Rotational Kinetic Energy Calculator
The energy stored in a spinning object — ½Iω² — for a disc, ring, sphere or a moment of inertia you supply.
How much energy a spinning wheel carries.
How the rotational kinetic energy calculator works
Rotational kinetic energy mirrors the linear form with moment of inertia in place of mass and angular velocity in place of speed: ½Iω².
The moment of inertia depends on where the mass sits. A ring, with all its mass at the rim, has twice the inertia of a solid disc of the same mass and radius — which is why flywheels are built heavy at the edge.
Formula: KE = ½ I ω²; I = k m r²
Worked examples
| Inputs | Rotational kinetic energy | Note |
|---|---|---|
| A 20 kg disc at 3,000 rpm | 44,413.22 J | 44.4 kJ |
| The same mass as a ring | 88,826.44 J | twice the energy |
| Half the speed | 11,103.3 J | a quarter of the energy |
FAQFrequently asked questions
What is moment of inertia?
The rotational equivalent of mass — how hard something is to spin up. It depends on where the mass sits, not just how much there is.
Why does a ring have twice the inertia of a disc?
Because all its mass sits at the full radius, while a disc has most of its mass closer to the centre where it contributes less.
How much energy is in a flywheel?
A 20 kg disc at 3,000 rpm holds about 44 kJ — enough to lift itself 226 metres. Flywheel storage systems run far faster than that.
Why do flywheels spin so fast?
Because energy scales with the square of angular velocity but only linearly with mass. Speed is the cheapest way to store more.
What limits flywheel speed?
Material strength. Rim stress grows with the square of speed, and the rim tears itself apart before the bearings give out.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Measurement Institute — Australia's measurement authority
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.