Orbital period calculator (Kepler's third law)
Enter the orbit's semi-major axis and pick the central body to get the time for one full orbit in days, hours and years.
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How to use it
- Enter central body, semi-major axis and distance unit.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
T = 2π √(a³ ÷ GM), where a is the semi-major axis and GM the central body's gravitational parameter. 1 au = 149,597,870,700 m exactly.
Example
Inputs: Central body = Sun, Semi-major axis = 1, Distance unit = Astronomical units (au). Result: Orbital period: 365.2569 days; In hours: 8,766.1656 h; In years (365.25 d): 1.00002 yr.
Limits and caveats
- Assumes the orbiting body's mass is tiny compared with the central body.
- Perturbations from other bodies and the central body's flattening are ignored.
Questions about this tool
What does Kepler's third law say?
The square of the orbital period is proportional to the cube of the semi-major axis.
Why does Earth give 365.2569 days, not 365.25?
The result is the sidereal year, which is slightly longer than the calendar year.
Does an elliptical orbit change the answer?
No. The period depends only on the semi-major axis, not on the eccentricity.