{"id":66835,"date":"2026-10-15T09:20:28","date_gmt":"2026-10-15T06:20:28","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=66835"},"modified":"2026-10-15T09:20:28","modified_gmt":"2026-10-15T06:20:28","slug":"sphere-volume-and-surface-area-calculator","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/mathematics\/sphere-volume-and-surface-area-calculator\/","title":{"rendered":"Sphere Volume and 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 Volume and Surface Area of a Sphere<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"66835\" data-favorite-title=\"Sphere Volume and Surface Area\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/mathematics\/sphere-volume-and-surface-area-calculator\/\" data-favorite-excerpt=\"Calculate the volume, surface area, and great-circle circumference of a sphere from its radius or diameter. Enter one dimension, choose a unit, and get instant results with steps.\" 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\/sphere-volume-and-surface-area-calculator\/\" method=\"POST\" class=\"calculator\" id=\"calculator-66835\" data-post=\"66835\"><fieldset class=\"fieldset-input is-2\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field\" id=\"input-1\"><label for=\"field-1\">Given dimension<\/label><div class=\"grid grid-cols-1\"><select id=\"field-1\" name=\"given_dimension\"><option value=\"radius\" selected>Radius<\/option><option value=\"diameter\">Diameter<\/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\" id=\"input-2\"><label for=\"field-2\">Size<\/label><div class=\"field-group\"><input type=\"text\" name=\"size\" id=\"field-2\" aria-describedby=\"calc-info-2\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"5\" min=\"0\" value=\"5\"\/><div class=\"grid grid-cols-1\"><select id=\"field-3\" name=\"unit\" aria-label=\"Unit\"><option value=\"m\">m<\/option><option value=\"cm\" selected>cm<\/option><option value=\"mm\">mm<\/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><small id=\"calc-info-2\">Radius (or diameter) of the sphere, measured from the centre to the surface (or edge to edge through the centre).<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"66835\">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 Sphere<\/h3><div class=\"result-box\"><div class=\"field-result is-column\" id=\"output-1\"><span class=\"field-title\"><span>Sphere volume<\/span><span class=\"result-term\">V<\/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 is-column\" id=\"output-2\"><span class=\"field-title\"><span>Surface area<\/span><span class=\"result-term\">A<\/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>Great-circle circumference<\/span><span class=\"result-term\">C<\/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=\"66835\" 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>Sphere Volume and 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\">\\[ V = \\frac{4}{3}\\pi r^3 \\]\n\\[ A = 4\\pi r^2 \\]\n\\[ C = 2\\pi r \\]<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(V\\) \u2014 volume of the sphere (cubic units)<\/li>\n<li>\\(A\\) \u2014 surface area of the sphere (square units)<\/li>\n<li>\\(C\\) \u2014 circumference of a great circle (same unit as the radius)<\/li>\n<li>\\(r\\) \u2014 radius of the sphere<\/li>\n<li>\\(\\pi \\approx 3.14159\\)<\/li>\n<\/ul>\n<p>If you know the diameter \\(d\\) instead of the radius, first convert it: \\(r = d\/2\\), then apply the same three formulas.<\/p>\n<p>These formulas describe a perfect sphere: the volume grows with the cube of the radius, while the surface area grows with its square.<\/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>Sphere Volume and Surface Area \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> a ball has a radius of 5 cm. Find its volume, surface area, and great-circle circumference.<\/p>\n<p>\n[ V = \\frac{4}{3}\\pi r^3 = \\frac{4}{3}\\pi \\cdot 5^3 = \\frac{4}{3}\\pi \\cdot 125 \\approx 523.599 \\text{ cm}^3 \\]<\/p>\n<p>\n[ A = 4\\pi r^2 = 4\\pi \\cdot 5^2 = 4\\pi \\cdot 25 \\approx 314.159 \\text{ cm}^2 \\]<\/p>\n<p>\n[ C = 2\\pi r = 2\\pi \\cdot 5 \\approx 31.416 \\text{ cm} \\]<\/p>\n<p><strong>Result:<\/strong> the volume is about 523.599 cm\u00b3, the surface area is about 314.159 cm\u00b2, and the great-circle circumference is about 31.416 cm.