Moment of Inertia Converter

Moment of inertia measures how much an object resists rotational acceleration. It depends on both the mass and how far that mass is from the axis of rotation.

All conversions use kg·m² as the base unit.

Metric units:

• 1 kg·m² = 10,000 g·cm² = 10,000,000 g·mm²
• 1 g·cm² = 0.0001 kg·m²

Imperial units:

• 1 lb·ft² = 0.042140 kg·m²
• 1 lb·in² = 0.00029264 kg·m²
• 1 slug·ft² = 1.35582 kg·m²
• 1 oz·in² = 0.000018290 kg·m²

Cross-system:

• 1 kg·m² = 23.7304 lb·ft²
• 1 kg·m² = 0.73756 slug·ft²

Common examples:

• Bicycle wheel: ~0.1 kg·m²
• Car wheel + tire: ~0.5-1.0 kg·m²
• Flywheel (industrial): 10-1000 kg·m²

Mass moment of inertia is the rotational version of mass: it measures how hard it is to start or stop something spinning. Just as a heavier object is harder to push, an object with more moment of inertia is harder to angularly accelerate. The twist is that it depends not only on how much mass there is, but on how far that mass sits from the axis, so mass out at the rim counts for far more than mass near the center.

That distance dependence explains a lot of design. A flywheel is built with a heavy rim precisely to maximize its moment of inertia and store rotational energy, while a figure skater pulls their arms in to reduce theirs and spin faster. Don’t confuse this with the second moment of area, also loosely called “moment of inertia,” which describes a beam’s stiffness and is measured in m⁴, not kg·m². Same nickname, completely different quantity and units, so always check which one a problem means.

Shapes worth knowing by heart. For a mass m at radius r, spinning about the axis at the centre:

The pattern is the coefficient in front, and it is entirely about where the mass sits. A hoop puts everything at the rim and scores 1.0; a solid disc of the same mass and radius scores 0.5, because half its material is inboard doing less work. That factor of two is why a flywheel is built as a heavy rim on a light spider rather than as a solid slab of the same weight.

Two things a moment of inertia lets you calculate immediately. Stored energy is E = ½ I ω², with ω in radians per second, which is RPM × 2π / 60. And the torque needed to spin something up is τ = I α, the rotational twin of F = ma, where α is the angular acceleration in rad/s². Between them those two equations size most flywheels, servo motors and spindle drives.

The ω² is worth staring at. Double the speed and you quadruple the stored energy, which is both why flywheel energy storage runs at tens of thousands of RPM and why a burst flywheel is genuinely dangerous. A 20 kg·m² rotor at 3,000 RPM holds about 987 kJ, which is the kinetic energy of a 1,500 kg car at 130 km/h, in a package you can put your arms around.

The parallel axis theorem covers the other common case. If you know the moment of inertia about an object’s own centre of mass, then about any parallel axis a distance d away it becomes I + m d². That single term is why an off-centre load punishes a motor so hard: move a 2 kg part just 200 mm off the axis and it adds 0.08 kg·m² all by itself, regardless of its own shape.