🪐 Kepler's Third Law Calculator
Enter a semi-major axis to get the orbital period — or a period to get the distance — for the Sun or any central mass.
Orbital period
1.881 years
≈ 687.18 days
Kepler\'s third law: P² = a³ ÷ M, with the period P in years, the semi-major axis a in astronomical units and the central mass M in solar masses. For the Sun (M = 1) it\'s simply P = √(a³) — Earth at 1 AU orbits in 1 year, Mars at 1.52 AU in 1.88 years. Set M to model other stars or planets. 🔒 In your browser.
How the kepler's third law calculator works
Kepler's third law says the square of an orbital period equals the cube of the semi-major axis, once you use the right units. In solar-system units that's simply P² = a³ ÷ M: period P in years, semi-major axis a in astronomical units, and central mass M in solar masses. So a planet at 1 AU around the Sun (M = 1) orbits in exactly 1 year, and one at 4 AU takes 8 years. The tool solves either direction and lets you change the central mass to model other stars or a planet's moons.
The law assumes one dominant central mass and an elliptical orbit described by its semi-major axis (the average of closest and farthest distance). It's the relationship behind everything from planet spotting to detecting exoplanets by their orbital timing.
Frequently asked questions
What is Kepler's third law?
It states that the square of a planet's orbital period is proportional to the cube of its semi-major axis: P² ∝ a³. In solar-system units (years, AU, solar masses) the constant is 1, giving P² = a³ ÷ M.
How do I calculate orbital period from distance?
P = √(a³ ÷ M), with a in AU and M in solar masses. For the Sun, a planet at 9 AU has a period of √(729) = 27 years. Enter your distance and mass to get the exact figure.
What is a semi-major axis?
Half the longest diameter of an elliptical orbit — effectively the orbit's average radius, the mean of its closest (perihelion) and farthest (aphelion) distances from the central body. It's the "a" in Kepler's third law.
Does Kepler's third law work for moons and other stars?
Yes, as long as one body dominates the mass. Change the central mass to that star or planet (in solar masses) and the same P² = a³ ÷ M applies. It's how astronomers weigh stars and planets from their satellites' orbits.
Why is Earth's period exactly 1 year in this formula?
Because the units are defined around Earth: 1 AU is Earth's average distance and 1 year is its period, with the Sun as 1 solar mass. Plugging a = 1 and M = 1 into P = √(a³ ÷ M) gives exactly 1.