{"id":66837,"date":"2026-10-15T09:20:27","date_gmt":"2026-10-15T06:20:27","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=66837"},"modified":"2026-10-15T09:20:27","modified_gmt":"2026-10-15T06:20:27","slug":"cylinder-surface-area-calculator","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/mathematics\/cylinder-surface-area-calculator\/","title":{"rendered":"Cylinder 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 a Cylinder from Radius and Height<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"66837\" data-favorite-title=\"Cylinder Surface Area\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/mathematics\/cylinder-surface-area-calculator\/\" data-favorite-excerpt=\"Calculate the curved (lateral) surface area, base area, and total surface area of a cylinder from its radius and height. Supports m, cm, mm, ft and in, with step-by-step working shown.\" 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\/cylinder-surface-area-calculator\/\" method=\"POST\" class=\"calculator\" id=\"calculator-66837\" data-post=\"66837\"><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\">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><div class=\"field-group\"><input type=\"text\" name=\"radius_r\" id=\"field-1\" aria-describedby=\"calc-info-1\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"5\" min=\"0\" value=\"5\"\/><div class=\"grid grid-cols-1\"><select id=\"field-2\" name=\"unit\" aria-label=\"Unit\"><option value=\"m\" selected>m<\/option><option value=\"cm\">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-1\">Distance from the centre of the base to its edge.<\/small><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-3\">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><div class=\"field-group\"><input type=\"text\" name=\"height_h\" 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\" selected>m<\/option><option value=\"cm\">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\">Perpendicular distance between the two bases.<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"66837\">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 Cylinder<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Curved (lateral) surface area<\/span><span class=\"result-term\">A_L<\/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>Base area (one base)<\/span><span class=\"result-term\">A_B<\/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>Total surface area<\/span><span class=\"result-term\">A<\/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=\"66837\" 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 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[]).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>Cylinder 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\\[ A = 2\\pi r h + 2\\pi r^2 = 2\\pi r (r + h) \\]<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(A\\) \u2014 total surface area of the cylinder<\/li>\n<li>\\(r\\) \u2014 radius of the circular base<\/li>\n<li>\\(h\\) \u2014 height of the cylinder (perpendicular distance between the bases)<\/li>\n<li>\\(\\pi \\approx 3.14159\\)<\/li>\n<\/ul>\n<p>The formula combines the two circular bases (each of area \\(\\pi r^2\\)) with the curved side, which unrolls into a rectangle of width \\(2\\pi r\\) (the circumference of the base) and height \\(h\\).<\/p>\n<p>The individual parts are:<\/p>\n<ul>\n<li>Curved (lateral) surface area: \\(A_L = 2\\pi r h\\)<\/li>\n<li>Area of one base: \\(A_B = \\pi r^2\\)<\/li>\n<li>Total surface area: \\(A = A_L + 2A_B\\)<\/li>\n<\/ul>\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>Cylinder Surface Area \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> a closed cylinder with a radius of 5 m and a height of 10 m.<\/p>\n<p>\\[ A_L = 2\\pi r h = 2\\pi \\cdot 5 \\cdot 10 = 100\\pi \\approx 314.159 \\text{ m}^2 \\]<\/p>\n<p>\\[ A_B = \\pi r^2 = \\pi \\cdot 5^2 = 25\\pi \\approx 78.540 \\text{ m}^2 \\]<\/p>\n<p>\\[ A = A_L + 2A_B = 314.159 + 157.080 \\approx 471.239 \\text{ m}^2 \\]<\/p>\n<p><strong>Result:<\/strong> the curved surface area is about 314.159 m\u00b2, each base is about 78.540 m\u00b2, and the total surface area is about 471.239 m\u00b2.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to Use the Cylinder Surface Area Calculator<\/h2>\n<ol>\n<li>Enter the <strong>Radius (r)<\/strong> \u2014 the distance from the centre of the circular base to its edge.<\/li>\n<li>Choose the unit for the radius (m, cm, mm, ft or in) from the dropdown next to the input field.<\/li>\n<li>Enter the <strong>Height (h)<\/strong> \u2014 the perpendicular distance between the two bases \u2014 and select its unit. It does not need to match the radius unit; the calculator converts it automatically.<\/li>\n<li>Read the results: the <strong>Curved (lateral) surface area<\/strong>, the <strong>Base area<\/strong> for one base, and the <strong>Total surface area<\/strong>, all expressed in the square of the radius unit.<\/li>\n<li>Check the <strong>Calculation steps<\/strong> section to see exactly how each value was obtained, including any unit conversion that was applied.<\/li>\n<\/ol>\n<h2>What Is the Surface Area of a Cylinder?