What this calculator does
Kepler's third law works out orbital period of a body from its orbit size and the mass it orbits. Enter your own figures above and the answer updates as you type: nothing is fixed in the code, so the result reflects exactly the numbers you supply.
The formula this calculator evaluates is printed under the tool and explained below, so you can check the working by hand or reuse it in a spreadsheet.
The formula
FormulaT = 2π√(a³/GM), G = 6.67430×10⁻¹¹ m³/(kg·s²)
The inputs explained
| Field | What to enter |
|---|---|
| Semi-major axis (km) | A number, measured in km. Starts at 149597870.7. |
| Central mass (kg) | A number, measured in kg. Starts at 1.98892e+30. |
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the answer changes with semi-major axis
Every other input is held at the calculator’s starting values while semi-major axis varies. Select any row to load that scenario into the calculator.
How the answer changes with semi-major axis
| Semi-major axis (km) | Orbital period | Orbital period | Orbital period |
|---|---|---|---|
| 74,798,935 | 129.121 days | 0.3535 years | 11,156,076 s |
| 112,198,403 | 237.211 days | 0.6494 years | 20,495,021 s |
| 149,597,871 | 365.210 days | 0.9999 years | 31,554,149 s |
| 224,396,806 | 670.934 days | 1.837 years | 57,968,673 s |
| 299,195,741 | 1,032.970 days | 2.828 years | 89,248,610 s |
| 448,793,612 | 1,897.687 days | 5.196 years | 163,960,166 s |