{"id":100052,"date":"2026-02-15T20:09:26","date_gmt":"2026-02-15T20:09:26","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100052"},"modified":"2026-02-15T20:09:26","modified_gmt":"2026-02-15T20:09:26","slug":"center-of-gravity-calculator","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/bn\/calculators\/center-of-gravity-calculator\/","title":{"rendered":"Center of Gravity Calculator | CG = \u03a3mi\u00d7xi \/ \u03a3mi"},"content":{"rendered":"\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Center of Gravity Calculator\",\"description\":\"Free CG calculator for up to 8 components with mass and position.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/center-of-gravity-calculator\/\",\"applicationCategory\":\"Engineering Calculator\",\"operatingSystem\":\"Any\",\"offers\":{\"@type\":\"Offer\",\"price\":\"0\",\"priceCurrency\":\"EUR\"},\"creator\":{\"@type\":\"Organization\",\"name\":\"Vibromera\",\"url\":\"https:\/\/vibromera.eu\/\"},\"datePublished\":\"2024-01-01\",\"dateModified\":\"2025-02-14\",\"inLanguage\":\"en\",\"isAccessibleForFree\":true}<\/script>\n\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[{\"@type\":\"Question\",\"name\":\"What is center of gravity?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"CG is the average location of mass, weighted by each component. The balance point.\"}},{\"@type\":\"Question\",\"name\":\"Why is CG important for lifting?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Lift point must be above CG to prevent tilting.\"}},{\"@type\":\"Question\",\"name\":\"How do I find CG for irregular shapes?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Divide into simple components and use weighted average.\"}},{\"@type\":\"Question\",\"name\":\"What about 3D?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Add Z coordinate: CG_z = \u03a3(mi\u00d7zi)\/\u03a3mi.\"}},{\"@type\":\"Question\",\"name\":\"Does CG change with orientation?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"No, CG is fixed relative to the object.\"}}]}<\/script>\n\n<script 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href=\"https:\/\/cdn.jsdelivr.net\/npm\/katex@0.16.11\/dist\/katex.min.css\">\n\n<style>:root{--vc-bg:#f4f1ec;--vc-surface:#fff;--vc-surface-alt:#f8f6f2;--vc-ink:#1a1a1a;--vc-ink-secondary:#5a5650;--vc-ink-muted:#8a857e;--vc-accent:#c85a2a;--vc-accent-hover:#b04d22;--vc-accent-light:#fdf0ea;--vc-blue:#2a5c8c;--vc-blue-light:#eaf1f8;--vc-green:#2a7a4b;--vc-green-light:#eaf8ef;--vc-yellow:#a67c00;--vc-yellow-light:#fef9e8;--vc-border:#d9d4cc;--vc-border-light:#e8e4dd;--vc-shadow:0 1px 3px rgba(26,26,26,.06),0 4px 12px rgba(26,26,26,.04);--vc-radius:8px;--vc-radius-lg:12px;--vc-font:'DM Sans',-apple-system,BlinkMacSystemFont,'Segoe UI',sans-serif;--vc-mono:'JetBrains Mono',Consolas,Monaco,monospace;--vc-display:Fraunces,Georgia,serif}.vc-calculator{font-family:var(--vc-font);font-size:15px;line-height:1.65;color:var(--vc-ink);max-width:960px;margin:0 auto;padding:20px 16px 40px;-webkit-font-smoothing:antialiased}.vc-calculator *,.vc-calculator *::before,.vc-calculator 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.15s}.vc-related-link:hover{border-color:var(--vc-accent);color:var(--vc-accent);background:var(--vc-accent-light)}.vc-promo{margin-top:24px;padding:20px;background:linear-gradient(135deg,var(--vc-accent-light),var(--vc-surface));border:1px solid var(--vc-border);border-radius:var(--vc-radius-lg);display:flex;align-items:center;gap:16px}.vc-promo-text{flex:1;font-size:14px;color:var(--vc-ink-secondary)}.vc-promo-text strong{color:var(--vc-ink)}.vc-promo-link{padding:8px 20px;font-size:13px;font-weight:700;color:#fff;background:var(--vc-accent);border-radius:var(--vc-radius);text-decoration:none;white-space:nowrap;transition:background .15s}.vc-promo-link:hover{background:var(--vc-accent-hover)}.vc-footer{text-align:center;padding:32px 16px;font-size:13px;color:var(--vc-ink-muted)}.vc-footer a{color:var(--vc-accent);text-decoration:none}.vc-footer a:hover{text-decoration:underline}.vc-footer-links{margin-top:8px;font-size:12px}.vc-footer-links a{margin:0 8px}.vc-viz{margin:20px 0;background:var(--vc-surface);border:1px solid var(--vc-border-light);border-radius:var(--vc-radius);padding:16px;overflow:hidden}.vc-viz svg{width:100%;height:auto;display:block}.vc-viz-title{font-family:var(--vc-mono);font-size:11px;font-weight:500;letter-spacing:.1em;text-transform:uppercase;color:var(--vc-ink-muted);margin-bottom:12px}@media 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}}<\/style>\n\n<div class=\"vc-calculator\"><header class=\"vc-header\"><p class=\"vc-header-eyebrow\">Free Engineering Tool #219<\/p><h1 class=\"vc-header-title\">Center of Gravity Calculator<\/h1><p class=\"vc-header-subtitle\">Calculate combined center of gravity for up to 8 components. Enter mass and (x,y) position.