Physics

Kepler's Third Law Calculator

Orbital period from semi-major axis, or the reverse.

Enter your values

Results update instantly as you type — no submit needed.

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)

At a glance

What it doesOrbital period from semi-major axis, or the reverse.
CategoryPhysics
Inputs neededSolve for, Known value, Central star mass
Main outputOrbital period
FormulaT² = a³ (years, AU)
CostFree — no sign-up, no download

How to use the Kepler's Third Law Calculator

  1. 1Pick whether you know the axis or the period.
  2. 2Enter that value in AU or years.
  3. 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 you are working with.
Central star mass(solar masses)
Enter the central star mass you are working with.

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.

Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.