Kepler's Third Law Calculator
Orbital period from semi-major axis, or the reverse.
Enter your values
ⓘ Live results
Results
- Orbital period
- 1.8814 years
- Semi-major axis
- 1.524 AU
- Period in days
- 687.2 days
- Axis in km
- 227,987,155 km
Quick answer
Kepler's third law states T² = a³ for solar orbits, where the period is in years and the semi-major axis in astronomical units.
T² = a³ (years, AU)
How to use the Kepler's Third Law Calculator
- 1Pick whether you know the axis or the period.
- 2Enter that value in AU or years.
- 3Adjust the star mass for non-solar systems.
Worked example
Using the values the calculator loads with:
Inputs
- Solve forPeriod from axis
- Known value1.524 AU or years
- Central star mass1 solar masses
Results
- Orbital period1.8814 years
- Semi-major axis1.524 AU
- Period in days687.2 days
- Axis in km227,987,155 km
Frequently asked questions
What is Kepler's third law in words?
The square of a planet's orbital period is proportional to the cube of its average distance from the Sun.
Does it work for moons?
Yes, once you set the central mass to that of the planet rather than the Sun.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.