{"id":67377,"date":"2026-10-21T10:07:04","date_gmt":"2026-10-21T07:07:04","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=67377"},"modified":"2026-10-21T10:07:04","modified_gmt":"2026-10-21T07:07:04","slug":"surface-area-calculator","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/mathematics\/surface-area-calculator\/","title":{"rendered":"Surface 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 Surface Area of Common 3D Shapes<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"67377\" data-favorite-title=\"Surface Area\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/mathematics\/surface-area-calculator\/\" data-favorite-excerpt=\"Calculate the total, lateral and base surface area of a cube, prism, cylinder, cone, sphere, hemisphere, pyramid, capsule or cone frustum. Pick a shape, enter its dimensions and get the area in the unit you choose.\" 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\/surface-area-calculator\/\" method=\"POST\" class=\"calculator\" id=\"calculator-67377\" data-post=\"67377\"><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\">Shape<\/label><div class=\"grid grid-cols-1\"><select id=\"field-1\" name=\"shape\"><option value=\"cube\">Cube<\/option><option value=\"rect\">Rectangular prism<\/option><option value=\"cylinder\" selected>Cylinder<\/option><option value=\"cone\">Cone<\/option><option value=\"sphere\">Sphere<\/option><option value=\"hemisphere\">Hemisphere<\/option><option value=\"pyramid\">Square pyramid<\/option><option value=\"tri_prism\">Triangular prism (equilateral base)<\/option><option value=\"capsule\">Capsule<\/option><option value=\"frustum\">Cone frustum<\/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 is-single\" id=\"input-2\"><label for=\"field-2\">Length unit<\/label><div class=\"grid grid-cols-1\"><select id=\"field-2\" name=\"length_unit\"><option value=\"mm\">mm<\/option><option value=\"cm\" selected>cm<\/option><option value=\"m\">m<\/option><option value=\"in\">in<\/option><option value=\"ft\">ft<\/option><option value=\"yd\">yd<\/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=\"is-single field\" id=\"input-3\"><span class=\"font-semibold\">Dimensions<\/span><\/div><div class=\"field has-term\" id=\"input-4\" hidden><label for=\"field-4\">Edge \/ 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=\"edge_side_a\" id=\"field-4\" aria-describedby=\"calc-info-4\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"6\"\/><small id=\"calc-info-4\">Cube edge, prism side a, square-pyramid base edge, or equilateral triangle side.<\/small><\/div><div class=\"field has-term\" id=\"input-5\" hidden><label for=\"field-5\">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-5\" aria-describedby=\"calc-info-5\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"4\"\/><small id=\"calc-info-5\">Second side of the rectangular prism.<\/small><\/div><div class=\"field has-term\" id=\"input-6\" hidden><label for=\"field-6\">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-6\" aria-describedby=\"calc-info-6\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"3\"\/><small id=\"calc-info-6\">Height of the rectangular prism.<\/small><\/div><div class=\"field has-term\" id=\"input-7\"><label for=\"field-7\">Radius (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><input type=\"text\" name=\"radius_r\" id=\"field-7\" aria-describedby=\"calc-info-7\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"5\"\/><small id=\"calc-info-7\">Radius of the cylinder, cone, sphere, hemisphere or capsule; top radius of the frustum.<\/small><\/div><div class=\"field has-term\" id=\"input-8\"><label for=\"field-8\">Height (h)<\/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_h\" id=\"field-8\" aria-describedby=\"calc-info-8\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"12\"\/><small id=\"calc-info-8\">Height of the cylinder, cone, pyramid, capsule or frustum; length of the triangular prism.<\/small><\/div><div class=\"field has-term\" id=\"input-9\" hidden><label for=\"field-9\">Bottom radius (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><input type=\"text\" name=\"bottom_radius_r\" id=\"field-9\" aria-describedby=\"calc-info-9\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"8\"\/><small id=\"calc-info-9\">Larger radius at the base of the cone frustum.