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

Kepler’s Third Law Definition

Kepler’s third law defines the relationship between mass, time, and orbital radius between two bodies of mass.

Kepler’s Third Law Example

How to calculate Kepler’s third law?

  1. First, determine the variable you are solving for.

    Determine which of the 3 variables you want to find.

  2. Next, find the known variable.

    Determine the values of the 2 known variables.

  3. Finally, calculate the missing variable.

    Using the formulas above, calculate the missing variable.


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.