{"id":55870,"date":"2015-10-24T16:03:18","date_gmt":"2015-10-24T14:03:18","guid":{"rendered":"http:\/\/wpcalc.com\/?p=55870"},"modified":"2026-09-28T09:31:53","modified_gmt":"2026-09-28T06:31:53","slug":"inertia","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/converters\/inertia\/","title":{"rendered":"Moment of Inertia Converter"},"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\">Convert Moment of Inertia Between Units<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"55870\" data-favorite-title=\"Moment of Inertia\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/converters\/inertia\/\" data-favorite-excerpt=\"Convert a moment of inertia between kg\u00b7m\u00b2, g\u00b7cm\u00b2, lb\u00b7ft\u00b2, lb\u00b7in\u00b2, and oz\u00b7in\u00b2. Enter a value, then choose the From unit and To unit.\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-physic\">\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\/converters\/inertia\/\" method=\"POST\" class=\"calculator\" id=\"calculator-55870\" data-post=\"55870\"><fieldset class=\"fieldset-input\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field is-single\" id=\"input-1\"><label for=\"field-1\">Inertia value<\/label><input type=\"text\" name=\"inertia_value\" id=\"field-1\" aria-describedby=\"calc-unit-1 calc-info-1\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"10\"\/><div class=\"unit\" id=\"calc-unit-1\"><\/div><small id=\"calc-info-1\">Enter the moment of inertia value to convert<\/small><\/div><div class=\"field\" id=\"input-2\"><label for=\"field-2\">From unit<\/label><div class=\"grid grid-cols-1\"><select id=\"field-2\" name=\"from_unit\"><option value=\"kg\u00b7m\u00b2\">Kilogram meter\u00b2 (kg\u00b7m\u00b2)<\/option><option value=\"g\u00b7cm\u00b2\">Gram centimeter\u00b2 (g\u00b7cm\u00b2)<\/option><option value=\"lb\u00b7ft\u00b2\">Pound foot\u00b2 (lb\u00b7ft\u00b2)<\/option><option value=\"lb\u00b7in\u00b2\">Pound inch\u00b2 (lb\u00b7in\u00b2)<\/option><option value=\"oz\u00b7in\u00b2\">Ounce inch\u00b2 (oz\u00b7in\u00b2)<\/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\" id=\"input-3\"><label for=\"field-3\">To unit<\/label><div class=\"grid grid-cols-1\"><select id=\"field-3\" name=\"to_unit\"><option value=\"kg\u00b7m\u00b2\">Kilogram meter\u00b2 (kg\u00b7m\u00b2)<\/option><option value=\"g\u00b7cm\u00b2\">Gram centimeter\u00b2 (g\u00b7cm\u00b2)<\/option><option value=\"lb\u00b7ft\u00b2\">Pound foot\u00b2 (lb\u00b7ft\u00b2)<\/option><option value=\"lb\u00b7in\u00b2\">Pound inch\u00b2 (lb\u00b7in\u00b2)<\/option><option value=\"oz\u00b7in\u00b2\">Ounce inch\u00b2 (oz\u00b7in\u00b2)<\/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><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"55870\">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> Your Results<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Converted Inertia<\/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><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=\"55870\" 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>Moment of Inertia Conversion 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\\[ I_{\\mathrm{to}}=I_{\\mathrm{from}}\\frac{F_{\\mathrm{from}}}{F_{\\mathrm{to}}} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(I_{\\mathrm{from}}\\) \u2014 the entered inertia value in the selected From unit<\/li>\n<li>\\(I_{\\mathrm{to}}\\) \u2014 the displayed value in the selected To unit<\/li>\n<li>\\(F_{\\mathrm{from}}\\) and \\(F_{\\mathrm{to}}\\) \u2014 the calculator\u2019s factors for the selected units, expressed relative to kg\u00b7m\u00b2<\/li>\n<\/ul>\n<p>The calculator multiplies the entered value by its From unit factor and divides by its To unit factor. Its lb\u00b7ft\u00b2 factor differs from the standard conversion factor; see the limitation below before relying on results involving that unit.<\/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>Moment of Inertia \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> enter the default Inertia value of 10, keep kg\u00b7m\u00b2 as the From unit, and select lb\u00b7ft\u00b2 as the To unit.<\/p>\n<p>\\[ 10\\times\\frac{1}{1.3558179483314}\\approx 7.3756\\ \\mathrm{lb\\,ft^2} \\]<\/p>\n<p><strong>Result:<\/strong> the calculator displays approximately 7.3756 lb\u00b7ft\u00b2. This reproduces its output, but it is not the standard physical conversion for lb\u00b7ft\u00b2.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to use the calculator<\/h2>\n<ol>\n<li>Enter a nonnegative number in <strong>Inertia value<\/strong>.<\/li>\n<li>Choose the unit of that number under <strong>From unit<\/strong>.<\/li>\n<li>Choose the unit you want under <strong>To unit<\/strong>.<\/li>\n<li>Read <strong>Converted Inertia<\/strong>, including the unit shown beside the result. If you change a selection, check the updated result before copying it.