What Is a Semi-Major Axis from Orbital Period Calculator?
This calculator applies Kepler's Third Law to find an orbit's semi-major axis — essentially its average distance from the object it orbits — using only the mass of the central body and how long one orbit takes. It works for planets circling stars, moons circling planets, or one star circling another, as long as the orbiting body's mass is small compared to the central mass.
Kepler's Third Law is one of the most useful tools in astronomy: measure a period with a telescope, know (or estimate) the central mass, and you can derive a distance you could never measure directly.
How to Read Your Results
Semi-Major Axis (AU)
This is the primary result, expressed in astronomical units (1 AU is the average Earth–Sun distance, about 150 million km). It is the half-length of the long axis of the elliptical orbit, which for a near-circular orbit is very close to the average orbital radius.
Semi-Major Axis (km / million km)
The same distance converted to kilometers, useful for comparing with spacecraft trajectory data or planetary fact sheets that use metric distances rather than AU.
Period Used
Confirms the orbital period the calculator actually used, in both days and years, so you can double-check your input against the source you got the period from.
Real-World Example
Suppose you want to verify Jupiter's orbit. Jupiter takes about 4,332.6 days (11.86 years) to orbit the Sun, and the Sun's mass is, by definition, 1 solar mass.
| Input | Value |
|---|---|
| Central body mass | 1 solar mass (the Sun) |
| Orbital period | 4,332.6 days |
| Calculated semi-major axis | ≈ 5.20 AU |
That result matches Jupiter's known semi-major axis of about 5.20 AU almost exactly — a good sanity check that the calculator is applying Kepler's Third Law correctly.
Tips for Using This Calculator
- For solar-system planets, central mass is always 1 solar mass, so only the period changes.
- For moons orbiting a planet, use the planet's mass in solar masses (Earth ≈ 0.000003, Jupiter ≈ 0.000955).
- For exoplanets, use the host star's mass from its catalog entry, not the Sun's, since stellar mass varies a lot.
- This formula assumes a two-body system and ignores the gravitational pull of any third body, which is a good approximation for most single-planet or single-moon systems.
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Last updated: August 2026 · Reviewed by: Simple Calculator Tools Editorial Team