Calculate moment of inertia (rotational inertia) for common shapes including cylinders, spheres, rods, and rectangular plates with unit conversions.
Enter to calculate angular momentum and kinetic energy
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Moment of inertia (rotational inertia) measures an object's resistance to rotational acceleration. Our calculator computes moment of inertia for common shapes, providing unit conversions and related quantities like radius of gyration.
Moment of inertia is the rotational equivalent of mass. While mass determines resistance to linear acceleration, moment of inertia determines resistance to angular acceleration. It depends on both the mass and how that mass is distributed relative to the axis of rotation. Objects with mass concentrated far from the axis have higher moment of inertia.
General Formula
I = Σ mᵢrᵢ²Design rotating machinery, flywheels, and drive systems.
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Mass measures resistance to linear (straight-line) acceleration, while moment of inertia measures resistance to rotational (angular) acceleration. Moment of inertia depends on how mass is distributed around the rotation axis—the same mass can have different moments of inertia depending on its shape.