{"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\/th\/calculators\/inertia-unit-converter\/","title":{"rendered":"Mass Moment of Inertia Unit Converter"},"content":{"rendered":"\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Mass Moment of Inertia Unit Converter\",\"description\":\"Convert a non-negative mass moment of inertia between SI and explicitly defined avoirdupois\/international-foot units using derived exact conversion factors.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/inertia-unit-converter\/\",\"applicationCategory\":\"Engineering 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var(--mono);letter-spacing:.1em;text-transform:uppercase;color:var(--mut)}.vc-rv{font:600 20px\/1.25 var(--mono);overflow-wrap:anywhere}.vc-primary .vc-rv{font-size:28px;color:var(--c)}.vc-note{font-size:13px;color:var(--sec);margin:18px 0 0}.vc-toggle{width:100%;padding:18px 24px;border:0;background:#fff;text-align:left;font:700 18px var(--display);cursor:pointer}.vc-body{max-height:0;overflow:hidden}.vc-section.vc-open .vc-body{max-height:30000px}.vc-inner{padding:0 24px 24px;border-top:1px solid var(--bl);color:var(--sec)}.vc-inner h3{font-family:var(--display);color:var(--ink);margin:24px 0 10px}.vc-formula{font:15px\/1.8 var(--mono);padding:14px;background:var(--alt);border:1px solid var(--bl);border-radius:6px;overflow-x:auto}.vc-table{width:100%;border-collapse:collapse;font-size:13px}.vc-table th,.vc-table td{padding:9px 10px;border:1px solid var(--bl);text-align:left}.vc-table th{background:var(--alt)}.vc-footer{text-align:center;padding:30px;color:var(--mut);font-size:13px}.vc-section a,.vc-footer a{color:var(--c)}@media(max-width:650px){.vc-grid,.vc-result-grid{grid-template-columns:1fr}.vc-wide,.vc-primary{grid-column:auto}.vc-form{padding:18px}.vc-calculator{padding-left:12px;padding-right:12px}.vc-header{padding:34px 12px 30px}.vc-rv{font-size:17px}.vc-primary .vc-rv{font-size:22px}.vc-table{font-size:11px}}<\/style>\n<div class=\"vc-calculator\" id=\"vc-inertia-converter\"><header class=\"vc-header\"><p class=\"vc-eyebrow\">Defined mass and length units<\/p><h1 class=\"vc-title\">Mass Moment of Inertia Unit Converter<\/h1><p class=\"vc-sub\">Convert one non-negative mass moment of inertia about a stated axis. This page does not convert area\/second moment of area, which has length-to-the-fourth units.<\/p><div class=\"vc-badges\"><span class=\"vc-badge\">kg\u00b7m\u00b2 SI basis<\/span><span class=\"vc-badge\">Exact derived factors<\/span><span class=\"vc-badge\">Mass \u2260 area inertia<\/span><\/div><\/header>\n<div class=\"vc-card\"><form id=\"vc-form\" class=\"vc-form\" autocomplete=\"off\"><div class=\"vc-grid\"><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-id\">Calculation \/ record identifier<\/label><input class=\"vc-input\" id=\"vc-id\" type=\"text\" maxlength=\"220\"><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-axis\">Body and reference axis<\/label><input class=\"vc-input\" id=\"vc-axis\" type=\"text\" maxlength=\"600\"><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-value\">Mass moment of inertia value<\/label><input class=\"vc-input\" id=\"vc-value\" type=\"text\" inputmode=\"decimal\" maxlength=\"90\"><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-unit\">Source unit<\/label><select class=\"vc-select\" id=\"vc-unit\"><option value=\"\">Select\u2026<\/option><option