Home›Converters›Science›Moment of Inertia Converter

Moment of Inertia Converter

Science

Convert moment of inertia (rotational inertia) between kg·m², g·cm², lb·ft², lb·in², and slug·ft² instantly — used for rotational dynamics calculations.

Reviewed by the thecalcu.com team · Last updated July 10, 2026

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.

Why Use a Moment of Inertia Converter?

Motor and component datasheets frequently specify moment of inertia in whatever unit system matches their country of origin, kg·m² for metric equipment, oz·in² or lb·ft² for US components, and comparing or combining values from different sources requires accurate conversion. Manually working through these conversions (some involving small fractional multipliers) is easy to get wrong.

Who Should Use This Converter?

  • Robotics and motor control engineers matching motor moment of inertia specifications (often in oz·in² or g·cm²) against load requirements calculated in SI units.
  • Mechanical engineering students working through rotational dynamics problems that mix moment of inertia units.
  • Automotive and aerospace engineers working with flywheel, wheel, or rotor moment of inertia data across metric and imperial unit systems.

What Insights Does the Moment of Inertia Converter Give You?

The main output is the converted value in your chosen target unit, calculated precisely from the fixed multiplier relationship between units. Because moment of inertia units span several orders of magnitude depending on the unit chosen (oz·in² values look very different from kg·m² values for the same physical object), the converter helps confirm you're comparing values on the same footing.

How to use this Moment of Inertia calculator

  1. Choose your starting unit from the source dropdown, for example, "Pound-Foot² (lb·ft²)".
  2. Enter the numeric value you want to convert in the input field.
  3. Choose your target unit from the destination dropdown, for example, "Kilogram-Metre² (kg·m²)".
  4. Read the converted result, which updates instantly as you type or change units.
  5. Use the swap (⇅) button if you need to reverse the conversion direction.
  6. Use the copy button to grab the result for a rotational dynamics calculation or motor sizing spreadsheet.
Show formula & methodology ↓Show less ↑

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.

Related Tools

You may also find these useful: Density Converter.

Frequently Asked Questions

What is moment of inertia?
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.
How do I convert lb·ft² to kg·m²?
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.
How does moment of inertia relate to torque?
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.
Why does mass distribution matter for moment of inertia, not just total mass?
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.
What is a slug, and why is it used for moment of inertia in the US?
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.
How do I convert between different imperial moment of inertia units?
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.
What's the moment of inertia of a simple shape like a solid disc?
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.
Why is moment of inertia important in flywheel design?
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.
Is moment of inertia the same for every axis of rotation?
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.
What fields commonly need moment of inertia unit conversion?
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
moment of inertia converterkg m2 to lb ft2 converterrotational inertia converterslug ft2 convertermoment of inertia units