Last updated: 2026-06-15

Rotational Kinetic Energy

A spinning flywheel, a turning grindstone, a rolling wheel — each stores energy purely by virtue of rotating. That energy is the rotational kinetic energy, and it follows a formula that mirrors the familiar $\tfrac{1}{2}mv^2$ of straight-line motion. This calculator finds whichever of the energy, the moment of inertia or the spin rate you do not already know.

The formula

where $I$ is the moment of inertia (the rotational stand-in for mass) and $\omega$ is the angular velocity in radians per second. Rearranging gives the two inverse forms the calculator also handles:

Because $\omega$ enters squared, doubling the spin rate quadruples the stored energy — the same steep dependence that makes high-speed flywheels such effective energy stores.

Worked example

A wheel with moment of inertia $I = 0.5\ \text{kg·m}^2$ spinning at $\omega = 10\ \text{rad/s}$:

The angular velocity must be in radians

The formula assumes $\omega$ is in radians per second. If you know the rate in revolutions per minute, convert with

So $60\ \text{rpm}$ is exactly $2\pi \approx 6.283\ \text{rad/s}$. You can also just pick rpm as the input unit and the calculator does the conversion.

Rolling: two energies at once

An object that rolls without slipping has both translational and rotational kinetic energy:

This is why a ball and a hoop released together down a ramp do not arrive at the same time — the hoop, with the larger moment of inertia, diverts more of its energy into spin and reaches the bottom slower, regardless of mass or radius.

Where it is used

Rotational kinetic energy underlies flywheel energy storage, the regenerative braking that recovers a vehicle's spin energy, the design of turbines and engine crankshafts, and the safe operating limits of any fast-spinning machinery — where the stored energy is exactly what is released if the part fails.