Moment of Inertia Calculator

Calculate the moment of inertia of common shapes (solid sphere, hollow sphere, solid cylinder, hoop, thin rod) from mass and characteristic dimension.

Frequently Asked Questions

What is moment of inertia?

It measures how hard it is to change an object's rotation about a chosen axis. It depends on the mass and on how that mass is distributed relative to the axis, scaling with the square of the distance.

Why does a hollow sphere have more inertia than a solid one?

A hollow shell keeps more of its mass far from the center, and inertia scales with the square of distance, so it resists rotation more. For the same mass and radius, I_hollow = (2/3)MR² is larger than I_solid = (2/5)MR².

What dimension do I enter for a rod?

Enter the full length of the rod and choose whether the axis runs through its center or its end. For a center axis I = (1/12)ML²; for an end axis I = (1/3)ML², four times larger. This is why a door is much harder to swing when pushed near the hinge than near the handle.

Important Disclaimer: Estimates for informational purposes only.

This calculator provides estimates for informational purposes only. Results are based on assumptions and may not reflect actual outcomes. Consult qualified professionals in relevant fields before making important decisions based on these results.