Orbital Period Calculator
Enter the semi-major axis and central body mass to instantly compute the orbital period using Kepler's third law.
Use the Orbital Period Calculator
Orbital Parameters
Distance from center of the central body
Use scientific notation: 1.989e30
Formula: T = 2π √(a³ / GM)
G = 6.674 × 10−11 N·m²/kg²
Select a preset or enter custom values, then click Calculate.
Earth
T = 2π√(a³/GM)Orbital Period
Seconds
Hours
Days
Years
Input Values Used
Solar System Comparison (planets around Sun)
| Planet | Period (days) | Bar |
|---|
Summary
The orbital period is the time a body takes to complete one full orbit around another. This calculator applies Kepler's third law: T = 2π√(a³ / GM), where a is the semi-major axis, G is the gravitational constant, and M is the mass of the central body. All Solar System planets are available as one-click presets so you can verify known values, and you can enter any custom orbit for satellites, moons, or exoplanets.
How it works
- Select a Solar System preset to load known orbital data, or choose Custom to enter your own values.
- For custom input, enter the semi-major axis in kilometers and the central body mass in kilograms.
- The calculator applies Kepler's third law: T = 2π × sqrt(a³ / (G × M)).
- Results are shown in seconds, hours, days, and years for easy comparison.
- A comparison bar shows how the period stacks up against Earth's orbital period (365.25 days).
Use cases
- Verify planetary periods using Kepler's third law for physics homework.
- Calculate the orbital period of an artificial satellite at a given altitude.
- Compare orbital periods across the Solar System for astronomy education.
- Model hypothetical exoplanet orbits in habitable zone calculations.
- Illustrate why outer planets move more slowly than inner planets.
- Compute geostationary orbit conditions (T = 24 hours).
- Prepare for astronomy olympiad or space science competitions.
- Explore how orbital radius affects period for science fair projects.