Kepler’s Third Law Calculator

Enter any two of the three variables in Kepler’s third law; mass, orbital radius, and time. The calculator will solve for the miss variable.

Kepler’s Third Law Formula

The following formula is created through Kepler’s third law of orbital motion.

G · m · t² = 4 · π² · r³

  • Where G is the gravitational constant
  • m is mass
  • t is time
  • and r is orbital radius

This equation can be further simplified into the following equations to solve for individual variables.

M= 4 · π² · r³ /t²*G

T = square root (4 · π² · r³ /m*G)

r = cube root (G · m · t²/4*π²)


What is Kepler’s Third Law?

This law states that the mass, orbital radius, and time are all related through the equation above.

What is orbital speed?

Orbital speed is the rate at which an object, typically called a satellite, rotates around a larger body due to a velocity and the force of gravity.

kepler's third law calculator