Moment of Inertia Calculator
Calculate the mass moment of inertia of discs, rings, spheres, and rods about their central axis.
How it works
- 1Pick the shape — solid cylinder, ring, hollow cylinder, sphere, or rod.
- 2Enter the mass and the radius (or length for a rod); add the inner radius for a hollow cylinder.
- 3Read the mass moment of inertia I in kg·m², with the formula used for the selected shape.
Use cases
- Sizing motors and brakes by finding the rotational inertia of a load.
- Computing flywheel and rotor inertia for energy-storage and dynamics problems.
- Checking physics homework on rotational motion and angular momentum.
Frequently asked questions
What is the moment of inertia?
The mass moment of inertia measures how strongly an object resists changes to its rotation about an axis. It depends on both the mass and how that mass is distributed relative to the axis.
What are the formulas for common shapes?
Solid disc I = ½mr², thin ring I = mr², solid sphere I = ⅖mr², a rod about its centre I = 1⁄12 mL², and a rod about its end I = ⅓mL².
Why is a ring’s inertia larger than a disc of the same mass?
A ring concentrates its mass at the outer radius, while a disc spreads mass toward the centre. Because inertia grows with the square of the distance from the axis, the ring resists rotation more.
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