{"id":100136,"date":"2026-02-15T20:19:40","date_gmt":"2026-02-15T20:19:40","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100136"},"modified":"2026-07-12T14:55:27","modified_gmt":"2026-07-12T14:55:27","slug":"inertia-unit-converter","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/fa\/calculators\/inertia-unit-converter\/","title":{"rendered":"\u0645\u0628\u062f\u0644 \u0648\u0627\u062d\u062f \u06af\u0634\u062a\u0627\u0648\u0631 \u0627\u06cc\u0646\u0631\u0633\u06cc | \u06a9\u06cc\u0644\u0648\u06af\u0631\u0645 \u00b7 \u0645\u062a\u0631 \u0645\u0631\u0628\u0639 \u00b7 \u067e\u0648\u0646\u062f \u00b7 \u0641\u0648\u062a \u0645\u0631\u0628\u0639 \u00b7 \u06af\u0631\u0645 \u00b7 \u0633\u0627\u0646\u062a\u06cc \u0645\u062a\u0631 \u0645\u0631\u0628\u0639"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Moment of Inertia Unit Converter\",\"description\":\"Free online moment of inertia unit converter. 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var(--vc-border);border-radius:var(--vc-radius-lg);display:flex;align-items:center;gap:16px}\n.vc-promo-text{flex:1;font-size:14px;color:var(--vc-ink-secondary)}\n.vc-promo-text strong{color:var(--vc-ink)}\n.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 0.15s}\n.vc-promo-link:hover{background:var(--vc-accent-hover)}\n.vc-footer{text-align:center;padding:32px 16px;font-size:13px;color:var(--vc-ink-muted)}\n.vc-footer a{color:var(--vc-accent);text-decoration:none}\n.vc-footer a:hover{text-decoration:underline}\n.vc-footer-links{margin-top:8px;font-size:12px}\n.vc-footer-links a{margin:0 8px}\n.vc-presets{display:flex;flex-wrap:wrap;gap:8px;margin-top:18px;padding-top:18px;border-top:1px solid var(--vc-border-light)}\n.vc-presets-label{font-family:var(--vc-mono);font-size:11px;font-weight:500;letter-spacing:0.1em;text-transform:uppercase;color:var(--vc-ink-muted);width:100%;margin-bottom:2px}\n.vc-preset-btn{padding:5px 12px;font-family:var(--vc-font);font-size:12px;font-weight:500;border:1px solid var(--vc-border);border-radius:6px;background:var(--vc-surface-alt);color:var(--vc-ink-secondary);cursor:pointer;transition:all 0.15s}\n.vc-preset-btn:hover{border-color:var(--vc-accent);color:var(--vc-accent);background:var(--vc-accent-light)}\n@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}}\n<\/style>\n\n<div class=\"vc-calculator\" id=\"vc-inertia-converter\">\n\n<header class=\"vc-header\">\n    <p class=\"vc-header-eyebrow\">Free Engineering Tool<\/p>\n    <h1 class=\"vc-header-title\">Moment of Inertia Unit Converter<\/h1>\n    <p class=\"vc-header-subtitle\">Convert mass moment of inertia between all common metric and imperial units instantly. Enter a value and see all conversions simultaneously.<\/p>\n    <div class=\"vc-badges\">\n        <span class=\"vc-badge\">kg\u00b7m\u00b2<\/span>\n        <span class=\"vc-badge\">lb\u00b7ft\u00b2<\/span>\n        <span class=\"vc-badge\">g\u00b7cm\u00b2<\/span>\n        <span class=\"vc-badge\">slug\u00b7ft\u00b2<\/span>\n    <\/div>\n<\/header>\n\n<div class=\"vc-card\">\n    <form class=\"vc-form\" id=\"vc-form\" autocomplete=\"off\">\n        <div class=\"vc-form-grid\">\n            <div class=\"vc-field\">\n                <label class=\"vc-label\" for=\"vc-value\">Value<\/label>\n                <input class=\"vc-input\" type=\"number\" id=\"vc-value\" inputmode=\"decimal\" step=\"any\" placeholder=\"e.g. 1.5\" value=\"1\">\n            <\/div>\n            <div class=\"vc-field\">\n                <label class=\"vc-label\" for=\"vc-unit\">Source Unit<\/label>\n                <select class=\"vc-select\" id=\"vc-unit\">\n                    <option value=\"kgm2\" selected>kg\u00b7m\u00b2 \u2014 kilogram meter squared<\/option>\n                    <option value=\"kgcm2\">kg\u00b7cm\u00b2 \u2014 kilogram centimeter squared<\/option>\n                    <option value=\"gcm2\">g\u00b7cm\u00b2 \u2014 gram centimeter