Flywheel Energy Calculator
Enter a moment of inertia and an angular velocity to get the rotational kinetic energy a flywheel stores in joules — and see why energy climbs with the square of spin speed.
Stored rotational energy
Enter the moment of inertia and the angular velocity and the calculator returns the stored kinetic energy (½Iω²) in joules.
Use SI units
Moment of inertia in kg·m² and angular velocity in rad/s give energy in joules — multiply rev/s by 2π to get rad/s before you start.
What is flywheel energy?
The energy of spinning mass
The flywheel energy calculator works out the rotational kinetic energy a spinning flywheel stores because of its rotation. A flywheel is a heavy rotating disc or rim that banks energy as it spins and releases it again when it slows — the rotational cousin of the energy a moving object carries. The stored energy grows with both how the mass is distributed (the moment of inertia) and — far more steeply — how fast the wheel spins. The calculator turns two measurements, the moment of inertia in kg·m² and the angular velocity in rad/s, into the energy in joules. It is the number behind energy-storage flywheels, engine smoothing, and the punch a press or potter's wheel can deliver between power strokes.
Enter a moment of inertia in kg·m² and an angular velocity in rad/s to get the stored rotational energy in joules instantly.
The stored rotational kinetic energy is half the moment of inertia multiplied by the angular velocity squared.
E = ½ × I × ω²The angular velocity is squared, so it dominates the result: a small change in spin speed produces a large change in stored energy. The moment of inertia stays to the first power, so it scales the energy in direct proportion. Use kg·m² and rad/s and the energy comes back in joules.
Suppose a flywheel has a moment of inertia of 5 kg·m² and spins at 100 rad/s.
Square the angular velocity
100² = 10,000 — the squared spin speed that drives the energy.
Multiply by the moment of inertia
5 × 10,000 = 50,000 — moment of inertia times angular velocity squared.
Take half
½ × 50,000 = 25,000 J (25 kJ) — the energy stored in the spinning flywheel.
The result is the energy the flywheel banks while it spins — and the energy it can hand back as it slows down. A flywheel stores rotational energy, not linear motion, so the figure tells you how much work the wheel can deliver to a load or how much energy a braking system must absorb to stop it. The crucial insight is that energy scales with the square of angular velocity: double the spin from 100 to 200 rad/s and the stored energy jumps fourfold, from 25,000 to 100,000 J, while the moment of inertia only changes things in direct proportion. That is exactly why engineers push flywheels to spin as fast as the material safely allows — speed is the lever that stores the most energy for the least mass — and why a runaway high-speed flywheel is so dangerous. A heavier or larger-radius rim raises the moment of inertia and helps, but only linearly; spin speed is what moves the result the most.
The formula is exact, but a couple of practical points are worth keeping in mind.
Rigid body and consistent units
This calculator treats the flywheel as a rigid body rotating about a fixed axis and gives only its rotational kinetic energy — it ignores any translational motion, bearing friction, and windage losses. The angular velocity must be in radians per second, not rev/min or rev/s: multiply rev/s by 2π, or rev/min by 2π/60, before you enter it, or the joules will be wrong.