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Orbital Period Calculator
Calculate how long one orbit takes with Kepler’s third law, T = 2π√(a³/GM). Pick the Sun, Earth or another planet, enter the orbit size as a semi-major axis or an altitude above the surface, and get the period, orbital speed and the full working.
Last updated:
Central body
kg
Scientific notation is fine, e.g. 5.97e24
kg
Leave empty for a small satellite; enter it for two massive bodies (e.g. the Moon)
Orbit size
Enter the orbit as
Enter your values to see the result.
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How to use the Orbital Period Calculator
- Choose the central body, or Custom and type its mass in kg.
- Choose how to give the orbit: semi-major axis, or altitude above the surface for a circular orbit.
- Enter the distance and pick its unit.
- Add the orbiting mass only if it is significant (a moon or planet).
- Read the period, speed and working, and see how it changes with distance in the table.
The orbital period formula
T = 2π √( a³ / G(M + m) )
T is the period in seconds, a the semi-major axis in metres, G the gravitational constant and M + m the combined mass of the two bodies. Rearranged, the semi-major axis for a wanted period is a = ∛( G(M + m) T² / 4π² ). The circular orbital speed at distance a is v = √( G(M + m) / a ), and the escape speed is √2 times that.
Reference orbits
| Orbit | Semi-major axis | Period |
|---|---|---|
| International Space Station | ~6,791 km (420 km altitude) | ~92.8 min |
| GPS satellites | 26,560 km | ~11 h 58 min (half a sidereal day) |
| Geostationary orbit | 42,164 km | 23 h 56 min |
| The Moon around Earth | 384,400 km | 27.32 days (sidereal) |
| Mercury around the Sun | 0.387 AU | 88.0 days |
| Earth around the Sun | 1.000 AU | 365.26 days |
| Mars around the Sun | 1.524 AU | 687 days (1.88 yr) |
| Jupiter around the Sun | 5.203 AU | 11.86 years |
| Neptune around the Sun | 30.07 AU | 164.8 years |
Standard gravitational parameters used
| Body | GM (m³/s²) | Mean radius |
|---|---|---|
| Sun | 1.32712440018 × 10²⁰ | 695,700 km |
| Earth | 3.986004418 × 10¹⁴ | 6,371 km |
| Moon | 4.9048695 × 10¹² | 1,737.4 km |
| Venus | 3.24858592 × 10¹⁴ | 6,051.8 km |
| Mars | 4.282837 × 10¹³ | 3,389.5 km |
| Jupiter | 1.26686534 × 10¹⁷ | 69,911 km |
| Saturn | 3.7931187 × 10¹⁶ | 58,232 km |
Frequently asked questions
What is Kepler's third law?
The square of the orbital period is proportional to the cube of the semi-major axis: T² = 4π²a³ / G(M + m). For planets around the Sun, T in years and a in AU gives the simple form T² ≈ a³.
How long does the ISS take to orbit Earth?
At about 420 km altitude the semi-major axis is about 6,791 km, giving a period of roughly 92.8 minutes, about 15.5 orbits per day.
What altitude gives a 24-hour orbit?
A sidereal day (23 h 56 min) needs a semi-major axis of 42,164 km, about 35,786 km above the equator. That is the geostationary orbit used by many communication satellites.
Does the satellite's mass change the period?
Only slightly, through the M + m term. For artificial satellites m is negligible. For the Moon (about 1.2% of Earth's mass) or Jupiter around the Sun it changes the result by a small but measurable amount.
Does the shape of the orbit matter?
No. For an elliptical orbit the period depends only on the semi-major axis (half the longest diameter), not on the eccentricity. The speed shown is the circular-orbit speed at that distance.
What value of G is used?
G = 6.67430 × 10⁻¹¹ m³ kg⁻¹ s⁻² (CODATA 2018). For the preset bodies the calculator uses their measured standard gravitational parameters GM, which are known far more precisely than G or M separately.
Are all the tools on FreeToolCabin tested for quality and accuracy?
Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.
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