squared<\/option>\n                    <option value=\"lbft2\">lb\u00b7ft\u00b2 \u2014 pound foot squared<\/option>\n                    <option value=\"lbin2\">lb\u00b7in\u00b2 \u2014 pound inch squared<\/option>\n                    <option value=\"ozin2\">oz\u00b7in\u00b2 \u2014 ounce inch squared<\/option>\n                    <option value=\"slugft2\">slug\u00b7ft\u00b2 \u2014 slug foot squared<\/option>\n                <\/select>\n            <\/div>\n        <\/div>\n        <div class=\"vc-presets\">\n            <div class=\"vc-presets-label\">Quick presets<\/div>\n            <button type=\"button\" class=\"vc-preset-btn\" data-v=\"1\" data-u=\"kgm2\">1 kg\u00b7m\u00b2<\/button>\n            <button type=\"button\" class=\"vc-preset-btn\" data-v=\"1\" data-u=\"lbft2\">1 lb\u00b7ft\u00b2<\/button>\n            <button type=\"button\" class=\"vc-preset-btn\" data-v=\"1\" data-u=\"slugft2\">1 slug\u00b7ft\u00b2<\/button>\n            <button type=\"button\" class=\"vc-preset-btn\" data-v=\"100\" data-u=\"kgcm2\">100 kg\u00b7cm\u00b2<\/button>\n        <\/div>\n    <\/form>\n\n    <div class=\"vc-results vc-visible\" id=\"vc-results\">\n        <div class=\"vc-results-head\">\n            <h2 class=\"vc-results-title\">All Conversions<\/h2>\n            <button type=\"button\" class=\"vc-copy-btn\" id=\"vc-copy-btn\">\n                <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>\n                Copy\n            <\/button>\n        <\/div>\n        <div class=\"vc-result-grid\">\n            <div class=\"vc-rcard vc-rcard-primary\">\n                <div class=\"vc-rcard-label\">kg\u00b7m\u00b2 (SI unit)<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-kgm2\">\u2014<\/div>\n            <\/div>\n            <div class=\"vc-rcard\">\n                <div class=\"vc-rcard-label\">kg\u00b7cm\u00b2<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-kgcm2\">\u2014<\/div>\n            <\/div>\n            <div class=\"vc-rcard\">\n                <div class=\"vc-rcard-label\">g\u00b7cm\u00b2<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-gcm2\">\u2014<\/div>\n            <\/div>\n            <div class=\"vc-rcard\">\n                <div class=\"vc-rcard-label\">lb\u00b7ft\u00b2<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-lbft2\">\u2014<\/div>\n            <\/div>\n            <div class=\"vc-rcard\">\n                <div class=\"vc-rcard-label\">lb\u00b7in\u00b2<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-lbin2\">\u2014<\/div>\n            <\/div>\n            <div class=\"vc-rcard\">\n                <div class=\"vc-rcard-label\">oz\u00b7in\u00b2<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-ozin2\">\u2014<\/div>\n            <\/div>\n            <div class=\"vc-rcard\">\n                <div class=\"vc-rcard-label\">slug\u00b7ft\u00b2<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-slugft2\">\u2014<\/div>\n            <\/div>\n        <\/div>\n    <\/div>\n<\/div>\n\n<!-- Theory -->\n<div class=\"vc-section vc-open\" id=\"vc-sec-theory\">\n    <button type=\"button\" class=\"vc-section-toggle\" aria-expanded=\"true\">\n        <span class=\"vc-section-toggle-text\">\n            <span class=\"vc-section-icon\">\ud83d\udcd8<\/span>\n            <span class=\"vc-section-title\">Theory &#038; Conversion Factors<\/span>\n        <\/span>\n        <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>\n    <\/button>\n    <div class=\"vc-section-body\">\n        <div class=\"vc-section-inner vc-theory\">\n            <h3>What is Moment of Inertia?<\/h3>\n            <p>The mass moment of inertia (also called rotational inertia) quantifies a body&#8217;s resistance to angular acceleration about a given axis. It is the rotational analog of mass in linear motion.