Kepler's Third Law Calculator
Find two-body orbital period from orbit size and central mass.
Connect orbit size with period
Newton's form of Kepler's third law relates orbital period to semi-major axis and central mass. This calculator takes two pi times the square root of axis cubed divided by gravitational constant times mass, then reports seconds and days. It works for circular or elliptical two-body orbits because semi-major axis, not instantaneous radius, sets the ideal period.
Using central mass 1.989 times ten to the thirtieth kilograms and semi-major axis 1.496 times ten to the eleventh meters gives 31554188 seconds, or 365.211 days. Those rounded Sun and Earth-orbit inputs produce a value near one year. Increasing semi-major axis raises period with the three-halves power, so distant orbits grow much slower.
Treat the result as a two-body approximation
The satellite mass is neglected relative to the central body; comparable masses require using their sum. Perturbations, non-spherical gravity, relativity, drag, and third bodies are omitted. The values never leave your browser. Use center-to-center semi-major axis in meters and validated masses, and rely on ephemeris or numerical propagation when timing precision matters.
Frequently Asked Questions
Can this calculate an elliptical orbit?
Yes. Enter the ellipse semi-major axis; ideal period does not depend on eccentricity.
Should I enter altitude as the semi-major axis?
No. Use center-to-center orbital semi-major axis, adding body radius when converting a circular altitude.
When should both masses be included?
Use the sum of masses when the orbiting body is not negligible compared with the central body.
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