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to Use the Sphere Calculator<\/h2>\n<ol>\n<li>In the <strong>Given dimension<\/strong> dropdown, choose whether the number you have is the <em>Radius<\/em> or the <em>Diameter<\/em> of the sphere.<\/li>\n<li>Enter the value in the <strong>Size<\/strong> field (for example, 5).<\/li>\n<li> Pick the unit of length (m, cm, mm, in, or ft) from the <strong>Unit<\/strong> dropdown next to the size field.<\/li>\n<li>The results appear instantly: <strong>Sphere volume<\/strong> in cubic units, <strong>Surface area<\/strong> in square units, and <strong>Great-circle circumference<\/strong> in the chosen length unit. The <strong>Calculation steps<\/strong> block shows exactly how each value was obtained.<\/li>\n<\/ol>\n<h2>What Is a Sphere?<\/h2>\n<p>A sphere is the set of all points in space that are the same distance (the radius) from a central point. It is the three-dimensional analogue of a circle: perfectly round, with no edges, corners, or flat faces. Everyday examples include balls, bubbles, planets (approximately), and water droplets.<\/p>\n<p>Two measurements fully define a sphere: the radius \\(r\\), which runs from the centre to the surface, and the diameter \\(d = 2r\\), which runs from one side of the surface to the other through the centre. Because one determines the other, the calculator accepts either \u2014 you do not need to convert manually.<\/p>\n<p>The volume tells you how much space the sphere encloses \u2014 useful for capacity, displacement, or material quantity. The surface area tells you how much material would cover the outside \u2014 relevant for paint, packaging, coating, or heat transfer. The great-circle circumference is the distance around the sphere at its widest point, the same as the circumference of a circle with radius \\(r\\).<\/p>\n<p>Notice the relationship between the results: the volume scales with \\(r^3\\) while the area scales with \\(r^2\\). Doubling the radius multiplies the surface area by 4 but the volume by 8. This is why, for example, larger spheres hold far more per unit of surface than smaller ones \u2014 a principle that matters in chemistry, biology, and engineering.<\/p>\n<h2>Assumptions, Limitations, and Tips<\/h2>\n<ul>\n<li><strong>Perfect sphere only.<\/strong> The formulas assume an ideal sphere. Real objects like the Earth are slightly flattened, so results are approximations for such shapes.<\/li>\n<li><strong>Exact dimension required.<\/strong> If your measurement is a circumference instead of a radius or diameter, first recover the radius with \\(r = C\/(2\\pi)\\). Simple <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/division-calculator\/\">division<\/a> and this relation get you the value to enter.<\/li>\n<li><strong>Unit consistency.<\/strong> The calculator converts the length unit automatically: a radius in cm gives volume in cm\u00b3 and area in cm\u00b2. Never mix units, e.g. entering a radius in inches while expecting a result in cm.<\/li>\n<li><strong>Reversing the formulas.<\/strong> To find the radius from a known volume, rearrange to \\(r = \\sqrt[3]{3V\/(4\\pi)}\\); from a known area, \\(r = \\sqrt{A\/(4\\pi)}\\). The cube-root step can be done with our <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/nth-root\/\">Nth Root calculator<\/a>.<\/li>\n<li><strong>Significant figures.<\/strong> Results are shown to three decimal places. For practical work, round according to the precision of your original measurement.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Calculate the volume, surface area, and great-circle circumference of a sphere from its radius or diameter. Enter one dimension, choose a unit, and get instant results with steps.<\/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-66835","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\/66835","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=66835"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66835\/revisions"}],"predecessor-version":[{"id":67062,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66835\/revisions\/67062"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=66835"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=66835"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=66835"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}