<\/p><div class=\"vc-badges\"><span class=\"vc-badge\">CG = \u03a3mi\u00b7xi \/ \u03a3mi<\/span><span class=\"vc-badge\">Up to 8 Points<\/span><span class=\"vc-badge\">2D<\/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-m1\">Mass 1 <span class=\"vc-label-hint\">(kg)<\/span><\/label><input class=\"vc-input\" type=\"number\" id=\"vc-m1\" step=\"any\" value=\"100\" ><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-x1\">X1 <span class=\"vc-label-hint\">(m)<\/span><\/label><input class=\"vc-input\" type=\"number\" id=\"vc-x1\" step=\"any\" value=\"0\" ><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-y1\">Y1 <span class=\"vc-label-hint\">(m)<\/span><\/label><input class=\"vc-input\" type=\"number\" id=\"vc-y1\" step=\"any\" value=\"0\" ><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-m2\">Mass 2 <span class=\"vc-label-hint\">(kg)<\/span><\/label><input class=\"vc-input\" type=\"number\" id=\"vc-m2\" step=\"any\" value=\"200\" ><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-x2\">X2 <span class=\"vc-label-hint\">(m)<\/span><\/label><input class=\"vc-input\" type=\"number\" id=\"vc-x2\" step=\"any\" value=\"2\" ><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-y2\">Y2 <span class=\"vc-label-hint\">(m)<\/span><\/label><input class=\"vc-input\" type=\"number\" id=\"vc-y2\" step=\"any\" value=\"0\" ><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-m3\">Mass 3 <span class=\"vc-label-hint\">(kg)<\/span><\/label><input class=\"vc-input\" type=\"number\" id=\"vc-m3\" step=\"any\" value=\"150\" ><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-x3\">X3 <span class=\"vc-label-hint\">(m)<\/span><\/label><input class=\"vc-input\" type=\"number\" id=\"vc-x3\" step=\"any\" value=\"1\" ><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-y3\">Y3 <span class=\"vc-label-hint\">(m)<\/span><\/label><input class=\"vc-input\" type=\"number\" id=\"vc-y3\" step=\"any\" value=\"1.5\" ><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-m4\">Mass 4 <span class=\"vc-label-hint\">(kg)<\/span><\/label><input class=\"vc-input\" type=\"number\" id=\"vc-m4\" step=\"any\"  ><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-x4\">X4 <span class=\"vc-label-hint\">(m)<\/span><\/label><input class=\"vc-input\" type=\"number\" id=\"vc-x4\" step=\"any\"  ><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-y4\">Y4 <span class=\"vc-label-hint\">(m)<\/span><\/label><input class=\"vc-input\" type=\"number\" id=\"vc-y4\" step=\"any\"  ><\/div><\/div>\n<div class=\"vc-presets\"><div class=\"vc-presets-label\">Quick presets<\/div><button type=\"button\" class=\"vc-preset-btn\" data-preset=\"beam\">2 masses on beam<\/button><button type=\"button\" class=\"vc-preset-btn\" data-preset=\"tri\">Triangle equal<\/button><button type=\"button\" class=\"vc-preset-btn\" data-preset=\"machine\">Machine 3-comp<\/button><\/div><\/form>\n<div class=\"vc-results\" id=\"vc-results\"><div class=\"vc-results-head\"><h2 class=\"vc-results-title\">Results<\/h2><button type=\"button\" class=\"vc-copy-btn\" id=\"vc-copy-btn\"><svg width=\"14\" height=\"14\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><rect x=\"9\" y=\"9\" width=\"13\" height=\"13\" rx=\"2\"\/><path d=\"M5 15H4a2 2 0 01-2-2V4a2 2 0 012-2h9a2 2 0 012 2v1\"\/><\/svg> Copy<\/button><\/div><div class=\"vc-result-grid\"><div class=\"vc-rcard vc-rcard-primary\"><div class=\"vc-rcard-label\">Center of Gravity<\/div><div class=\"vc-rcard-value\" id=\"vc-r-cg\">\u2014<\/div><\/div><div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Total Mass<\/div><div class=\"vc-rcard-value\" id=\"vc-r-mass\">\u2014<\/div><\/div><div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Components<\/div><div