong>Apothem (a)<\/strong>, or <strong>Circumradius (R)<\/strong> \u2014 and pick its unit (m, cm, mm, ft, or in).<\/li>\n<li>Read the results: <strong>Area<\/strong> (in the square of your unit), plus <strong>Perimeter<\/strong>, <strong>Side length<\/strong>, <strong>Apothem<\/strong>, <strong>Circumradius<\/strong>, <strong>Interior angle<\/strong>, and a step-by-step derivation.<\/li>\n<\/ol>\n<h2>What Is a Regular Polygon?<\/h2>\n<p>A regular polygon is a closed, straight-sided figure in which every side has the same length and every interior angle is equal. Familiar examples are the equilateral triangle (\\(n=3\\)), the square (\\(n=4\\)), the regular pentagon (\\(n=5\\)), and the regular hexagon (\\(n=6\\)). Because all sides and angles match, a regular polygon is fully determined by just two numbers: the number of sides and one linear dimension.<\/p>\n<p>The area formula works by slicing the polygon into \\(n\\) congruent triangles that meet at the center. Each triangle has a base \\(s\\) (one side of the polygon) and a height \\(a\\) (the apothem), so its area is \\(\\tfrac{1}{2}sa\\). Multiplying by \\(n\\) sides gives \\(A = \\tfrac{1}{2}na s = \\tfrac{1}{2}Pa\\). This is the same logic used to find the area of a circle in the limit: as \\(n\\) grows very large, the polygon becomes indistinguishable from a circle of radius \\(R\\), and the formula approaches \\(\\pi R^2\\).<\/p>\n<p>Two derived dimensions are worth understanding. The <strong>apothem<\/strong> is the radius of the inscribed circle \u2014 the largest circle that fits inside the polygon, touching every side at its midpoint. The <strong>circumradius<\/strong> is the radius of the circumscribed circle that passes through every vertex. The three dimensions are linked by the identities \\(s = 2a\\tan(\\pi\/n) = 2R\\sin(\\pi\/n)\\) and \\(a = R\\cos(\\pi\/n)\\), which is why the calculator can derive all of them from any single one.<\/p>\n<p>The <strong>interior angle<\/strong> shown in the results comes from \\(\\alpha = (n-2) \\cdot 180\u00b0\/n\\). It is useful in construction, tiling, and woodworking: for example, a hexagon has 120\u00b0 corners, so you cut boards at a 60\u00b0 miter to join them.<\/p>\n<h2>Assumptions, Limitations, and Tips<\/h2>\n<ul>\n<li><strong>Regular polygons only.<\/strong> The formulas rely on all sides and angles being equal. For an irregular polygon, split it into triangles or trapezoids and add the areas.<\/li>\n<li><strong>Units must be consistent.<\/strong> The unit dropdown converts the input automatically, and the area is returned in the corresponding square unit (e.g. cm \u2192 cm\u00b2). If you work by hand, keep every length in the same unit before applying the formula.<\/li>\n<li><strong>Choose the dimension you actually measured.<\/strong> In practical work you often know the distance across flats (twice the apothem, for even \\(n\\)) or the bolt-circle radius (circumradius) rather than a side \u2014 pick that option to avoid rounding errors from an intermediate conversion.<\/li>\n<li><strong>Large \\(n\\).<\/strong> Values up to 10,000 are accepted; for such figures the result is essentially the area of a circle with radius \\(R\\), since \\(A \\to \\pi R^2\\) as \\(n \\to \\infty\\).<\/li>\n<li><strong>Rounding.<\/strong> Results are shown to three decimal places. Intermediate values in the calculation steps are rounded for display, so a hand check may differ in the last digit.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Calculate the area of any regular polygon from its side length, apothem, or circumradius. Enter the number of sides and one known dimension to get the area, perimeter, and angles.<\/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-66844","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\/66844","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=66844"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66844\/revisions"}],"predecessor-version":[{"id":67119,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66844\/revisions\/67119"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=66844"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=66844"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=66844"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}