Moment of Inertia Calculator
Moment of inertia, radius of gyration and rotational kinetic energy for common rigid bodies.
How to use the Moment of Inertia Calculator
- Enter or select: Shape, Mass m, Radius r, or length L / side a.
- Fill in what you know of: Second side b (plate only), Angular velocity ω (optional) — leave the unknown empty.
- The results (Moment of inertia I, Radius of gyration, Rotational kinetic energy, Angular momentum, Formula used) are calculated instantly as you type.
- Use “Copy link” to share the calculation with the same input values.
Formula
- I = Σ mᵢrᵢ² = ∫ r² dm
- K = ½Iω²
- L = Iω
- Parallel axis: I = I_cm + Md²
About this tool
The parallel-axis theorem lets you move any of these axes by a distance d: add M·d².