By Zencalcy Editorial TeamLast reviewed About us
Moment of inertia is rotational mass: it measures how strongly an object resists changes to its spin. It depends on both the mass and how that mass is distributed around the rotation axis, which is why a hoop is harder to spin than a solid disk of the same mass.
Rotational inertia for common shapes about a standard axis.
Point: I = m r² Rod about centre: I = m L² / 12 Rod about end: I = m L² / 3 Disk: I = ½ m r² Hoop: I = m r² Solid sphere: I = ⅖ m r² Hollow sphere: I = ⅔ m r²
These are standard results for uniform bodies rotating about the stated axis. For another axis, use the parallel-axis theorem: I = I_cm + m d².
| Symbol | Meaning |
|---|---|
| I | Moment of inertia, in kg·m². |
| m | Mass, in kilograms. |
| r | Radius, in metres. |
| L | Rod length, in metres. |
A solid disk has I = ½ × 2 × 0.5² = 0.25 kg·m². A hoop of the same mass and radius would have 0.5 kg·m², twice as much, because all its mass sits at the rim.
Continue with the Physical Pendulum Calculator, Rolling Kinetic Energy Calculator, or the Rolling Motion Calculator — or browse more rotational and periodic motion tools and all physics calculators.
Mass farther from the axis requires more torque to accelerate. A hoop puts all its mass at the rim, while a disk spreads it closer to the centre.
Results are computed from the standard equations of classical mechanics. Unit conversions use the SI definitions published by NIST. Air resistance is ignored unless the calculator names a drag model.
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Content updated: September 2026