<\/small><\/div><div class=\"field is-checkbox\" id=\"input-10\" hidden><input type=\"checkbox\" id=\"field-10\" value=\"1\" checked=\"checked\"\/><label for=\"field-10\">Include flat base<\/label><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"67377\">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> Surface Area Results<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Total surface area<\/span><span class=\"result-term\">A\u209c<\/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>Lateral \/ curved area<\/span><span class=\"result-term\">A\u2097<\/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>Base area(s)<\/span><span class=\"result-term\">A_b<\/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>Area in square centimeters<\/span><\/span><span class=\"field-value\" id=\"result-4\" data-unit=\"cm\u00b2\"><\/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>Area in square meters<\/span><\/span><span class=\"field-value\" id=\"result-5\" data-unit=\"m\u00b2\"><\/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>Area in square inches<\/span><\/span><span class=\"field-value\" id=\"result-6\" data-unit=\"in\u00b2\"><\/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-7\"><span class=\"field-title\"><span>Area in square feet<\/span><\/span><span class=\"field-value\" id=\"result-7\" data-unit=\"ft\u00b2\"><\/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-8\"><span class=\"field-title\"><span>Formula with your values<\/span><\/span><span class=\"field-value\" id=\"result-8\"><\/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-9\"><span class=\"field-title\"><span>Shape diagram<\/span><\/span><span class=\"field-value\" id=\"result-9\"><\/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-10\"><span class=\"field-title\"><span>Related calculator<\/span><\/span><span class=\"field-value\" id=\"result-10\"><\/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=\"67377\" 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>Surface 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\\[ \\begin{array}{ll}\n\\text{Cube:} &amp; A_t = 6a^2 \\\\\n\\text{Rectangular prism:} &amp; A_t = 2(ab + bc + ca) \\\\\n\\text{Cylinder:} &amp; A_t = 2\\pi r^2 + 2\\pi r h \\\\\n\\text{Cone:} &amp; A_t = \\pi r^2 + \\pi r l, \\quad l = \\sqrt{r^2 + h^2} \\\\\n\\text{Sphere:} &amp; A_t = 4\\pi r^2 \\\\\n\\text{Hemisphere:} &amp; A_t = 2\\pi r^2 \\;(+ \\pi r^2 \\text{ if the flat base is included}) \\\\\n\\text{Square pyramid:} &amp; A_t = a^2 + 2 a l, \\quad l = \\sqrt{h^2 + \\left(\\tfrac{a}{2}\\right)^2} \\\\\n\\text{Triangular prism:} &amp; A_t = 3 a h + \\tfrac{\\sqrt{3}}{2} a^2 \\\\\n\\text{Capsule:} &amp; A_t = 2\\pi r h + 4\\pi r^2 \\\\\n\\text{Cone frustum:} &amp; A_t = \\pi (R + r) l + \\pi R^2 + \\pi r^2, \\quad l = \\sqrt{h^2 + (R - r)^2}\n\\end{array} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(A_t\\) \u2014 total surface area (all faces of the solid)<\/li>\n<li>\\(a\\), \\(b\\), \\(c\\) \u2014 edges of the cube, rectangular prism, pyramid base or equilateral triangle side<\/li>\n<li>\\(r\\) \u2014 radius of the cylinder, cone, sphere, hemisphere or capsule (top radius of the frustum)<\/li>\n<li>\\(R\\) \u2014 bottom (larger) radius of the cone frustum<\/li>\n<li>\\(h\\) \u2014 height of the solid (the cylinder length of the capsule)<\/li>\n<li>\\(l\\) \u2014 slant height along the sloped surface<\/li>\n<\/ul>\n<p>The total area is split into the lateral (curved or side) surface and the flat base(s). For every shape except the sphere and the capsule, the calculator reports \\(A_t\\), \\(A_l\\) and \\(A_b\\) separately, so you can use only the part you need, for example when painting walls but not the floor.<\/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>Surface Area \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> a closed cylindrical tank with radius \\(r = 5\\) cm and height \\(h = 12\\) cm \u2014 the calculator's default values.<\/p>\n<p>\\[ A_l = 2\\pi r h = 2\\pi \\times 5 \\times 12 = 120\\pi \\approx 376.991 \\text{ cm}^2 \\]<\/p>\n<p>\\[ A_b = 2\\pi r^2 = 2\\pi \\times 5^2 = 50\\pi \\approx 157.08 \\text{ cm}^2 \\]<\/p>\n<p>\\[ A_t = A_l + A_b \\approx 376.991 + 157.08 = 534.071 \\text{ cm}^2 \\]<\/p>\n<p><strong>Result:<\/strong> the total surface area is about 534.071 cm\u00b2 (0.0534 m\u00b2, roughly 82.76 in\u00b2). The curved side of the cylinder alone is 376.991 cm\u00b2 and the two circular ends add 157.08 cm\u00b2.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to use the calculator<\/h2>\n<ol>\n<li>Pick the solid in the <strong>Shape<\/strong> dropdown \u2014 cube, rectangular prism, cylinder, cone, sphere, hemisphere, square pyramid, triangular prism, capsule or cone frustum. The form automatically shows only the dimensions the chosen shape needs.<\/li>\n<li>Choose the <strong>Length unit<\/strong> (mm, cm, m, in, ft or yd). Enter all dimensions in that unit; areas are returned in the same unit squared.<\/li>\n<li>Fill in the visible <strong>Dimensions<\/strong> fields: <strong>Edge \/ side (a)<\/strong>, <strong>Side (b)<\/strong> and <strong>Side (c)<\/strong> for box-like shapes, <strong>Radius (r)<\/strong> and <strong>Height (h)<\/strong> for round shapes, and <strong>Bottom radius (R)<\/strong> for the frustum.