Orbital Period (Kepler)

The Orbital Period (Kepler) computes T (seconds) from 2 inputs: semi-major axis (m), central mass (kg). T = 2π √(a³/GM).

Physics is the toolkit for turning a real-world observation into a prediction. Whether it’s a falling object, a moving car, or a stressed beam, the equations here are the same ones every engineer relies on. The Orbital Period (Kepler) sits in that toolkit — it T = 2π √(a³/GM). Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

Where

a_m

Semi-major axis (m)

M

Central mass (kg)

T (seconds)

Output value

T (days)

Output value

1. 01Start by noting the input — Semi-major axis (m): 149600000000.
2. 02Start by noting the input — Central mass (kg): 1.989e+30.
3. 03Substitute these values into the formula: T (seconds) = 2 × π × √((t)^(3) / (6674e-14 × a)) | T (days) = 2 × π × √((t)^(3) / (6674e-14 × a)) / 86400
4. 04Compute T (seconds): the calculator returns 31554900.
5. 05Compute T (days): the calculator returns 365.219.
6. 06Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.