Rotational Kinetic Energy Calculator

Rotational kinetic energy is the energy stored in a rotating object due to its angular motion. Just as linear kinetic energy depends on mass and velocity, rotational kinetic energy depends on the moment of inertia (I) and angular velocity (ω). It is a form of mechanical energy and is measured in Joules (J).

The formula is E = ½ × I × ω², where E is the kinetic energy in Joules, I is the moment of inertia in kg·m², and ω (omega) is the angular velocity in radians per second (rad/s). If your angular velocity is in RPM, it must first be converted to rad/s using ω = RPM × 2π / 60.

First, determine the moment of inertia (I) of your object in kg·m². Next, find the angular velocity (ω) in rad/s — convert from RPM if needed by multiplying by 2π/60. Finally, plug the values into E = ½ × I × ω². For example, with I = 2.5 kg·m² and ω = 10 rad/s: E = 0.5 × 2.5 × 100 = 125 J.

The moment of inertia (I) is the rotational equivalent of mass — it measures how much an object resists changes to its rotation. Its value depends on the object's mass distribution relative to the axis of rotation. Common formulas include I = ½mr² for a solid disk and I = mr² for a thin ring. It is measured in kg·m².

To convert revolutions per minute (RPM) to radians per second (rad/s), use the formula: ω (rad/s) = RPM × 2π / 60. For example, 100 RPM = 100 × 2π / 60 ≈ 10.472 rad/s. This calculator performs the conversion automatically when you select RPM as the unit.

Rotational kinetic energy is critical in many engineering and physics applications, including flywheels used for energy storage, electric motors and servomotors, turbines, spinning wheels, gyroscopes, and carousel or amusement park rides. Understanding it helps engineers design efficient rotating machinery and energy storage systems.

Linear kinetic energy (KE = ½mv²) describes the energy of an object moving in a straight line, depending on mass and linear speed. Rotational kinetic energy (E = ½Iω²) describes the energy of a spinning object, depending on moment of inertia and angular velocity. For a rolling object, both forms of energy are present simultaneously and must be added together.

Yes. A rolling object, such as a ball or wheel rolling along a surface, has both translational kinetic energy (from its center of mass moving forward) and rotational kinetic energy (from its spin). The total kinetic energy in that case is KE_total = ½mv² + ½Iω², where v is the linear speed and ω is the angular velocity.