<\/li>\n<li>For a hemisphere, decide whether to tick <strong>Include flat base<\/strong> \u2014 this adds the circular disk \\(\\pi r^2\\) to the total.<\/li>\n<li>Read the results: <strong>Total surface area<\/strong>, <strong>Lateral \/ curved area<\/strong>, <strong>Base area(s)<\/strong>, plus handy conversions to cm\u00b2, m\u00b2, in\u00b2 and ft\u00b2, the formula with your values substituted, and a labelled diagram of the shape.<\/li>\n<\/ol>\n<h2>What is surface area?<\/h2>\n<p>Surface area is the total area of all the faces or curved surfaces that enclose a three-dimensional object \u2014 the amount of material you would need to wrap the shape completely. It is measured in square units: if the dimensions are in centimetres, the area comes out in square centimetres (cm\u00b2).<\/p>\n<p>The calculator separates the area into three parts, and the distinction matters in practice. The <strong>lateral (or curved) area<\/strong> covers just the sides or the curved wall of the solid \u2014 think of the label wrapped around a can. The <strong>base area(s)<\/strong> are the flat ends: the two circles of a cylinder, the single square under a pyramid. Adding them gives the <strong>total surface area<\/strong>. When you estimate paint for the outside of a water tank, you need the total; when you estimate wallpaper for a living room, only the lateral area of its walls counts.<\/p>\n<p>Surface area is closely related to volume, but they behave differently. Doubling every dimension of a shape multiplies its volume by 8, yet its surface area only by 4 \u2014 because area grows with the square of the scale factor, not the cube. This is why small objects lose heat quickly (high area relative to volume), and why grinding coffee into fine powder makes it brew faster.<\/p>\n<p>The conversions to cm\u00b2, m\u00b2, in\u00b2 and ft\u00b2 are useful when shopping for materials: fabric is often sold by the square metre, paint coverage is rated in square feet per litre, and packaging labels may use any of the four.<\/p>\n<h2>Assumptions, limitations and tips<\/h2>\n<ul>\n<li>The calculator handles <strong>ideal, regular shapes<\/strong>. Real objects have seams, rims and rounded edges, so add 5\u201310% to the result when ordering material such as fabric, foil or paint.<\/li>\n<li>The <strong>triangular prism<\/strong> assumes an equilateral triangle base with side \\(a\\); a prism with a different triangle needs the general formula \\(A_t = (\\text{perimeter}) \\times h + 2 \\times (\\text{triangle area})\\). A <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/triangle-area-calculator\/\">triangle area calculator<\/a> can supply the base area.<\/li>\n<li>The <strong>square pyramid<\/strong> uses the true slant height \\(l\\) of the face, not the edge from apex to corner, and requires a square base; the <strong>capsule<\/strong> height \\(h\\) is only the straight cylinder part, not the tip-to-tip length.<\/li>\n<li>For the <strong>hemisphere<\/strong>, remember to set <strong>Include flat base<\/strong> according to your situation \u2014 a dome standing on the floor needs the base disk counted only if the floor itself is part of the surface.<\/li>\n<li>Always enter positive numbers, and in the <strong>cone frustum<\/strong> keep the bottom radius \\(R\\) greater than or equal to the top radius \\(r\\).<\/li>\n<li>For cylinders, spheres and cones you can explore further with the dedicated <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/cylinder-surface-area-calculator\/\">cylinder surface area<\/a>, <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/sphere-volume-and-surface-area-calculator\/\">sphere volume and surface area<\/a> and <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/cone-volume-and-surface-area-calculator\/\">cone volume and surface area<\/a> calculators.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Calculate the total, lateral and base surface area of a cube, prism, cylinder, cone, sphere, hemisphere, pyramid, capsule or cone frustum. Pick a shape, enter its dimensions and get the area in the unit you choose.<\/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-67377","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\/67377","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=67377"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/67377\/revisions"}],"predecessor-version":[{"id":67378,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/67377\/revisions\/67378"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=67377"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=67377"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=67377"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}