value=\"kgm2\">kg\u00b7m\u00b2<\/option><option value=\"kgcm2\">kg\u00b7cm\u00b2<\/option><option value=\"gcm2\">g\u00b7cm\u00b2<\/option><option value=\"lbft2\">lbm\u00b7ft\u00b2 (avoirdupois; international foot)<\/option><option value=\"lbin2\">lbm\u00b7in\u00b2 (avoirdupois; international inch)<\/option><option value=\"ozin2\">oz(avdp)\u00b7in\u00b2<\/option><option value=\"slugft2\">slug\u00b7ft\u00b2 (standard-gravity definition)<\/option><\/select><\/div><\/div><p class=\"vc-error\" id=\"vc-error\" role=\"alert\"><\/p><div class=\"vc-warning\"><strong>Quantity gate:<\/strong> use this only for mass moment of inertia about a specified axis, dimension M\u00b7L\u00b2. Area\/second moment of area has dimension L\u2074 and cannot be converted here. A physical mass moment is non-negative; zero is permitted.<\/div><\/form>\n<div class=\"vc-results\" id=\"vc-results\" aria-live=\"polite\"><div class=\"vc-results-head\"><h2 class=\"vc-results-title\">Converted mass moment<\/h2><button class=\"vc-copy\" id=\"vc-copy\" type=\"button\">Copy<\/button><\/div><div class=\"vc-result-grid\"><div class=\"vc-r vc-primary\"><div class=\"vc-rl\">SI basis<\/div><div class=\"vc-rv\" id=\"vc-r-kgm2\">\u2014<\/div><\/div><div class=\"vc-r\"><div class=\"vc-rl\">kg\u00b7cm\u00b2<\/div><div class=\"vc-rv\" id=\"vc-r-kgcm2\">\u2014<\/div><\/div><div class=\"vc-r\"><div class=\"vc-rl\">g\u00b7cm\u00b2<\/div><div class=\"vc-rv\" id=\"vc-r-gcm2\">\u2014<\/div><\/div><div class=\"vc-r\"><div class=\"vc-rl\">lbm\u00b7ft\u00b2<\/div><div class=\"vc-rv\" id=\"vc-r-lbft2\">\u2014<\/div><\/div><div class=\"vc-r\"><div class=\"vc-rl\">lbm\u00b7in\u00b2<\/div><div class=\"vc-rv\" id=\"vc-r-lbin2\">\u2014<\/div><\/div><div class=\"vc-r\"><div class=\"vc-rl\">oz(avdp)\u00b7in\u00b2<\/div><div class=\"vc-rv\" id=\"vc-r-ozin2\">\u2014<\/div><\/div><div class=\"vc-r\"><div class=\"vc-rl\">slug\u00b7ft\u00b2<\/div><div class=\"vc-rv\" id=\"vc-r-slugft2\">\u2014<\/div><\/div><\/div><p class=\"vc-note\" id=\"vc-note\"><\/p><\/div><\/div>\n<div class=\"vc-section vc-open\"><button class=\"vc-toggle\" type=\"button\" aria-expanded=\"true\">Definitions, exact factors and standards status<\/button><div class=\"vc-body\"><div class=\"vc-inner\"><h3>Quantity and dimensions<\/h3><div class=\"vc-formula\">J = \u222b r\u22a5\u00b2 dm &nbsp; [kg\u00b7m\u00b2]<\/div><p>This scalar expression is for mass moment about a stated axis; r\u22a5 is perpendicular distance to that axis. For rigid rotation about a fixed axis, \u03c4=J\u03b1 is the scoped scalar relation. The parallel-axis theorem is J=J<sub>CM<\/sub>+md\u00b2 for parallel axes.<\/p><h3>Implemented factors to kg\u00b7m\u00b2<\/h3><table class=\"vc-table\"><thead><tr><th>Source unit<\/th><th>Factor<\/th><th>Basis<\/th><\/tr><\/thead><tbody><tr><td>kg\u00b7m\u00b2<\/td><td>1<\/td><td>SI basis<\/td><\/tr><tr><td>kg\u00b7cm\u00b2<\/td><td>0.0001<\/td><td>(0.01 m)\u00b2<\/td><\/tr><tr><td>g\u00b7cm\u00b2<\/td><td>0.0000001<\/td><td>0.001 kg \u00d7 (0.01 m)\u00b2<\/td><\/tr><tr><td>lbm\u00b7ft\u00b2<\/td><td>0.0421401100938048<\/td><td>0.45359237 kg \u00d7 (0.3048 m)\u00b2<\/td><\/tr><tr><td>lbm\u00b7in\u00b2<\/td><td>0.0002926396534292<\/td><td>0.45359237 kg \u00d7 (0.0254 m)\u00b2<\/td><\/tr><tr><td>oz(avdp)\u00b7in\u00b2<\/td><td>0.000018289978339325<\/td><td>(0.45359237\/16) kg \u00d7 (0.0254 