About the Moment of Inertia Calculator
Moment of inertia for common shapes — rod, disc, sphere, hoop and rectangular plate.
Also known as: rotational inertia, second moment of mass, inertia calculator.
How to use this calculator
- Enter shape, mass, radius or length.
- The result updates instantly as you type — press Calculate (or Enter) at any time.
- Review the breakdown shown under the main result.
- Use Copy result or Share to save the answer or send a link with your inputs.
Formula
I = k·m·r² (k depends on the shape)
Worked example
Using the values pre-filled in the calculator above:
- Shape: Solid disc / cylinder (½mr²)
- Mass = 10 kg
- Radius or length = 0.5 m
the calculator returns:
- Moment of inertia: 1.25 kg·m²
- Factor: 0.5
- Torque for 1 rad/s²: 1.25 N·m
- Rotational KE at 10 rad/s: 62.5 J