💿 Moment of Inertia of a Disk Calculator

How to Use This Calculator

This calculator finds the moment of inertia of a solid uniform disk about its central axis. Enter the mass and radius and the result appears in kg m^2.

Moment of Inertia of a Solid Disk

Moment of inertia measures resistance to angular acceleration: the rotational equivalent of mass. But unlike mass, it depends on where the mass sits. Mass far from the axis counts heavily because of the R^2 term, which is why a hoop of the same mass and radius has double the moment of inertia of a solid disk. Every bit of the hoop's mass rides at the rim, while the disk's mass is spread from center to edge.

The 1/2 factor is the result of adding up r^2 for every speck of mass across the disk's face. Specks near the hub contribute almost nothing, specks at the rim contribute fully, and the average lands exactly halfway. This is a solved integral, not an approximation, as long as the disk is uniform and thin relative to its radius.

Worked Example

Where This Comes Up

Disks are everywhere in rotating machinery: flywheels, grinding wheels, saw blades, hard drive platters, and pottery wheels. Engineers need the moment of inertia to size motors, because angular acceleration follows torque = I x alpha: double the moment of inertia and you need double the torque for the same spin-up time. Underestimating I burns out motors; overestimating wastes money on oversized ones.

Make sure you use the radius, not the diameter: entering the diameter quadruples the answer. And check the axis. This formula is only for the central axis perpendicular to the face. A disk tumbling end over end uses a different formula, I = (1/4)MR^2, so picture the rotation before you calculate.