Kepler’s Third Law Calculator
🪐 Gravity & circular motion. Use the Kepler’s third law formula to find period, orbit radius, planet mass: pick the value you want, type the others, and the answer updates as you go.
Pick the ○ next to the value you want to find, fill in the others, and it solves as you type.
What each letter means
| Quantity | Unit |
|---|---|
| Period | s |
| Orbit radius | m |
| Planet mass | kg |
Worked example
Find the period when Orbit radius = 6.79 × 10⁶ m, Planet mass = 5.97 × 10²⁴ kg.
Using T² = (4π² r³)/GM: Period = 5569.3 s.
Frequently asked questions
What is the formula for Kepler’s third law?
T² = (4π² r³)/GM.
What do the letters stand for, and what units are used?
Period in s, Orbit radius in m, Planet mass in kg.
How do you calculate period?
Put the values into T² = (4π² r³)/GM. For example, with Orbit radius = 6.79 × 10⁶ m, Planet mass = 5.97 × 10²⁴ kg, period = 5569.3 s.
Can I solve for a different value?
Yes. In the calculator above, pick the circle next to any value (period, orbit radius, planet mass) and fill in the others: it rearranges the formula for you.
