Moment of Inertia Calculator

Calculate the moment of inertia for spheres, cylinders, hoops, and rods from mass and a characteristic dimension

Frequently Asked Questions

What is moment of inertia?

It measures how hard it is to change an object's rotation about an axis, depending on both mass and how that mass is distributed.

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.

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 difference explains why a door is much harder to swing when pushed near the hinge than near the handle, even though the mass and length are identical.

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.