{"id":100118,"date":"2026-02-15T20:18:47","date_gmt":"2026-02-15T20:18:47","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100118"},"modified":"2026-07-12T10:56:39","modified_gmt":"2026-07-12T10:56:39","slug":"geometry-calculator","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/el\/calculators\/geometry-calculator\/","title":{"rendered":"Geometry Calculator: Surface Area &#038; Volume"},"content":{"rendered":"\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Geometry Calculator for Closed Solids\",\"description\":\"Calculate total surface area and volume of a cylinder,cone,sphere,ring torus or rectangular prism with strict dimensions and exact unit conversion.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/geometry-calculator\/\",\"applicationCategory\":\"Engineering Calculator\",\"operatingSystem\":\"Any (Web Browser)\",\"offers\":{\"@type\":\"Offer\",\"price\":\"0\",\"priceCurrency\":\"EUR\"},\"creator\":{\"@type\":\"Organization\",\"name\":\"Vibromera\",\"url\":\"https:\/\/vibromera.eu\/\"},\"dateModified\":\"2026-07-12\",\"inLanguage\":\"en\",\"isAccessibleForFree\":true}<\/script>\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[{\"@type\":\"Question\",\"name\":\"What surface area does this calculator report?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Total area of the closed ideal solid:both cylinder ends,the cone base,the entire sphere or ring torus,and all six prism faces.\"}},{\"@type\":\"Question\",\"name\":\"How is a ring torus defined?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"The entered major diameter is twice the distance from the axis to the tube centreline,and the tube diameter is twice the tube radius. This calculator requires major diameter greater than tube diameter.\"}},{\"@type\":\"Question\",\"name\":\"Does volume times density give weight?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Volume times mass density gives mass when units are consistent. Weight is force and additionally requires the applicable acceleration due to gravity.\"}},{\"@type\":\"Question\",\"name\":\"Can volumes of component shapes simply be added?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Only for a non-overlapping decomposition that exactly covers the object. Overlap must be subtracted and voids must not be added.\"}}]}<\/script>\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"BreadcrumbList\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/vibromera.eu\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Calculators\",\"item\":\"https:\/\/vibromera.eu\/calculators\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Geometry Calculator\",\"item\":\"https:\/\/vibromera.eu\/calculators\/geometry-calculator\/\"}]}<\/script>\n<link rel=\"preconnect\" 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print{.vc-section-body{max-height:none!important}.vc-faq-a{max-height:none!important}.vc-results{max-height:none!important;padding:24px!important}.vc-copy-btn,.vc-section-chevron,.vc-faq-chevron,.vc-presets,.vc-promo{display:none!important}}.vc-error{margin:.75rem 0 0;color:#b42318}.vc-result-note{font-size:13px;color:var(--vc-ink-secondary);margin:0}.vc-domain{background:var(--vc-blue-light);border-left:3px solid var(--vc-blue);padding:14px 16px;border-radius:0 6px 6px 0;margin:14px 0}.vc-domain p{margin:0}@media(max-width:600px){.vc-field[hidden]{display:none!important}}<\/style>\n<div class=\"vc-calculator\" id=\"vc-geometry\"><header class=\"vc-header\"><p class=\"vc-header-eyebrow\">Euclidean closed-solid geometry<\/p><h1 class=\"vc-header-title\">Geometry Calculator: Surface Area &amp; Volume<\/h1><p class=\"vc-header-subtitle\">Calculate a closed cylinder,cone,sphere,ring torus or rectangular prism. Inputs use one selected length unit;results are also normalized to SI.