Kepler's Third Law Calculator
Orbital period from semi-major axis, or the reverse.
Enter your values
Choose one of: Period from axis, Axis from period.
Enter the known value in AU or years.
Enter the central star mass in solar masses.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- 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)
At a glance
| What it does | Orbital period from semi-major axis, or the reverse. |
|---|---|
| Category | Physics |
| Inputs needed | Solve for, Known value, Central star mass |
| Main output | Orbital period |
| Formula | T² = a³ (years, AU) |
| Cost | Free — no sign-up, no download |
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.
Inputs explained
- Solve for
- Choose one of: Period from axis, Axis from period.
- Known value(AU or years)
- Enter the known value in AU or years.
- Central star mass(solar masses)
- Enter the central star mass in solar masses.
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.
What do I need to enter into the Kepler's Third Law Calculator?
Just 3 values: solve for, known value, central star mass. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Kepler's Third Law Calculator work out the 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. It applies the formula T² = a³ (years, AU) and shows the working so you can check each step by hand.
Is the Kepler's Third Law Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.