Moment of Inertia Calculator
Compare rotational inertia formulas for common ideal shapes and axes.
Match mass distribution to an axis
Moment of inertia measures how mass distribution resists angular acceleration about a specified axis. This calculator includes a point mass, thin hoop, solid disk, solid sphere, hollow sphere, slender rod about its center, and slender rod about one end. Selecting a shape applies its textbook coefficient to mass and the square of radius or length.
The default solid disk has mass four kilograms and radius 0.5 meter, producing moment of inertia 0.5 kilogram-square-meters about its symmetry axis. A thin hoop with the same mass and radius would produce 1, because more mass lies farther from the axis. For a rod, the length input replaces radius in the selected formula.
Treat each listed shape as an idealization
Every formula assumes uniform density, ideal geometry, and the named axis through the center or end. A displaced parallel axis requires adding mass times offset squared, while composite bodies need component inertias summed about one common axis. Calculations run in your browser. Confirm whether a real part is solid, hollow, thin, or thick before choosing a model.
Frequently Asked Questions
Why does the rotation axis matter?
Moment of inertia weights each mass element by squared distance from the chosen axis, so moving the axis changes the result.
What input does a rod use?
The rod formulas use full rod length; the radius field is ignored for those two selections.
Can I calculate a composite object?
Calculate each component about the same axis and add the inertias, applying the parallel-axis theorem where needed.
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