<\/p><div class=\"vc-badges\"><span class=\"vc-badge\">5 ideal solids<\/span><span class=\"vc-badge\">Exact unit conversion<\/span><span class=\"vc-badge\">Strict positive dimensions<\/span><\/div><\/header>\n<div class=\"vc-card\"><form class=\"vc-form\" id=\"vc-form\" autocomplete=\"off\"><div class=\"vc-form-grid\"><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-shape\">Ideal solid<\/label><select class=\"vc-select\" id=\"vc-shape\"><option value=\"\">Select\u2026<\/option><option value=\"cyl\">Closed circular cylinder<\/option><option value=\"cone\">Right circular cone with base<\/option><option value=\"sphere\">Sphere<\/option><option value=\"torus\">Ring torus<\/option><option value=\"rect\">Rectangular prism<\/option><\/select><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-unit\">Input length unit<\/label><select class=\"vc-select\" id=\"vc-unit\"><option value=\"\">Select\u2026<\/option><option value=\"mm\">millimetre (mm)<\/option><option value=\"cm\">centimetre (cm)<\/option><option value=\"m\">metre (m)<\/option><option value=\"in\">inch (in)<\/option><\/select><\/div><div class=\"vc-field\" id=\"vc-f1\"><label class=\"vc-label\" for=\"vc-d1\" id=\"vc-l1\">Dimension 1<\/label><input class=\"vc-input\" type=\"text\" id=\"vc-d1\" inputmode=\"decimal\" maxlength=\"80\" placeholder=\"strict positive number\"><\/div><div class=\"vc-field\" id=\"vc-f2\"><label class=\"vc-label\" for=\"vc-d2\" id=\"vc-l2\">Dimension 2<\/label><input class=\"vc-input\" type=\"text\" id=\"vc-d2\" inputmode=\"decimal\" maxlength=\"80\" placeholder=\"strict positive number\"><\/div><div class=\"vc-field\" id=\"vc-f3\"><label class=\"vc-label\" for=\"vc-d3\" id=\"vc-l3\">Dimension 3<\/label><input class=\"vc-input\" type=\"text\" id=\"vc-d3\" inputmode=\"decimal\" maxlength=\"80\" placeholder=\"strict positive number\"><\/div><\/div><p class=\"vc-error\" id=\"vc-error\" role=\"alert\"><\/p><div class=\"vc-domain\"><p id=\"vc-domain\"><strong>Select an ideal solid.<\/strong> Dimensions must describe the formulas shown below.<\/p><\/div><\/form>\n<div class=\"vc-results\" id=\"vc-results\" aria-live=\"polite\"><div class=\"vc-results-head\"><h2 class=\"vc-results-title\">Geometry result<\/h2><button type=\"button\" class=\"vc-copy-btn\" id=\"vc-copy-btn\">Copy<\/button><\/div><div class=\"vc-result-grid\"><div class=\"vc-rcard vc-rcard-primary\"><div class=\"vc-rcard-label\">Volume<\/div><div class=\"vc-rcard-value\" id=\"vc-r-vol\">\u2014<\/div><\/div><div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Total closed-surface area<\/div><div class=\"vc-rcard-value\" id=\"vc-r-area\">\u2014<\/div><\/div><div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Normalized SI volume<\/div><div class=\"vc-rcard-value\" id=\"vc-r-vol-si\">\u2014<\/div><\/div><div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Normalized SI area<\/div><div class=\"vc-rcard-value\" id=\"vc-r-area-si\">\u2014<\/div><\/div><div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Formula used<\/div><div class=\"vc-rcard-value\" id=\"vc-r-formula\">\u2014<\/div><\/div><div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Solid \/ domain<\/div><div class=\"vc-rcard-value\" id=\"vc-r-shape\">\u2014<\/div><\/div><\/div><p class=\"vc-result-note\" id=\"vc-r-note\"><\/p><\/div><\/div>\n<div class=\"vc-section vc-open\"><button type=\"button\" class=\"vc-section-toggle\" aria-expanded=\"true\"><span class=\"vc-section-toggle-text\"><span class=\"vc-section-icon\">\ud83d\udcd8<\/span><span class=\"vc-section-title\">Definitions,formulas and limits<\/span><\/span><\/button><div class=\"vc-section-body\"><div class=\"vc-section-inner vc-theory\"><h3>General geometry\u2014not an ISO acceptance calculation<\/h3><p>These are exact Euclidean formulas for ideal solids. They are not attributed to an ISO standard and do not include wall thickness,fillets,chamfers,threads,roughness,deformation or manufacturing tolerance. Total area means every exterior face of the closed ideal solid,including both cylinder ends and the cone base.