Moment of Inertia Converter
ScienceConvert moment of inertia (rotational inertia) between kg·m², g·cm², lb·ft², lb·in², and slug·ft² instantly — used for rotational dynamics calculations.
From
To
All conversionsfor 1 Pound-Foot² (lb·ft²)
| Kilogram-Metre² (kg·m²) | 0.0421401 |
| Gram-Centimetre² (g·cm²) | 421401 |
| Pound-Foot² (lb·ft²) | 1 |
| Pound-Inch² (lb·in²) | 143.99979 |
| Ounce-Inch² (oz·in²) | 2303.9967 |
| Slug-Foot² (slug·ft²) | 0.031080896 |
What is a Moment of Inertia?
The Moment of Inertia Converter converts rotational inertia between kilogram-metres squared (kg·m²), gram-centimetres squared, and the imperial units pound-foot², pound-inch², ounce-inch², and slug-foot². Moment of inertia measures an object's resistance to changes in rotational speed, combining both its mass and how that mass is distributed relative to the rotation axis — it's the rotational counterpart to mass in linear dynamics.
Enter a value in any supported unit and the converter calculates the equivalent instantly. For the related quantities in a rotational dynamics calculation, see the Torque Converter and Angular Acceleration Converter.
How to use this Moment of Inertia calculator
- Choose your starting unit from the source dropdown — for example, "Pound-Foot² (lb·ft²)".
- Enter the numeric value you want to convert in the input field.
- Choose your target unit from the destination dropdown — for example, "Kilogram-Metre² (kg·m²)".
- Read the converted result, which updates instantly as you type or change units.
- Use the swap (⇅) button if you need to reverse the conversion direction.
- Use the copy button to grab the result for a rotational dynamics calculation or motor sizing spreadsheet.
Formula & Methodology
The converter's base unit is kilogram-metre squared (kg·m²). Every supported unit has a fixed multiplier to kg·m²: - 1 gram-centimetre² (g·cm²) = 0.0000001 kg·m² - 1 pound-foot² (lb·ft²) = 0.0421401 kg·m² - 1 pound-inch² (lb·in²) = 0.00029264 kg·m² - 1 ounce-inch² (oz·in²) = 0.0000182900 kg·m² - 1 slug-foot² (slug·ft²) = 1.35582 kg·m² Any conversion follows: Result = Input × (toBase of source unit ÷ toBase of target unit) Worked example — converting 10 lb·ft² to kg·m²: Result = 10 × 0.0421401 = 0.421401 kg·m² This is the value you'd use directly in a metric torque calculation (τ = Iα) alongside angular acceleration in rad/s².
Frequently Asked Questions
Moment of inertia (also called rotational inertia) measures how resistant an object is to changes in its rotational speed, depending on both its mass and how that mass is distributed relative to the axis of rotation. It's the rotational equivalent of mass in linear motion — just as mass resists linear acceleration, moment of inertia resists angular acceleration.
Multiply the lb·ft² value by 0.0421401, since one pound-foot² equals approximately 0.0421401 kilogram-metres². Enter your value with 'Pound-Foot² (lb·ft²)' as the source and 'Kilogram-Metre² (kg·m²)' as the target to apply this automatically.
Torque equals moment of inertia multiplied by angular acceleration (τ = Iα), the rotational equivalent of Newton's second law — a larger moment of inertia requires more torque to achieve the same angular acceleration. See the [Angular Acceleration Converter](/angular-acceleration-converter/) and [Torque Converter](/torque-converter/) for the other quantities in this formula.
Moment of inertia depends on mass multiplied by the square of its distance from the rotation axis, so mass concentrated far from the axis contributes much more to moment of inertia than the same mass close to the axis — this is why a hollow cylinder has a higher moment of inertia than a solid cylinder of the same mass and outer radius.
A slug is the US customary unit of mass (distinct from pounds, which measure weight/force), defined so that a 1-pound force accelerates a 1-slug mass at 1 ft/s². Slug-foot² is the natural moment of inertia unit in this system, avoiding the awkward mass/weight distinction that pound-based units can introduce.
Select your source unit (lb·ft², lb·in², oz·in², or slug·ft²) and target unit, and the converter handles the conversion through the common kg·m² base internally, so any pair of units — even two imperial ones — converts accurately.
For a solid disc rotating about its central axis, moment of inertia equals ½ × mass × radius² — this converter handles unit conversion for a moment of inertia value you've already calculated or looked up, not the geometric calculation itself.
Flywheels are specifically designed with a high moment of inertia to store rotational kinetic energy efficiently and resist changes in rotational speed, smoothing out fluctuations in engine or machinery output — engineers need accurate moment of inertia values, often in mixed unit systems, when sizing a flywheel.
No — moment of inertia depends on the specific axis of rotation chosen, and the same object can have very different moment of inertia values depending on whether it rotates about its centre, an edge, or some other axis, so always confirm which axis a given moment of inertia value refers to.
Mechanical and aerospace engineering (rotating machinery, flywheels, gyroscopes), robotics (motor sizing for rotational joints), and automotive engineering (wheel and drivetrain dynamics) all routinely require moment of inertia values, often needing conversion between metric design data and imperial legacy specifications.
Also known as