What is rotational kinetic energy?

Rotational kinetic energy is the kinetic energy associated with the rotation of an object. It equals one-half the product of the moment of inertia and the square of the angular velocity: KE = 0.5 × I × ω².

What is the moment of inertia?

The moment of inertia (I) measures how mass is distributed around a rotation axis. A solid cylinder rotating about its central axis has I = 0.5 × m × r², while a thin hoop has I = m × r². Higher I means more energy is needed to achieve the same angular velocity.

What units does this calculator use?

Moment of inertia is entered in kg·m². Angular velocity can be entered in radians per second (rad/s), revolutions per minute (RPM), or degrees per second (deg/s). The result is output in joules (J).

Why does angular velocity appear squared in the formula?

The squared relationship mirrors translational kinetic energy (KE = 0.5 × m × v²). Doubling the angular velocity quadruples the rotational kinetic energy, which is why high-speed rotors store enormous amounts of energy.

How do I convert RPM to rad/s?

Multiply RPM by 2π and divide by 60: ω (rad/s) = RPM × 2π / 60. This calculator performs that conversion automatically when you select RPM.

Can this be used for any rotating object?

Yes, as long as you know the correct moment of inertia for the object's shape and axis of rotation. Refer to the formula reference table in the calculator for common shapes.

Rotational Kinetic Energy Calculator

Name: Rotational Kinetic Energy Calculator
Availability: InStock
Author: Nham Vu

Enter the moment of inertia and angular velocity of a spinning object to instantly calculate its rotational kinetic energy.

Inputs

Moment of Inertia (I)

kg·m²

Angular Velocity (ω)

Result

Enter values and click Calculate to see the result.

Common Moments of Inertia

Shape / Axis	Formula
Solid cylinder (central axis)	I = ½ m r²
Thin hoop (central axis)	I = m r²
Solid sphere (diameter)	I = ⅖ m r²
Thin spherical shell (diameter)	I = ⅔ m r²
Solid rectangular plate (center)	I = 1/12 m(a²+b²)
Rod (perpendicular, end)	I = ⅓ m L²

m = mass (kg), r = radius (m), L = length (m), a/b = side lengths (m)

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Summary

Enter the moment of inertia and angular velocity of a spinning object to instantly calculate its rotational kinetic energy.

How it works

Enter the moment of inertia (I) of the object in kg·m².
Enter the angular velocity (ω) in your preferred unit: rad/s, RPM, or deg/s.
The calculator converts angular velocity to rad/s automatically.
It applies the formula KE = 0.5 × I × ω² and displays the result in joules.
Use the formula reference panel to identify the correct moment of inertia for common shapes.

Use cases

Engineering design of rotating machinery such as flywheels and motors.
Physics homework and exam preparation involving rotational dynamics.
Checking energy budgets for wind turbines or electric motor rotors.
Analyzing gyroscopes, centrifuges, and spinning satellites.
Teaching rotational mechanics concepts in classrooms.
Comparing energy stored at different RPMs for mechanical system design.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu