Rotational Kinetic Energy Calculator (Flywheel Energy)
By Santaji GadepatilinUpdated October 29, 2026
A spinning body stores kinetic energy that depends on its moment of inertia and the square of its angular velocity. This rotational kinetic energy calculator works out the moment of inertia of common shapes and the stored energy from rpm — useful for flywheels, motor rotors, grinding wheels and coast-down estimates.
How to use the rotational kinetic energy calculator
Choose the shape, then enter the mass, the radius and the speed in rpm. You get the moment of inertia, the angular velocity and the stored rotational kinetic energy. For other shapes, clear the mass and enter a known moment of inertia directly.
Rotational kinetic energy formula
E = ½ I ω² · I = k m r² · ω = 2π N ÷ 60
Example
A 20 kg solid steel disc of radius 250 mm spinning at 1,000 rpm:
- I = ½ × 20 × 0.25² = 0.6250 kg·m²
- ω = 2π × 1000 ÷ 60 = 104.72 rad/s
- E = ½ × 0.625 × 104.72² = 3,427 J (0.952 Wh)
Moments of inertia of common shapes
| Shape (about central axis) | I |
|---|---|
| Solid disc or cylinder | ½ m r² |
| Thin ring or hoop | m r² |
| Thick ring, radii r₁ and r₂ | ½ m (r₁² + r₂²) |
| Solid sphere | ⅖ m r² |
| Thin hollow sphere | ⅔ m r² |
| Rod about its centre, length L | m L² ÷ 12 |
| Rod about one end | m L² ÷ 3 |
Energy vs speed for the example disc
| Speed | Energy |
|---|---|
| 500 rpm | 857 J |
| 1,000 rpm | 3,427 J |
| 1,500 rpm | 7,711 J |
| 3,000 rpm | 30,843 J |
| 6,000 rpm | 123,370 J |
Frequently asked questions
What is the formula for rotational kinetic energy?
E = ½ I ω², where I is the moment of inertia in kg·m² and ω the angular velocity in rad/s. It mirrors ½ m v² for straight-line motion.
What is the moment of inertia of a solid disc?
I = ½ m r². A thin ring of the same mass and radius has twice that, m r², because all its mass is at the rim.
Why are flywheels shaped like rims?
Putting mass far from the axis raises the moment of inertia, so a rim-heavy flywheel stores more energy for the same weight.
How does speed affect stored energy?
Energy rises with the square of speed — doubling rpm stores four times the energy, which is also why overspeed failures are so violent.