<\/li>\n<\/ol>\n<p>The available selections are kilogram square meters (kg\u00b7m\u00b2), gram square centimeters (g\u00b7cm\u00b2), pound square feet (lb\u00b7ft\u00b2), pound square inches (lb\u00b7in\u00b2), and ounce square inches (oz\u00b7in\u00b2). The tool converts an existing value; it does not calculate an object\u2019s moment of inertia from its dimensions and mass.<\/p>\n<h2>What moment of inertia means<\/h2>\n<p>Moment of inertia, also called <em>mass moment of inertia<\/em>, describes how an object\u2019s mass is distributed around a chosen axis of rotation. Mass farther from the axis contributes more: for a set of point masses, \\(I=\\sum m_i r_i^2\\), where \\(r_i\\) is each mass\u2019s perpendicular distance from the axis. This gives moment of inertia units of mass multiplied by length squared, such as kg\u00b7m\u00b2.<\/p>\n<p>A larger moment of inertia means more torque is needed to produce the same angular acceleration about the same axis, according to \\(\\tau=I\\alpha\\). For example, moving a flywheel\u2019s mass toward its rim increases its moment of inertia even if its total mass stays the same. You can use the <a href=\"https:\/\/wpcalc.com\/en\/converters\/torque\/\">torque converter<\/a> when the torque in a rotational calculation is given in a different unit.<\/p>\n<p>Converting units changes only how a known moment of inertia is expressed. It does not account for a change in rotational axis, an altered mass distribution, or a different object. Before comparing two values, confirm that both refer to the same axis and that neither is a different quantity, such as an area moment of inertia used in beam bending.<\/p>\n<h2>Conversion factors and limitations<\/h2>\n<p>The following factors are the values used by this calculator. In its formula, each factor represents the number of kg\u00b7m\u00b2 assigned to one unit in the first column.<\/p>\n<table>\n<thead>\n<tr>\n<th>Selected unit<\/th>\n<th>Calculator factor<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>kg\u00b7m\u00b2<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td>g\u00b7cm\u00b2<\/td>\n<td>0.0000001<\/td>\n<\/tr>\n<tr>\n<td>lb\u00b7ft\u00b2<\/td>\n<td>1.3558179483314<\/td>\n<\/tr>\n<tr>\n<td>lb\u00b7in\u00b2<\/td>\n<td>0.0002926397<\/td>\n<\/tr>\n<tr>\n<td>oz\u00b7in\u00b2<\/td>\n<td>0.00001827<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><strong>Important:<\/strong> the calculator\u2019s lb\u00b7ft\u00b2 factor is not the standard factor for pound-mass square feet. The standard value is approximately \\(1\\ \\mathrm{lb\\,ft^2}=0.04214011\\ \\mathrm{kg\\,m^2}\\); the calculator instead uses approximately \\(1.35581795\\ \\mathrm{kg\\,m^2}\\), a value associated with slug\u00b7ft\u00b2. Thus, the default example\u2019s 10 kg\u00b7m\u00b2 is approximately <strong>237.30 lb\u00b7ft\u00b2<\/strong> by standard conversion, not the displayed 7.3756 lb\u00b7ft\u00b2. Do not use results involving the lb\u00b7ft\u00b2 selection where an accurate physical conversion is required.<\/p>\n<p>The oz\u00b7in\u00b2 factor is also rounded differently from a conversion based on standard ounce-mass and inch definitions, so it can introduce a smaller discrepancy. The displayed result is rounded to ten decimal places. For very small values, that display rounding may hide significant digits; keep more precision in a separate calculation if your application needs it.<\/p>\n<p>Enter mass-based inertia units only. A pound-force is a unit of force, not the pound-mass assumed by lb\u00b7in\u00b2 and lb\u00b7ft\u00b2. If you are relating inertia to a rotation rate, the <a href=\"https:\/\/wpcalc.com\/en\/converters\/frequency\/\">frequency converter<\/a> can help align frequency units, but frequency alone does not determine moment of inertia.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Convert a moment of inertia between kg\u00b7m\u00b2, g\u00b7cm\u00b2, lb\u00b7ft\u00b2, lb\u00b7in\u00b2, and oz\u00b7in\u00b2. Enter a value, then choose the From unit and To unit.<\/p>\n","protected":false},"author":70,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[3],"tags":[34],"class_list":["post-55870","post","type-post","status-publish","format-standard","hentry","category-converters","tag-physics-units"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/55870","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\/70"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/comments?post=55870"}],"version-history":[{"count":2,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/55870\/revisions"}],"predecessor-version":[{"id":65300,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/55870\/revisions\/65300"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=55870"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=55870"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=55870"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}