class=\"vc-rcard-value\" id=\"vc-r-n\">\u2014<\/div><\/div><\/div>\n<div class=\"vc-viz\" id=\"vc-viz\"><div class=\"vc-viz-title\">Component Positions &amp; CG<\/div><svg id=\"vc-viz-svg\" viewBox=\"0 0 400 400\"><\/svg><\/div><\/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\">Theory &amp; Formulas<\/span><\/span><svg class=\"vc-section-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg><\/button><div class=\"vc-section-body\"><div class=\"vc-section-inner vc-theory\"><h3>Center of Gravity<\/h3><div class=\"vc-formula-box\" id=\"vc-katex-1\"><\/div><p>Where m<sub>i<\/sub> is mass and (x<sub>i<\/sub>, y<sub>i<\/sub>) is position of each component.<\/p><\/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\">\ud83d\udd17<\/span><span class=\"vc-section-title\">Related Calculators<\/span><\/span><svg class=\"vc-section-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg><\/button><div class=\"vc-section-body\"><div class=\"vc-section-inner\"><div class=\"vc-related\"><a class=\"vc-related-link\" href=\"\/calculators\/sling-capacity-angle\/\">Sling Capacity<\/a><a class=\"vc-related-link\" href=\"\/calculators\/wire-rope-capacity\/\">Wire Rope Capacity<\/a><\/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><svg class=\"vc-section-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg><\/button><div class=\"vc-section-body\"><div class=\"vc-section-inner\"><div class=\"vc-faq-list\"><div class=\"vc-faq-item\"><button type=\"button\" class=\"vc-faq-q\"><span>What is center of gravity?<\/span><svg class=\"vc-faq-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg><\/button><div class=\"vc-faq-a\"><div class=\"vc-faq-a-inner\"><p>CG is the average location of mass, weighted by each component. The balance point.<\/p><\/div><\/div><\/div><div class=\"vc-faq-item\"><button type=\"button\" class=\"vc-faq-q\"><span>Why is CG important for lifting?<\/span><svg class=\"vc-faq-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg><\/button><div class=\"vc-faq-a\"><div class=\"vc-faq-a-inner\"><p>Lift point must be above CG to prevent tilting.<\/p><\/div><\/div><\/div><div class=\"vc-faq-item\"><button type=\"button\" class=\"vc-faq-q\"><span>How do I find CG for irregular shapes?<\/span><svg class=\"vc-faq-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg><\/button><div class=\"vc-faq-a\"><div class=\"vc-faq-a-inner\"><p>Divide into simple components and use weighted average.<\/p><\/div><\/div><\/div><div class=\"vc-faq-item\"><button type=\"button\" class=\"vc-faq-q\"><span>What about 3D?<\/span><svg class=\"vc-faq-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg><\/button><div class=\"vc-faq-a\"><div class=\"vc-faq-a-inner\"><p>Add Z coordinate: CG_z = \u03a3(mi\u00d7zi)\/\u03a3mi.<\/p><\/div><\/div><\/div><div class=\"vc-faq-item\"><button type=\"button\" class=\"vc-faq-q\"><span>Does CG change with orientation?<\/span><svg class=\"vc-faq-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg><\/button><div class=\"vc-faq-a\"><div class=\"vc-faq-a-inner\"><p>No, CG is fixed relative to the object.<\/p><\/div><\/div><\/div><\/div><\/div><\/div><\/div>\n<div class=\"vc-promo\"><div class=\"vc-promo-text\"><strong>Vibromera \u2014 Portable Balancing &amp; Vibration Analysis<\/strong><br>Professional instruments for industrial applications.<\/div><a class=\"vc-promo-link\" href=\"https:\/\/vibromera.eu\/\" target=\"_blank\" rel=\"noopener\">Learn More<\/a><\/div>\n<footer class=\"vc-footer\"><p>&copy; 2024&ndash;2025 <a href=\"https:\/\/vibromera.eu\/\">Vibromera<\/a> &mdash; Engineering Calculators<\/p><div class=\"vc-footer-links\"><a href=\"\/calculators\/engineering-calculators\/\">All Calculators<\/a><a href=\"https:\/\/vibromera.eu\/contacts\/\">Contact<\/a><\/div><\/footer><\/div>\n<script src=\"https:\/\/cdn.jsdelivr.net\/npm\/katex@0.16.11\/dist\/katex.min.js\"><\/script>\n<script>(function(){var $=function(id){return document.getElementById(id)};function fmt(n,d){return isNaN(n)?'\u2014':n.toFixed(d||2)}\nvar presetData={beam:{m:[100,200,'',''],x:[0,2,'',''],y:[0,0,'','']},tri:{m:[100,100,100,''],x:[0,2,1,''],y:[0,0,2,'']},machine:{m:[500,300,200,''],x:[0,3,1.5,''],y:[0,0,2,'']}};\nfunction calculate(){var ms=[],xs=[],ys=[];for(var i=1;i<=4;i++){var 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