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Rotational Kinetic Energy Calculator

Find the rotational kinetic energy of a spinning object.

How it is calculated

The energy is KE = ½ × I × ω², where I is the moment of inertia in kg·m² and ω is the angular velocity in radians per second. The result is in joules and is rounded to two decimals.

The moment of inertia must be greater than zero, otherwise there is no result. Angular velocity is squared, so a negative value (the opposite direction of spin) gives the same energy as the positive one. The tool does not convert from rpm: multiply revolutions per minute by 2π ÷ 60 (about 0.10472) first. It also does not compute I for you; for a solid disk of mass m and radius r it is ½ m r², for example.

Worked example

A solid disk of 5 kg and radius 0.2 m has I = ½ × 5 × 0.2² = 0.1 kg·m². It spins at 600 rpm, which is 600 × 0.10472 ≈ 62.83 rad/s.

Square the speed: 62.83² = 3947.61. Then KE = 0.5 × 0.1 × 3947.61 = 197.38 J. Doubling the speed to 125.66 rad/s would raise the energy fourfold.

Try this example →

Common mistakes

  • Typing rpm directly into the angular velocity field. The formula needs rad/s, so a raw 600 would give a result about 91 times too large.
  • Using the mass instead of the moment of inertia. I depends on how the mass is spread around the axis, not just on the mass.
  • Using grams or centimetres when computing I. For a joule result, I must be in kg·m².
  • Forgetting that energy grows with the square of speed. A 10% increase in ω raises the energy by 21%.
  • Using the diameter in place of the radius in the I formula, which makes I four times too large for a disk or sphere.

Sources

About this calculator

This calculator finds rotational kinetic energy using KE = ½·I·ω², the rotational analogue of the familiar ½·m·v² formula for straight-line motion. Here, moment of inertia I (in kg·m²) replaces mass and captures how an object's mass is distributed relative to its rotation axis — a solid disk, a hollow ring, and a sphere all have different I formulas for the same mass and radius — while angular velocity ω (in radians per second) replaces linear velocity.

Mechanical and automotive engineers use this to size flywheels that store energy smoothly in engines and machinery, to analyze spinning components like turbine rotors, gears, and crankshafts, and to model wheel and wind-turbine blade dynamics; physics students use it to connect linear and rotational mechanics in coursework.

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Comments (1)

  • Editorial team

    This gives only the energy of spinning about one axis. A wheel that also travels, such as a rolling cylinder, carries translational energy of half m v squared on top of the figure shown, so the two must be added. The tool wants radians per second, and the speed is squared, so a unit slip changes the answer a lot. Which object are you spinning, and do you already know its moment of inertia?

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