Rotational Kinetic Energy Calculator
Calculate the rotational kinetic energy of a spinning body from its moment of inertia and angular speed.
How it works
E_rot = ½·I·ω² · ω(rad/s) = rpm·2π/60
Rotational kinetic energy is the spinning equivalent of ½mv²: the moment of inertia I plays the role of mass, and the angular speed ω plays the role of linear speed. Because energy scales with the square of ω, doubling the spin rate quadruples the stored energy — which is why flywheels store so much energy at high rpm. The moment of inertia depends on both the mass and how far that mass sits from the axis.
Worked example
A wheel with I = 0.5 kg·m² spinning at 10 rad/s stores E = ½ × 0.5 × 10² = 25 J. At 20 rad/s the same wheel would hold 100 J — four times as much.
Sources: Rotational energy — Wikipedia
Frequently asked questions
How is this different from ordinary kinetic energy?
Ordinary (translational) kinetic energy ½mv² describes an object moving through space; rotational kinetic energy ½Iω² describes an object spinning in place. A rolling wheel has both at once, and its total energy is the sum.
What is the moment of inertia?
It measures how hard a body is to spin up, depending on its mass and how that mass is distributed around the axis. A solid disc is ½MR², a thin hoop is MR² — the same mass resists spinning more when it sits farther out.
Why convert rpm to rad/s?
The formula needs angular speed in radians per second. One revolution is 2π radians and one minute is 60 seconds, so rad/s = rpm × 2π / 60.
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Educational estimate. Check the formula and units for your exact case.