<\/p>\n            <div class=\"vc-formula-box\">J = \u03a3 m\u1d62 r\u1d62\u00b2 &nbsp;&nbsp;or&nbsp;&nbsp; J = \u222b r\u00b2 dm &nbsp;&nbsp;[kg\u00b7m\u00b2]<\/div>\n            <p>Where <strong>m<\/strong> is mass and <strong>r<\/strong> is the perpendicular distance from the axis of rotation.<\/p>\n\n            <h3>Conversion Table<\/h3>\n            <table class=\"vc-table\">\n                <thead><tr><th>Unit<\/th><th>Symbol<\/th><th>= kg\u00b7m\u00b2<\/th><\/tr><\/thead>\n                <tbody>\n                    <tr><td>kilogram meter squared<\/td><td>kg\u00b7m\u00b2<\/td><td>1<\/td><\/tr>\n                    <tr><td>kilogram centimeter squared<\/td><td>kg\u00b7cm\u00b2<\/td><td>1 \u00d7 10\u207b\u2074<\/td><\/tr>\n                    <tr><td>gram centimeter squared<\/td><td>g\u00b7cm\u00b2<\/td><td>1 \u00d7 10\u207b\u2077<\/td><\/tr>\n                    <tr><td>pound foot squared<\/td><td>lb\u00b7ft\u00b2<\/td><td>0.042140<\/td><\/tr>\n                    <tr><td>pound inch squared<\/td><td>lb\u00b7in\u00b2<\/td><td>2.9264 \u00d7 10\u207b\u2074<\/td><\/tr>\n                    <tr><td>ounce inch squared<\/td><td>oz\u00b7in\u00b2<\/td><td>1.8290 \u00d7 10\u207b\u2075<\/td><\/tr>\n                    <tr><td>slug foot squared<\/td><td>slug\u00b7ft\u00b2<\/td><td>1.35582<\/td><\/tr>\n                <\/tbody>\n            <\/table>\n\n            <h3>Common Formulas for Simple Shapes<\/h3>\n            <table class=\"vc-table\">\n                <thead><tr><th>Shape<\/th><th>Axis<\/th><th>Formula<\/th><\/tr><\/thead>\n                <tbody>\n                    <tr><td>Solid cylinder\/disk<\/td><td>Central axis<\/td><td>J = \u00bd m r\u00b2<\/td><\/tr>\n                    <tr><td>Hollow cylinder<\/td><td>Central axis<\/td><td>J = \u00bd m (r\u2081\u00b2 + r\u2082\u00b2)<\/td><\/tr>\n                    <tr><td>Solid sphere<\/td><td>Through center<\/td><td>J = \u2156 m r\u00b2<\/td><\/tr>\n                    <tr><td>Thin rod<\/td><td>Through center<\/td><td>J = \u00b9\u2044\u2081\u2082 m L\u00b2<\/td><\/tr>\n                    <tr><td>Thin rod<\/td><td>Through end<\/td><td>J = \u2153 m L\u00b2<\/td><\/tr>\n                <\/tbody>\n            <\/table>\n\n            <div class=\"vc-info-box\">\n                <p><strong>Note:<\/strong> In the imperial system, <strong>slug\u00b7ft\u00b2<\/strong> is the dynamically consistent unit (force = mass \u00d7 acceleration without a conversion factor). 1 slug = 1 lb\u00b7s\u00b2\/ft = 14.594 kg.<\/p>\n            <\/div>\n\n            <h3>Relationship to Torque and Angular Motion<\/h3>\n            <div class=\"vc-formula-box\">\u03c4 = J \u00d7 \u03b1 &nbsp;&nbsp;(Newton&#8217;s 2nd law for rotation)<\/div>\n            <p>Where <strong>\u03c4<\/strong> is torque (N\u00b7m), <strong>J<\/strong> is moment of inertia (kg\u00b7m\u00b2), and <strong>\u03b1<\/strong> is angular acceleration (rad\/s\u00b2).<\/p>\n\n            <h3>Parallel Axis Theorem<\/h3>\n            <div class=\"vc-formula-box\">J = J_cm + m \u00d7 d\u00b2<\/div>\n            <p>The moment of inertia about any parallel axis equals the inertia about the center of mass plus <strong>m \u00d7 d\u00b2<\/strong>, where d is the distance between axes.<\/p>\n        <\/div>\n    <\/div>\n<\/div>\n\n<!-- Related -->\n<div class=\"vc-section\" id=\"vc-sec-related\">\n    <button type=\"button\" class=\"vc-section-toggle\" aria-expanded=\"false\">\n        <span class=\"vc-section-toggle-text\">\n            <span class=\"vc-section-icon\">\ud83d\udd17<\/span>\n            <span class=\"vc-section-title\">Related Calculators<\/span>\n        <\/span>\n        <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>\n    <\/button>\n    <div class=\"vc-section-body\">\n        <div class=\"vc-section-inner\">\n            <div class=\"vc-related\">\n                <a class=\"vc-related-link\" href=\"\/calculators\/speed-velocity-converter\/\">Speed &#038; 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They are different physical quantities \u2014 this calculator handles mass moment of inertia only.