Rotational Kinetic Energy Calculator

Rotational kinetic energy is KE = 1/2 x I x omega^2, where I is the moment of inertia in kg x m^2 and omega is the angular velocity in rad/s. The calculator squares omega and multiplies by half the inertia.

Linear energy uses mass and speed as 1/2 m v^2, while rotational energy swaps in the moment of inertia for mass and the angular velocity for speed. A rolling object carries both forms at once.

The moment of inertia depends on the shape and how its mass is spread from the spin axis, for example 1/2 m r^2 for a solid disk or m r^2 for a thin ring. Use a moment of inertia calculator for your shape, then bring that number here.

Multiply revolutions per minute by 2 pi and divide by 60, so 60 RPM is about 6.283 rad/s. This tool needs radians per second, so convert first if your speed is given in RPM.

No. Because omega is squared, spinning clockwise or counterclockwise at the same rate gives the same energy. The result is always zero or positive.

A real rotating body has mass distributed at some distance from the axis, so its moment of inertia is positive. Entering zero or a negative value is rejected because it has no physical meaning here.

An object that is not turning stores no rotational kinetic energy, so an omega of zero returns 0 J. Any negative angular velocity is accepted and gives the same energy as its positive counterpart.

With the moment of inertia in kg x m^2 and the angular velocity in rad/s, the energy is in joules. Values are rounded to nine decimal places to keep the display clean.

Yes. The formula runs in your browser and nothing you enter is transmitted to a server, so your numbers stay on your device.