Free Kepler's Third Law Calculator
Relate orbital period and semi-major axis for bodies orbiting the Sun using T^2 = a^3 (years and AU).
yr
Semi-Major Axis
1.000000 AU
Semi-Major Axis (km)149,597,871 km
Semi-Major Axis vs Orbital Period
Kepler's Third Law
For bodies orbiting the same central mass, the square of the period is proportional to the cube of the semi-major axis.
Simplified Form (Solar System)
T² = a³ when T is in Earth years and a is in AU.
Rearranging: a = T^(2/3)
Example Calculation
Mars has an orbital period of 1.881 years. Find its semi-major axis.
- 01a = T^(2/3)
- 02T² = 1.881² = 3.538
- 03a = 3.538^(1/3) = 1.524 AU
- 04In km: 1.524 × 149 597 870.7 ≈ 228 million km