{"id":67425,"date":"2026-10-21T10:27:05","date_gmt":"2026-10-21T07:27:05","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=67425"},"modified":"2026-10-21T10:27:05","modified_gmt":"2026-10-21T07:27:05","slug":"volume-calculator","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/mathematics\/volume-calculator\/","title":{"rendered":"Volume 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 of Common 3D Shapes<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"67425\" data-favorite-title=\"Volume\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/mathematics\/volume-calculator\/\" data-favorite-excerpt=\"Volume calculator for 12 common 3D shapes: cube, box, cylinder, cone, sphere, hemisphere, pyramid, prism, capsule, frustum, ellipsoid and tube. Pick a shape, enter its dimensions, and get the volume in cubic units, liters and gallons.\" 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\/volume-calculator\/\" method=\"POST\" class=\"calculator\" id=\"calculator-67425\" data-post=\"67425\"><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 (box)<\/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\">Pyramid (rectangular base)<\/option><option value=\"tri_prism\">Triangular prism<\/option><option value=\"capsule\">Capsule<\/option><option value=\"frustum\">Cone frustum (truncated cone)<\/option><option value=\"ellipsoid\">Ellipsoid<\/option><option value=\"tube\">Hollow cylinder (tube)<\/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, box side a, pyramid base length, triangular prism base, or ellipsoid semi-axis a.<\/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 box, pyramid base width, or ellipsoid semi-axis b.<\/small><\/div><div class=\"field has-term\" id=\"input-6\" hidden><label for=\"field-6\">Side \/ height (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_height_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 box, triangle height of the prism, or ellipsoid semi-axis c.<\/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 \/ length (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_length_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 or length of the cylinder, cone, pyramid, capsule, frustum, triangular prism or tube.<\/small><\/div><div class=\"field has-term\" id=\"input-9\" hidden><label for=\"field-9\">Bottom \/ outer 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_outer_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\">Bottom radius of the frustum; outer radius of the tube.<\/small><\/div><div class=\"field has-term\" id=\"input-10\" hidden><label for=\"field-10\">Inner radius (tube)<\/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=\"inner_radius_tube\" id=\"field-10\" aria-describedby=\"calc-info-10\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"3\"\/><small id=\"calc-info-10\">Tube only: radius of the hole; must be smaller than the outer radius R.<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"67425\">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> Volume Results<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>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\" id=\"output-2\"><span class=\"field-title\"><span>Volume in cubic centimeters<\/span><\/span><span class=\"field-value\" id=\"result-2\" data-unit=\"cm\u00b3\"><\/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>Volume in cubic meters<\/span><\/span><span class=\"field-value\" id=\"result-3\" data-unit=\"m\u00b3\"><\/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>Volume in cubic inches<\/span><\/span><span class=\"field-value\" id=\"result-4\" data-unit=\"in\u00b3\"><\/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>Volume in cubic feet<\/span><\/span><span class=\"field-value\" id=\"result-5\" data-unit=\"ft\u00b3\"><\/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>Volume in cubic yards<\/span><\/span><span class=\"field-value\" id=\"result-6\" data-unit=\"yd\u00b3\"><\/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>Volume in liters<\/span><\/span><span class=\"field-value\" id=\"result-7\" data-unit=\"L\"><\/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-8\"><span class=\"field-title\"><span>Volume in US gallons<\/span><\/span><span class=\"field-value\" id=\"result-8\" data-unit=\"US