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Flywheel Energy Storage Calculator

Enter the flywheel's mass, radius and RPM to find the energy it stores.

How it is calculated

The tool treats the flywheel as a uniform solid disk. Moment of inertia: I = ½ × m × r², with mass m in kg and radius r in metres. Angular speed: ω = rpm × 2π ÷ 60 in rad/s. Stored kinetic energy: E = ½ × I × ω² in joules, also shown in watt-hours (E ÷ 3600). Mass and radius must be above zero. The rpm field is not range-checked: a negative rpm only flips the sign of ω, and zero gives zero energy. Spoked wheels, rims and hollow rotors have a different moment of inertia, so the result does not apply to them. It is the total energy at that speed, not the usable energy, because a real flywheel only delivers the part between its top and bottom speeds.

Worked example

A solid steel disk of 50 kg and 0.3 m radius spins at 3,000 rpm. Step 1: I = 0.5 × 50 × 0.3² = 2.2500 kg·m². Step 2: ω = 3,000 × 2π ÷ 60 = 314.16 rad/s. Step 3: E = 0.5 × 2.25 × 314.16² = 111,033.05 J. Step 4: 111,033.05 ÷ 3,600 = 30.8425 Wh. At 6,000 rpm, the speed doubles and the energy becomes 444,132.20 J, four times as much.

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Common mistakes

  • Entering the diameter as the radius. Radius is half the diameter, and since energy scales with r² the result would be four times too large.
  • Using centimetres or grams. The tool expects kilograms and metres, so a 30 cm radius must be written as 0.3.
  • Entering rad/s or Hz in the rpm field. A speed of 314 rad/s is 3,000 rpm; typing 314 would give about 90 times too little energy.
  • Treating the result as usable energy. A flywheel loses speed as it delivers energy, so the energy you can draw is the difference between its energies at the start and end speeds.
  • Using the formula for a rim-heavy or spoked wheel. A thin ring has I = m·r², twice a solid disk of the same mass and radius, so this tool underestimates it.

About this calculator

A solid-disk flywheel's rotational kinetic energy is KE = ½Iω², where the moment of inertia of a solid disk is I = ½mr² (m = mass, r = radius) and angular velocity ω is the rotation speed in RPM converted to radians per second (ω = RPM × 2π ÷ 60). Combining these gives KE = ¼mr²ω² — energy that scales with the square of both radius and rotation speed, which is why flywheels favor spinning faster over building bigger.

Mechanical and energy-storage engineers use this relationship to size flywheels for kinetic energy recovery systems (KERS) in motorsport and regenerative braking, uninterruptible power supplies, and grid-scale flywheel energy-storage installations, where spinning mass stores energy mechanically instead of chemically the way a battery does.

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  • Editorial team

    If you plan to draw energy from the wheel, work out the usable share rather than the total. Because stored energy follows the square of speed, letting the rotor slow from 3,000 to 1,500 rpm releases 75 percent of what it held at 3,000 rpm, and the last quarter stays locked in at low speed. Run the tool at both speeds and subtract. Which speed window does your design work in? Tell us the mass, radius and rpm range you are sizing for.

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