<\/p>' },\n        { q: 'What is a slug?', a: '<p>A slug is the imperial unit of mass in the gravitational system. 1 slug = 14.5939 kg. When force in pounds-force is divided by acceleration in ft\/s\u00b2, the result is in slugs. 1 slug\u00b7ft\u00b2 = 1.3558 kg\u00b7m\u00b2.<\/p>' },\n        { q: 'Why is moment of inertia important in rotating machinery?', a: '<p>Moment of inertia determines how much torque is needed to change a rotor\\'s speed. It affects startup time, braking distance, critical speeds, and torsional vibration behavior. For balancing, it affects centrifugal forces generated by unbalance.<\/p>' },\n        { q: 'How do I convert lb\u00b7ft\u00b2 to kg\u00b7m\u00b2?', a: '<p>Multiply lb\u00b7ft\u00b2 by <strong>0.04214<\/strong> to get kg\u00b7m\u00b2. For example, 10 lb\u00b7ft\u00b2 = 10 \u00d7 0.04214 = 0.4214 kg\u00b7m\u00b2.<\/p>' }\n    ];\n    var faqList = $('vc-faq-list');\n    faqData.forEach(function(faq) {\n        faqList.innerHTML += '<div class=\"vc-faq-item\"><button type=\"button\" class=\"vc-faq-q\"><span>' + faq.q + '<\/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\">' + faq.a + '<\/div><\/div><\/div>';\n    });\n    faqList.addEventListener('click', function(e) {\n        var btn = e.target.closest('.vc-faq-q');\n        if (!btn) return;\n        btn.closest('.vc-faq-item').classList.toggle('vc-open');\n    });\n\n    function loadParams() {\n        var p = new URLSearchParams(window.location.search);\n        if (p.get('v')) $('vc-value').value = p.get('v');\n        if (p.get('u')) $('vc-unit').value = p.get('u');\n    }\n\n    loadParams();\n    calculate();\n})();\n<\/script>\n","protected":false},"excerpt":{"rendered":"<p>\u0645\u0628\u062f\u0644 \u0648\u0627\u062d\u062f \u06af\u0634\u062a\u0627\u0648\u0631 \u0627\u06cc\u0646\u0631\u0633\u06cc \u0622\u0646\u0644\u0627\u06cc\u0646 \u0631\u0627\u06cc\u06af\u0627\u0646. \u062a\u0628\u062f\u06cc\u0644 \u0628\u06cc\u0646 \u06a9\u06cc\u0644\u0648\u06af\u0631\u0645 \u0628\u0631 \u0645\u062a\u0631 \u0645\u0631\u0628\u0639\u060c \u06a9\u06cc\u0644\u0648\u06af\u0631\u0645 \u0628\u0631 \u0633\u0627\u0646\u062a\u06cc \u0645\u062a\u0631 \u0645\u0631\u0628\u0639\u060c \u06af\u0631\u0645 \u0628\u0631 \u0633\u0627\u0646\u062a\u06cc \u0645\u062a\u0631 \u0645\u0631\u0628\u0639\u060c \u067e\u0648\u0646\u062f \u0628\u0631 \u0641\u0648\u062a \u0645\u0631\u0628\u0639\u060c \u067e\u0648\u0646\u062f \u0628\u0631 \u0627\u06cc\u0646\u0686 \u0645\u0631\u0628\u0639\u060c \u0627\u0648\u0646\u0633 \u0628\u0631 \u0627\u06cc\u0646\u0686 \u0645\u0631\u0628\u0639 \u0648 \u0627\u0633\u0644\u0627\u06af \u0628\u0631 \u0641\u0648\u062a \u0645\u0631\u0628\u0639. \u0646\u062a\u0627\u06cc\u062c \u0641\u0648\u0631\u06cc.<\/p>","protected":false},"featured_media":0,"template":"","meta":{"ai_generated_summary":"","footnotes":""},"categories":[],"tags":[],"class_list":["post-100136","calculator","type-calculator","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/vibromera.eu\/fa\/wp-json\/wp\/v2\/calculator\/100136","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vibromera.eu\/fa\/wp-json\/wp\/v2\/calculator"}],"about":[{"href":"https:\/\/vibromera.eu\/fa\/wp-json\/wp\/v2\/types\/calculator"}],"version-history":[{"count":2,"href":"https:\/\/vibromera.eu\/fa\/wp-json\/wp\/v2\/calculator\/100136\/revisions"}],"predecessor-version":[{"id":102458,"href":"https:\/\/vibromera.eu\/fa\/wp-json\/wp\/v2\/calculator\/100136\/revisions\/102458"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/fa\/wp-json\/wp\/v2\/media?parent=100136"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/fa\/wp-json\/wp\/v2\/categories?post=100136"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/fa\/wp-json\/wp\/v2\/tags?post=100136"}],"curies":[{"name":"\u0648\u0631\u062f\u067e\u0631\u0633","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}