Kepler's Third Law Calculator

About this calculator

This calculator finds an orbit's period from its size using Kepler's third law: T² = 4π²a³/(GM), where a is the semi-major axis of the orbit, M is the mass of the central body, and G is the gravitational constant. In the simplified form for solar-system objects, T² (in years) equals a³ (in AU) when orbiting the Sun.

Astronomers use this to determine orbital periods of planets, moons, exoplanets, and artificial satellites from their orbital distance, and — run in reverse — to infer a central body's mass from an orbiting object's period and distance, which is how astronomers weigh stars and planets they can't put on a scale. Enter the semi-major axis and central mass to get the orbital period.