gal\"><\/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>Formula with your values<\/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>Shape diagram<\/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 class=\"field-result is-column\" id=\"output-11\"><span class=\"field-title\"><span>Related calculator<\/span><\/span><span class=\"field-value\" id=\"result-11\"><\/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=\"67425\" 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>Volume 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\\[ V = \\pi r^2 h \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(V\\) \u2014 volume of the shape<\/li>\n<li>\\(r\\) \u2014 radius of the circular base<\/li>\n<li>\\(h\\) \u2014 height or length of the shape<\/li>\n<li>\\(\\pi \\approx 3.14159\\)<\/li>\n<\/ul>\n<p>The formula \\(V = \\pi r^2 h\\) above is the one used for the default shape, the cylinder. Each shape in the calculator has its own formula:<\/p>\n<table>\n<thead>\n<tr>\n<th>Shape<\/th>\n<th>Formula<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Cube<\/td>\n<td>\\(V = a^3\\)<\/td>\n<\/tr>\n<tr>\n<td>Rectangular prism (box)<\/td>\n<td>\\(V = a \\cdot b \\cdot c\\)<\/td>\n<\/tr>\n<tr>\n<td>Cylinder<\/td>\n<td>\\(V = \\pi r^2 h\\)<\/td>\n<\/tr>\n<tr>\n<td>Cone<\/td>\n<td>\\(V = \\tfrac{1}{3}\\pi r^2 h\\)<\/td>\n<\/tr>\n<tr>\n<td>Sphere<\/td>\n<td>\\(V = \\tfrac{4}{3}\\pi r^3\\)<\/td>\n<\/tr>\n<tr>\n<td>Hemisphere<\/td>\n<td>\\(V = \\tfrac{2}{3}\\pi r^3\\)<\/td>\n<\/tr>\n<tr>\n<td>Pyramid (rectangular base)<\/td>\n<td>\\(V = \\tfrac{1}{3} a b h\\)<\/td>\n<\/tr>\n<tr>\n<td>Triangular prism<\/td>\n<td>\\(V = \\tfrac{1}{2} a c h\\)<\/td>\n<\/tr>\n<tr>\n<td>Capsule<\/td>\n<td>\\(V = \\pi r^2 h + \\tfrac{4}{3}\\pi r^3\\)<\/td>\n<\/tr>\n<tr>\n<td>Cone frustum<\/td>\n<td>\\(V = \\tfrac{\\pi h}{3}(R^2 + Rr + r^2)\\)<\/td>\n<\/tr>\n<tr>\n<td>Ellipsoid<\/td>\n<td>\\(V = \\tfrac{4}{3}\\pi abc\\)<\/td>\n<\/tr>\n<tr>\n<td>Hollow cylinder (tube)<\/td>\n<td>\\(V = \\pi h (R^2 - r^2)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>In every formula, the dimensions combine so that the result carries the cube of the length unit: if you enter centimeters, the volume comes out in \\(\\text{cm}^3\\); if you enter inches, it comes out in \\(\\text{in}^3\\).<\/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>Volume \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> a cylindrical water glass has a radius of 5 cm and a height of 12 cm. How much water does it hold? These are the calculator's default values, so you can reproduce the result directly.<\/p>\n<p>\\[ V = \\pi r^2 h = \\pi \\times 5^2 \\times 12 = 300\\pi \\approx 942.48 \\;\\text{cm}^3 \\]<\/p>\n<p><strong>Result:<\/strong> the glass holds about 942.48 cm\u00b3, which equals roughly 0.942 liters, 57.51 cubic inches or 0.249 US gallons.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to Use the Volume Calculator<\/h2>\n<ol>\n<li>Open the <strong>Shape<\/strong> dropdown and choose the solid you are working with \u2014 the form instantly shows only the dimensions that shape needs.<\/li>\n<li>Set the <strong>Length unit<\/strong> (mm, cm, m, in, ft or yd). All dimensions you enter are interpreted in this unit, and the result is shown in this unit cubed.<\/li>\n<li>Fill in the visible dimension fields, for example <strong>Radius (r)<\/strong> and <strong>Height \/ length (h)<\/strong> for a cylinder, or the three sides for a box. For a tube, enter the outer radius in <strong>Bottom \/ outer radius (R)<\/strong> and the hole size in <strong>Inner radius (tube)<\/strong>.<\/li>\n<li>Read the <strong>Volume<\/strong> result at the top, then check the conversions below it: cubic centimeters, cubic meters, cubic inches, cubic feet, cubic yards, liters and US gallons.<\/li>\n<li>The <strong>Formula with your values<\/strong> block shows the exact calculation with your numbers substituted, and the <strong>Shape diagram<\/strong> labels each dimension on a drawing so you can verify your inputs.<\/li>\n<\/ol>\n<h2>What Volume Means and Why It Matters<\/h2>\n<p>Volume is the amount of three-dimensional space a solid object occupies. It answers practical questions everywhere: how much concrete fills a footing, how much water fits in a tank, how much soil a raised bed holds, how much air a room contains, or how much liquid a bottle can carry. Whatever the shape, volume is always measured in cubic units \u2014 cubic meters, cubic feet, liters, gallons \u2014 because it is the product of three lengths.