Rotational Kinetic Energy Calculator
Rotational kinetic energy (KE) is the energy contained in the spinning motion of a rigid body. The formula KE = (1/2) I ω² is the rotational analog of the familiar translational kinetic energy (1/2) mv². Moment of inertia (I) plays the same role as mass, and angular velocity (ω) plays the same role as linear speed. This calculator is useful for analyzing flywheels, spinning machinery, rolling objects, and any rotating system. Enter the moment of inertia in kg m² and the angular velocity in rad/s, or convert RPM first using ω = RPM × 2π / 60.
Rotational kinetic energy formula
KE = (1/2) × I × ω²
Where I is the moment of inertia in kg m² and ω is angular velocity in rad/s. Energy is in Joules (J). To convert to watt-hours: divide Joules by 3,600.
Understanding rotational kinetic energy
- Doubling the angular velocity quadruples the rotational kinetic energy, because KE depends on omega squared.
- Doubling the moment of inertia (by moving mass farther from the axis) doubles the kinetic energy for the same rotation rate.
- A solid sphere rolling without slipping has total KE = (7/10) mv², of which (2/7) is rotational and (5/7) is translational.
- Flywheels are effective energy stores because they can spin at very high omega while being designed with large I.
- When a spinning object slows down due to friction, rotational KE converts to heat.
Rotational kinetic energy: frequently asked questions
What is rotational kinetic energy?
Rotational kinetic energy is the energy stored in the rotation of a rigid body. It is the rotational analog of translational kinetic energy (1/2 mv²), with mass replaced by moment of inertia I and linear velocity replaced by angular velocity omega: KE = (1/2) I omega².
How does rotational KE compare to translational KE?
A rolling object has both translational KE (from its center of mass moving) and rotational KE (from spinning about its own axis). For a rolling solid sphere, rotational KE is 2/7 of the total, and translational KE is 5/7. For a hollow cylinder, rotational KE is half the total.
What units does rotational kinetic energy use?
Rotational kinetic energy is measured in Joules (J) in the SI system. One Joule equals one kg m² / s², which follows from I (kg m²) times omega² (rad²/s²).
How does a flywheel store energy?
A flywheel stores rotational kinetic energy as KE = (1/2) I omega². Engineers maximize energy storage by using a large moment of inertia (mass concentrated at the rim) and a high angular velocity. Flywheel energy storage is used in power grids, hybrid vehicles, and industrial machinery.
How do I convert RPM to rad/s for this calculation?
Multiply RPM by 2pi and divide by 60: omega = RPM x 2pi / 60. For example, 3,000 RPM = 3000 x 2pi / 60 = 314.16 rad/s.
Official sources
- OpenStax University Physics Volume 1: Moment of Inertia and Rotational Kinetic Energy.
- NIST Reference on Constants, Units, and Uncertainty: NIST Physics.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.