m)\u00b2<\/td><\/tr><tr><td>slug\u00b7ft\u00b2<\/td><td>1.3558179483314004<\/td><td>4.4482216152605 N \u00d7 0.3048 m \u00d7 s\u00b2<\/td><\/tr><\/tbody><\/table><p><a href=\"https:\/\/www.nist.gov\/pml\/special-publication-811\/nist-guide-si-appendix-b-conversion-factors\" target=\"_blank\" rel=\"noopener\">NIST SP 811 Appendix B<\/a> states how derived factors are formed and gives the defining component conversions. International foot\/inch, avoirdupois pound\/ounce and standard gravity are used; no U.S. survey foot is used.<\/p><h3>ISO status and boundary<\/h3><p><a href=\"https:\/\/www.iso.org\/standard\/64975.html\" target=\"_blank\" rel=\"noopener\">ISO 80000-4:2019<\/a>, edition 2, is Published and covers names, symbols, definitions and units for mechanics. <a href=\"https:\/\/www.iso.org\/standard\/87101.html\" target=\"_blank\" rel=\"noopener\">Amendment 1:2025<\/a> is Published. <a href=\"https:\/\/www.iso.org\/standard\/94907.html\" target=\"_blank\" rel=\"noopener\">ISO\/AWI 80000-4<\/a>, planned edition 3, entered development on 2 July 2026 and is intended to replace the 2019 edition. Exact entries, symbols and amendment wording remain <strong>NEEDS_LICENSED_SOURCE<\/strong>; the conversion factors here are derived from unit definitions, not claimed as an ISO table.<\/p><h3>Common uniform-body formulas (reference only)<\/h3><table class=\"vc-table\"><tbody><tr><td>Uniform solid disk\/cylinder, symmetry axis<\/td><td>J=mr\u00b2\/2<\/td><\/tr><tr><td>Uniform thick cylindrical annulus, symmetry axis<\/td><td>J=m(r\u2081\u00b2+r\u2082\u00b2)\/2<\/td><\/tr><tr><td>Uniform solid sphere, diameter<\/td><td>J=2mr\u00b2\/5<\/td><\/tr><tr><td>Uniform slender rod, transverse center axis<\/td><td>J=mL\u00b2\/12<\/td><\/tr><tr><td>Uniform slender rod, transverse end axis<\/td><td>J=mL\u00b2\/3<\/td><\/tr><\/tbody><\/table><p>Real components require the actual mass distribution and axis. Mass moment alone does not determine static unbalance or centrifugal force; those require the first mass moment\/eccentricity and speed.<\/p><\/div><\/div><\/div>\n<footer class=\"vc-footer\">\u00a9 2024\u20132026 <a href=\"https:\/\/vibromera.eu\/\">Vibromera<\/a> \u00b7 Scientific review July 2026<\/footer><\/div>\n<script>(function(){'use strict';function $(i){return document.getElementById(i)}var factor={kgm2:1,kgcm2:1e-4,gcm2:1e-7,lbft2:0.0421401100938048,lbin2:0.0002926396534292,ozin2:0.000018289978339325,slugft2:1.3558179483314004},label={kgm2:'kg\u00b7m\u00b2',kgcm2:'kg\u00b7cm\u00b2',gcm2:'g\u00b7cm\u00b2',lbft2:'lbm\u00b7ft\u00b2',lbin2:'lbm\u00b7in\u00b2',ozin2:'oz(avdp)\u00b7in\u00b2',slugft2:'slug\u00b7ft\u00b2'},map={mi_id:'vc-id',mi_axis:'vc-axis',mi_value:'vc-value',mi_unit:'vc-unit'};function num(raw){var s=String(raw).trim().replace(',','.');if(s.length>90||!\/^[-+]?(?:\\d+(?:\\.\\d*)?|\\.\\d+)(?:[eE][+-]?\\d+)?$\/.test(s))return NaN;return Number(s)}function fmt(v){if(!Number.isFinite(v))return'\u2014';if(Object.is(v,-0)||v===0)return'0';return Number(v.toPrecision(15)).toString()}function clear(){Object.keys(factor).forEach(function(u){$('vc-r-'+u).textContent='\u2014'});$('vc-note').textContent='';$('vc-results').classList.remove('vc-visible')}function fail(m){clear();$('vc-error').textContent=m}function setUrl(){var u=new URL(location);Object.keys(map).forEach(function(k){var v=$(map[k]).value.trim();if(v)u.searchParams.set(k,v);else u.searchParams.delete(k)});history.replaceState(null,'',u.toString())}function calc(){setUrl();var x={};Object.keys(map).forEach(function(k){x[k]=$(map[k]).value.trim()});if(!Object.keys(x).some(function(k){return x[k]})){$('vc-error').textContent='';clear();return}if(!Object.keys(x).every(function(k){return x[k]})){fail('Enter the record identifier, body\/axis, value and source unit.');return}if(!