🔁Orbital Period Calculator
Apply Kepler's third law to find the orbital period of any body from its semi-major axis and the central body's mass.
Free Orbital Period Calculator
Our free orbital period calculator applies Kepler's third law, T = 2π√(a³/GM), to find how long a planet, moon, or satellite takes to complete one orbit. Choose a preset central body — the Sun, Earth, Mars, or Jupiter — or enter a custom mass, then type in the semi-major axis of the orbit in astronomical units, kilometers, or meters.
Switch modes to solve the reverse problem: given a known orbital period, find the semi-major axis the orbit must have. Every result shows the full substitution into Kepler's third law so you can follow exactly how the number was derived, not just see the final answer.
This makes the tool useful for astronomy homework, satellite mission planning estimates, and quick sanity checks against real orbital data like Earth's 365.25-day year or Mars's roughly 687-day year. No sign-up, no downloads — everything runs instantly in your browser.
About the Orbital Period Calculator
Features
Two solve modes
Solve for orbital period or for semi-major axis, whichever value you're missing.
Preset central bodies
Choose the Sun, Earth, Mars, Jupiter, or enter any custom mass.
Multiple units
Enter distances in AU, km, or m; periods in years, days, or hours.
Step-by-step working
See the full substitution into Kepler's third law, not just the final answer.
Frequently Asked Questions
What is Kepler's third law?
Kepler's third law states that the square of an orbital period is proportional to the cube of the semi-major axis of the orbit. In its full form, T = 2π√(a³/GM), where G is the gravitational constant and M is the mass of the central body.
What is the semi-major axis?
The semi-major axis is half the longest diameter of an elliptical orbit. For a circular orbit it equals the radius. It is the key distance measurement used in Kepler's third law.
Does this calculator work for any orbiting body?
Yes. Choose a preset central body mass such as the Sun, Earth, Mars, or Jupiter, or enter a custom mass in kilograms for any other star or planet.
Can I find the semi-major axis from a known period?
Yes. Switch to 'Solve for Semi-Major Axis' mode, enter the known orbital period and central body mass, and the calculator solves Kepler's third law for the distance.
Why does Earth take exactly one year to orbit the Sun?
A year is defined as the time Earth takes to complete one orbit of the Sun, roughly 365.25 days, based on Earth's semi-major axis of 1 astronomical unit and the Sun's mass.
How accurate is the result?
The calculator uses the standard gravitational constant and Kepler's third law, giving results accurate to several significant figures for two-body orbital mechanics. It does not account for perturbations from other bodies.
What units can I use for the semi-major axis?
You can enter the semi-major axis in astronomical units (AU), kilometers, or meters. The calculator converts internally to meters for the calculation.
What units are used for the orbital period?
Results are shown in years, days, hours, and seconds simultaneously so you can use whichever unit fits your context.
Can this calculate a satellite's orbital period around Earth?
Yes. Select Earth as the central body and enter the satellite's semi-major axis (its altitude plus Earth's radius) in kilometers or meters.
Is this calculator free to use?
Yes, the orbital period calculator is completely free with no sign-up, and all calculations run instantly in your browser.