<\/p>\n<p>Every volume formula reduces to the same idea: take the area of a base or cross-section and stretch it through a third dimension. A box is a rectangle swept through height \\(c\\), giving \\(abc\\). A cylinder is a circle of area \\(\\pi r^2\\) swept through height \\(h\\). A cone or pyramid tapers to a point, so it holds exactly one third of the cylinder or prism with the same base and height \u2014 that is where the factor \\(\\tfrac{1}{3}\\) in their formulas comes from. A sphere's \\(\\tfrac{4}{3}\\pi r^3\\) can be read as four stacked circle-sweeps of radius \\(r\\) divided by three.<\/p>\n<p>When you interpret a result, pay attention to the unit. Multiplying lengths in meters gives cubic meters directly, which suits rooms, pools and construction quantities. For containers, liters and gallons are usually more meaningful: 1 liter equals 1000 cm\u00b3, and 1 US gallon equals 231 in\u00b3. The calculator performs all of these conversions for you, so you can move freely between metric and imperial figures without memorizing conversion factors.<\/p>\n<h2>Assumptions, Limitations and Practical Tips<\/h2>\n<ul>\n<li>All shapes are assumed to be <em>regular<\/em>: circular bases are perfect circles, boxes have square corners, prisms have constant cross-sections. For irregular objects, volume is best measured by water displacement.<\/li>\n<li>Dimensions must be interior measurements for capacity questions. The wall thickness of a real tank, pipe or glass reduces the usable volume, so measure the inside.<\/li>\n<li>For a cone frustum, the top radius \\(r\\) and bottom radius \\(R\\) may differ, but both must be greater than zero. Set \\(r = R\\) only if you actually want a cylinder.<\/li>\n<li>For a hollow cylinder (tube), the inner radius must be strictly smaller than the outer radius; the calculator rejects an entry of the same size or larger because it describes an impossible shape (or zero material).<\/li>\n<li>For an ellipsoid, the inputs are semi-axes \u2014 half the full width in each direction. Entering the full diameters will overestimate the volume by a factor of 8.<\/li>\n<li>A capsule's height \\(h\\) is the length of the straight cylindrical middle section only, not the tip-to-tip length. The total length of the capsule is \\(h + 2r\\).<\/li>\n<li>Keep all dimensions in the same unit before entering them, or use the <strong>Length unit<\/strong> selector consistently \u2014 mixing units (for example, feet with inches) is the most common source of wrong volume results.<\/li>\n<\/ul>\n<p>If you also need the surface area of the same solid \u2014 for paint, material or heat-exchange estimates \u2014 use the <a href=\"https:\/\/wpcalc.com\/en\/surface-area-calculator\/\">Surface Area Calculator<\/a>. For more detail on a single shape, see the <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/cylinder-volume-calculator\/\">Cylinder Volume Calculator<\/a>, the <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/sphere-volume-and-surface-area-calculator\/\">Sphere Volume and Surface Area Calculator<\/a> and the <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/cone-volume-and-surface-area-calculator\/\">Cone Volume and Surface Area Calculator<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Volume calculator for 12 common 3D shapes: cube, box, cylinder, cone, sphere, hemisphere, pyramid, prism, capsule, frustum, ellipsoid and tube. Pick a shape, enter its dimensions, and get the volume in cubic units, liters and gallons.<\/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-67425","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\/67425","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=67425"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/67425\/revisions"}],"predecessor-version":[{"id":67426,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/67425\/revisions\/67426"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=67425"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=67425"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=67425"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}