<\/h2>\n<p>A cylinder is a three-dimensional solid with two identical circular bases connected by a curved side. Its surface area is the total area you would cover if you painted the entire outside of the object. It is made of three parts: the curved wall and the two flat circular ends.<\/p>\n<p>The curved (lateral) surface has a particularly elegant property: if you imagine peeling the label off a can and flattening it, you get a rectangle. Its width equals the circumference of the base, \\(2\\pi r\\), and its height equals the cylinder's height \\(h\\). That is why the lateral area is simply \\(2\\pi r h\\). The two bases are ordinary circles, each with area \\(\\pi r^2\\).<\/p>\n<p>Surface area matters whenever material, coating, or heat exchange is involved. Manufacturers use it to estimate how much sheet metal a tank needs, painters to estimate how much paint a silo requires, and engineers to design containers, pipes and heat exchangers. A larger surface area relative to volume means faster heat loss or gain \u2014 a key consideration in thermodynamics and food packaging.<\/p>\n<p>When interpreting the result, keep in mind which quantity you actually need. The <strong>total<\/strong> surface area includes both circular ends. If your cylinder is open at one end (like a drinking cup or an open tank), you need \\(A_L + A_B\\); if it is open at both ends (like a pipe segment or a tube of label paper), you only need the lateral area \\(A_L\\). The calculator shows all three values so you can pick the one that fits your situation.<\/p>\n<h2>Assumptions, Limitations and Practical Tips<\/h2>\n<ul>\n<li>The calculator assumes a <strong>right circular cylinder<\/strong>: the sides are perpendicular to the bases and both bases are circles of the same radius. Oblique (tilted) cylinders and shapes with elliptical bases need different formulas.<\/li>\n<li>Both radius and height must be <strong>positive numbers<\/strong>. A zero or negative value does not describe a real cylinder, and the calculator will ask you to correct it.<\/li>\n<li>The radius and height may be entered in <strong>different units<\/strong> \u2014 for example a radius in cm and a height in ft. The height is converted to the radius unit before computing, and all areas are reported in the square of the radius unit (e.g. cm\u00b2).<\/li>\n<li>Results are rounded to three decimal places. Because \\(\\pi\\) is irrational, exact answers only exist in terms of \\(\\pi\\) (such as \\(150\\pi\\) for the default example).<\/li>\n<li>If you use the result for ordering material, add a practical margin (typically 5\u201310%) for seams, overlaps and cutting waste.<\/li>\n<li>Want to verify the arithmetic by hand? You can break \\(2\\pi r h\\) into simple chained operations with the <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/multiplication-calculator\/\">multiplication calculator<\/a>, or check unit conversions with the <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/division-calculator\/\">division calculator<\/a>.<\/li>\n<\/ul>\n<p>One quick sanity check: the total surface area must always be greater than the lateral area alone, and greater than twice the base area. If a number looks off, verify that the height was not accidentally entered with the wrong unit \u2014 a common slip when working between metric and imperial measurements.<\/p>\n<h2>Quick Reference Table<\/h2>\n<p>Exact surface areas for a few simple cylinders (areas in terms of \\(\\pi\\)):<\/p>\n<table>\n<thead>\n<tr>\n<th>Radius \\(r\\)<\/th>\n<th>Height \\(h\\)<\/th>\n<th>Lateral \\(A_L = 2\\pi r h\\)<\/th>\n<th>One base \\(A_B = \\pi r^2\\)<\/th>\n<th>Total \\(A = 2\\pi r(r+h)\\)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>1<\/td>\n<td>1<\/td>\n<td>\\(2\\pi \\approx 6.283\\)<\/td>\n<td>\\(\\pi \\approx 3.142\\)<\/td>\n<td>\\(4\\pi \\approx 12.566\\)<\/td>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td>5<\/td>\n<td>\\(20\\pi \\approx 62.832\\)<\/td>\n<td>\\(4\\pi \\approx 12.566\\)<\/td>\n<td>\\(28\\pi \\approx 87.965\\)<\/td>\n<\/tr>\n<tr>\n<td>5<\/td>\n<td>10<\/td>\n<td>\\(100\\pi \\approx 314.159\\)<\/td>\n<td>\\(25\\pi \\approx 78.540\\)<\/td>\n<td>\\(150\\pi \\approx 471.239\\)<\/td>\n<\/tr>\n<tr>\n<td>10<\/td>\n<td>10<\/td>\n<td>\\(200\\pi \\approx 628.319\\)<\/td>\n<td>\\(100\\pi \\approx 314.159\\)<\/td>\n<td>\\(400\\pi \\approx 1256.637\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"<p>Calculate the curved (lateral) surface area, base area, and total surface area of a cylinder from its radius and height. Supports m, cm, mm, ft and in, with step-by-step working shown.<\/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-66837","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\/66837","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=66837"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66837\/revisions"}],"predecessor-version":[{"id":67125,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66837\/revisions\/67125"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=66837"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=66837"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=66837"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}