Moment of Inertia Converter
What this converter does
The mass moment of inertia, I, measures how strongly a body resists a change in its rotational speed about a chosen axis. Motor catalogues list rotor inertia in kg·cm², servo sizing guides use kg·m², and American drivetrain data often uses lb·ft² or lb·in². This page converts a known inertia between those units. It works with mass moments of inertia (mass × length²), not with the second moment of area used for beam bending, which has units of length⁴.
How the conversion works
Each unit is converted through kilogram square metres (kg·m²). The table shows how many target units equal 1 kg·m²:
| Unit | Amount equal to 1 kg·m² |
|---|---|
| kg·cm² | 10,000 |
| kg·mm² | 1,000,000 |
| g·cm² | 10,000,000 |
| g·mm² | 1,000,000,000 |
| kgf·m·s² | 0.1019716213 |
| kgf·cm·s² | 10.19716213 |
| oz·in² | 54,674.750 |
| ozf·in·s² | 141.61193 |
| lb·ft² | 23.7303604 |
| lb·in² | 3,417.1719 |
| slug·ft² = lbf·ft·s² | 0.7375621 |
Because length appears squared, prefixes compound: one metre is 100 cm, so one kg·m² is 100² = 10,000 kg·cm². The "force" forms such as kgf·m·s² come from rewriting mass as force divided by acceleration; with standard gravity they are fixed multiples of the mass-based units.
Worked example
A solid steel disk of 2 kg and radius 0.15 m spinning about its central axis has I = ½ m r² = ½ × 2 × 0.15² = 0.0225 kg·m². In motor-catalogue units that is 0.0225 × 10,000 = 225 kg·cm², and in US units 0.0225 × 3,417.17 = 76.89 lb·in².
A gearbox datasheet in the other direction lists 12 lb·ft². Dividing by 23.7303604 gives 0.5057 kg·m².
What the result means
The converted value is the same resistance to angular acceleration: applying torque τ still produces α = τ / I, whichever unit you display. When matching a motor to a load, compare inertias in one unit only; mixing kg·cm² with kg·m² introduces a 10,000-fold error that can make a drive look drastically oversized or undersized.
Accuracy and limitations
- The inertia belongs to a specific axis. Converting units does not move the axis; use the parallel-axis relation I = I꜀ + m d² for that.
- Values reflected through gears scale with the square of the gear ratio, which is a separate calculation from unit conversion.
- The converter does not derive inertia from shape, density or CAD data; enter a value you already have.
- Older published tables sometimes rounded customary factors, so a small last-digit difference from a printed table is expected.
Sources
- BIPM SI Brochure — coherent SI units for derived mechanical quantities.
- NIST SP 811 Appendix B.9 — factors for moment of inertia grouped by quantity.
- NIST SP 811 Appendix B.8 — exact definitions of the pound, ounce, foot and inch.
Editorial record
Written and reviewed by the SoupCalc Editorial Team. Last reviewed: September 25, 2026.