Orbital Period Calculator (Kepler's Third Law)
Find how long a planet takes to orbit its star from its distance, or the distance from its orbital period. Works for our solar system and for exoplanets around other stars.
Solar system check
Kepler's law predicts each planet's year from its distance alone:
| Planet | Distance (AU) | Predicted year | In Earth days |
|---|
How it works
What is Kepler's third law?
The square of a planet's orbital period is proportional to the cube of its average distance from the star. Using years, astronomical units (AU), and solar masses, it becomes simply P² = a³ ÷ M. For our Sun (M = 1), a planet 4 AU out takes 8 years to orbit.
What is an AU?
One astronomical unit is the average Earth–Sun distance, about 149.6 million km (93 million miles).
Does it work for exoplanets?
Yes. Enter the host star's mass in solar masses. A planet 1 AU from a star half the Sun's mass takes about 1.41 years to orbit, because weaker gravity means a slower orbit.