<\/p><h3>Formulas in entered length unit u<\/h3><div class=\"vc-formula-box\"><strong>Closed cylinder:<\/strong> V=\u03c0d\u00b2h\/4; A=\u03c0dh+\u03c0d\u00b2\/2<br><strong>Right cone with base:<\/strong> s=\u221a((d\/2)\u00b2+h\u00b2); V=\u03c0d\u00b2h\/12; A=\u03c0(d\/2)(d\/2+s)<br><strong>Sphere:<\/strong> V=\u03c0d\u00b3\/6; A=\u03c0d\u00b2<br><strong>Ring torus:<\/strong> V=\u03c0\u00b2Dd\u00b2\/4; A=\u03c0\u00b2Dd; require D&gt;d&gt;0<br><strong>Rectangular prism:<\/strong> V=lwh; A=2(lw+lh+wh)<\/div><p>For the torus,D=2R is the major\/centreline diameter and d=2r is the tube diameter. Requiring D&gt;d restricts this calculator to a non-self-intersecting ring torus. A horn or spindle torus needs a different geometric interpretation.<\/p><h3>Unit normalization<\/h3><div class=\"vc-formula-box\">1mm=10\u207b\u00b3m; 1cm=10\u207b\u00b2m; 1in=0.0254m exactly<br>A<sub>m\u00b2<\/sub>=A<sub>u\u00b2<\/sub>k\u00b2; V<sub>m\u00b3<\/sub>=V<sub>u\u00b3<\/sub>k\u00b3<\/div><p>The affine-temperature issue does not arise here:length conversion is purely multiplicative. Display uses up to12 significant digits;the unrounded IEEE-754 result drives every output.<\/p><div class=\"vc-warning-box\"><p style=\"margin:0\"><strong>Engineering boundary:<\/strong> compare the idealized shape with the drawing\/model. A volume-to-mass calculation additionally requires compatible mass-density units. Weight is force,not mass,and requires the applicable gravitational acceleration.<\/p><\/div><\/div><\/div><\/div>\n<div class=\"vc-section\"><button type=\"button\" class=\"vc-section-toggle\" aria-expanded=\"false\"><span class=\"vc-section-toggle-text\"><span class=\"vc-section-icon\">\u2753<\/span><span class=\"vc-section-title\">Frequently Asked Questions<\/span><\/span><\/button><div class=\"vc-section-body\"><div class=\"vc-section-inner\"><div class=\"vc-faq-list\" id=\"vc-faq-list\"><\/div><\/div><\/div><\/div><footer class=\"vc-footer\"><p>\u00a92024\u20132026 <a href=\"https:\/\/vibromera.eu\/\">Vibromera<\/a><\/p><p>Exact ideal-solid arithmetic;not a dimensional inspection,manufacturing-tolerance or conformity decision. Scientific review:July2026.<\/p><\/footer><\/div>\n<script src=\"\/wp-content\/mu-plugins\/vbm-assets\/c100118-geometry.js?ver=20260712-1\" defer><\/script>\n","protected":false},"excerpt":{"rendered":"<p>Calculate total surface area and volume of a cylinder,cone,sphere,ring torus or rectangular prism with strict dimensions and exact unit conversion.<\/p>","protected":false},"featured_media":0,"template":"","meta":{"ai_generated_summary":"","footnotes":""},"categories":[],"tags":[],"class_list":["post-100118","calculator","type-calculator","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/vibromera.eu\/el\/wp-json\/wp\/v2\/calculator\/100118","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vibromera.eu\/el\/wp-json\/wp\/v2\/calculator"}],"about":[{"href":"https:\/\/vibromera.eu\/el\/wp-json\/wp\/v2\/types\/calculator"}],"version-history":[{"count":7,"href":"https:\/\/vibromera.eu\/el\/wp-json\/wp\/v2\/calculator\/100118\/revisions"}],"predecessor-version":[{"id":102436,"href":"https:\/\/vibromera.eu\/el\/wp-json\/wp\/v2\/calculator\/100118\/revisions\/102436"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/el\/wp-json\/wp\/v2\/media?parent=100118"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/el\/wp-json\/wp\/v2\/categories?post=100118"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/el\/wp-json\/wp\/v2\/tags?post=100118"}],"curies":[{"name":"\u03b5\u03c1\u03b3\u03b1\u03c3\u03af\u03b1","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}