Kepler's Third Law Calculator

About this calculator

Kepler's third law, T² = a³ (period T in years, semi-major axis a in astronomical units), holds for anything orbiting the Sun — it comes from balancing gravitational and centripetal force and, in its general form T² = 4π²a³/(GM), applies to any body orbiting a central mass M once you know that mass.

Astronomers use it to find the orbital period of a newly discovered asteroid or comet from its measured distance alone, and the same law (rescaled for the relevant central mass) determines the orbital periods of moons around planets and exoplanets around their host stars — a foundational relationship taught in every introductory astronomy course to show that farther orbits are always slower, not just longer.