(x.mi_unit in factor)){fail('Select a supported mass-moment unit.');return}var v=num(x.mi_value);if(!Number.isFinite(v)){fail('Value must be a complete finite decimal number.');return}if(v<0||Math.abs(v)>1e100){fail('Mass moment must be non-negative and no greater than 10\u00b9\u2070\u2070.');return}var base=v*factor[x.mi_unit],vals={};Object.keys(factor).forEach(function(u){vals[u]=base\/factor[u]});if(!Object.keys(vals).every(function(u){return Number.isFinite(vals[u])&&Math.abs(vals[u])<=1e110})){fail('Converted value exceeds the finite numerical range.');return}$('vc-error').textContent='';Object.keys(vals).forEach(function(u){$('vc-r-'+u).textContent=fmt(vals[u])+' '+label[u]});$('vc-note').textContent='Record: '+x.mi_id+' | Body\/axis: '+x.mi_axis+' | Entered: '+x.mi_value+' '+label[x.mi_unit]+'. Mass-moment unit conversion only.';$('vc-results').classList.add('vc-visible')}$('vc-form').addEventListener('input',calc);$('vc-form').addEventListener('change',calc);$('vc-copy').addEventListener('click',function(){if(navigator.clipboard)navigator.clipboard.writeText($('vc-results').innerText)});document.querySelectorAll('.vc-toggle').forEach(function(b){b.addEventListener('click',function(){var s=this.closest('.vc-section');s.classList.toggle('vc-open');this.setAttribute('aria-expanded',s.classList.contains('vc-open'))})});var q=new URLSearchParams(location.search);Object.keys(map).forEach(function(k){if(q.has(k))$(map[k]).value=q.get(k)});calc()})();<\/script>\n","protected":false},"excerpt":{"rendered":"<p>\u0e42\u0e1b\u0e23\u0e41\u0e01\u0e23\u0e21\u0e41\u0e1b\u0e25\u0e07\u0e2b\u0e19\u0e48\u0e27\u0e22\u0e42\u0e21\u0e40\u0e21\u0e19\u0e15\u0e4c\u0e04\u0e27\u0e32\u0e21\u0e40\u0e09\u0e37\u0e48\u0e2d\u0e22\u0e2d\u0e2d\u0e19\u0e44\u0e25\u0e19\u0e4c\u0e1f\u0e23\u0e35 \u0e41\u0e1b\u0e25\u0e07\u0e2b\u0e19\u0e48\u0e27\u0e22\u0e23\u0e30\u0e2b\u0e27\u0e48\u0e32\u0e07 kg\u00b7m\u00b2, kg\u00b7cm\u00b2, g\u00b7cm\u00b2, lb\u00b7ft\u00b2, lb\u00b7in\u00b2, oz\u00b7in\u00b2 \u0e41\u0e25\u0e30 slug\u00b7ft\u00b2 \u0e44\u0e14\u0e49\u0e1c\u0e25\u0e25\u0e31\u0e1e\u0e18\u0e4c\u0e17\u0e31\u0e19\u0e17\u0e35.<\/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\/th\/wp-json\/wp\/v2\/calculator\/100136","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vibromera.eu\/th\/wp-json\/wp\/v2\/calculator"}],"about":[{"href":"https:\/\/vibromera.eu\/th\/wp-json\/wp\/v2\/types\/calculator"}],"version-history":[{"count":2,"href":"https:\/\/vibromera.eu\/th\/wp-json\/wp\/v2\/calculator\/100136\/revisions"}],"predecessor-version":[{"id":102458,"href":"https:\/\/vibromera.eu\/th\/wp-json\/wp\/v2\/calculator\/100136\/revisions\/102458"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/th\/wp-json\/wp\/v2\/media?parent=100136"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/th\/wp-json\/wp\/v2\/categories?post=100136"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/th\/wp-json\/wp\/v2\/tags?post=100136"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}