Angular Momentum Calculator

About this calculator

This calculator finds the angular momentum of a particle moving in a circular or curved path using L = m · v · r, where m is mass, v is the (tangential) velocity, and r is the radius from the axis of rotation — the rotational analog of linear momentum p = mv. Angular momentum is a vector quantity, but this formula gives its magnitude for motion perpendicular to the radius.

Because angular momentum is conserved in the absence of external torque, it explains phenomena from a spinning figure skater speeding up as they pull in their arms (reducing r increases the required v), to why planets sweep out equal areas in equal times as they orbit (Kepler's second law), to the stability of a spinning gyroscope or bicycle wheel.

Physics students studying rotational mechanics, engineers analyzing rotating machinery and flywheels, and astronomers modeling orbital dynamics all use this calculation to find angular momentum from mass, velocity, and radius.