Calculates the kinetic energy stored in a rotating object, the rotational counterpart to linear kinetic energy.
How it works
Half the moment of inertia is multiplied by the square of the angular velocity.
What this does not include
This does not include linear kinetic energy from an object’s overall motion through space — for that, use this site’s kinetic energy calculator instead. An object that’s both spinning and translating (like a rolling ball) has both forms of energy separately.
How to use this calculator
- Enter the moment of inertia and angular velocity.
A worked example
A moment of inertia of 2 kg·m² spinning at 3 rad/s: rotational KE = ½Iω² = 0.5 × 2 × 3² = 9 J.
A moment of inertia of 1 kg·m² at 4 rad/s: rotational KE = 8 J.
What the variables mean
| Variable | Meaning |
|---|---|
| Moment of inertia | Resistance to changes in rotation, based on mass distribution |
| Angular velocity | Rotational speed, in radians per second |
Edge cases worth knowing
Rotational kinetic energy scales with the square of angular velocity, not linearly. Doubling the spin rate quadruples the stored energy — the same squared relationship seen in linear kinetic energy (½mv²).
A negative moment of inertia has no physical meaning, so the calculator declines to show a result for one.
Frequently asked questions
Why does angular velocity get squared in this formula?
The same reason linear kinetic energy squares velocity — energy scales with the square of speed, whether that speed is linear or rotational.
What’s a real-world example of rotational kinetic energy?
A spinning flywheel storing energy, a rotating turbine, or a thrown frisbee’s spin all carry rotational kinetic energy separate from their motion through the air.
Can an object have both linear and rotational kinetic energy at once?
Yes — a rolling ball, for example, has linear kinetic energy from moving forward and rotational kinetic energy from spinning, and its total kinetic energy is the sum of both.
