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Flywheel Energy Storage Calculator

Our flywheel energy storage calculator allows you to calculate the capacity of an interesting type of battery!

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Usable energy2.5793 MJ0.71646 kWh, between 4,000 and 12,000 rpm
Energy at full speed2.9017 MJ0.806018 kWh
Energy still stored at the floor speed322.4071 kJ11.11% of full — unrecoverable without going slower
Usable fraction88.89%1 − (ω_min/ω_max)² — energy goes as speed squared, so halving the speed releases three quarters
Moment of inertia3.675 kg·m²Solid disc or cylinder
Rim speed at full rotation439.82 m/s1.282× the speed of sound in air — rim speed, not rpm, is what limits a flywheel, because hoop stress depends on it
Specific energy42,987.61 J/kg11.941003 Wh/kg
Discharge time at 30 kW85.975 s1.4329 minutes
Power to recharge in one minute42.9876 kW
At twice the speed10.317 MJfour times the energy — which is why flywheels are made to spin fast rather than made heavy
At twice the mass5.1585 MJonly double, for twice the weight

The formula

E = ½Iω²; usable energy comes from the speed range

Speed beats mass

Rotational energy goes as the square of angular velocity but only linearly with mass, so a flywheel gains far more from spinning faster than from being heavier. Doubling the speed quadruples the storage; doubling the mass merely doubles it, at twice the weight. Modern flywheels are therefore light composite rotors spinning very fast, not the heavy steel discs of the nineteenth century.

What limits them is rim speed rather than rpm. The hoop stress trying to tear the rotor apart depends on the tangential velocity at the rim, so a small rotor can safely spin much faster than a large one. This is why the figure above is quoted next to the speed of sound — it is the number an engineer checks against the material's strength.

Not all the stored energy is usable. Extracting it slows the rotor, and most machines have a minimum working speed, below which the energy is stranded. Because energy goes as speed squared, the arithmetic is friendlier than it sounds: running down to half speed releases three quarters of the stored energy.