# Orbital Period Calculator (Kepler’s Third Law)

URL: https://speedycalculator.com/calculators/physics/orbital-period/
Last updated: 2026-10-25

> The orbital period calculator uses Kepler’s third law to find how long a satellite or planet takes to complete an orbit, from the central body’s mass and the orbit’s semi-major axis.

## Inputs

- Central body mass (kg)
- Semi-major axis (from centre) (m, km, AU)

## Results

- Orbital period
- Mean orbital speed

## Formula

```
T = 2π √(a³ ÷ GM)
```

## Explanation

Kepler found that the square of a planet’s orbital period is proportional to the cube of its distance from the Sun.

### How to use the Orbital Period Calculator

- **Central body mass**
- **Semi-major axis (from centre)**
- Want to work backwards? Type a value into **Orbital period** and **Semi-major axis (from centre)** is calculated for you.

Results update as you type, and every field accepts the units shown in its menu.

### How it works

Cube the semi-major axis, divide by G times the central mass, take the square root and multiply by 2π.

### Inputs explained

FieldWhat to enterCentral body massIn kgSemi-major axis (from centre)Units: m, km, AU

### What each result means

- **Orbital period** = 2×pi×sqrt([Semi-major axis (from centre)]^3 ÷ (6.6743e-11 × [Central body mass]))
- **Mean orbital speed** = 2×pi×[Semi-major axis (from centre)] ÷ [Orbital period]

### Example values

How the main result changes when **Semi-major axis** changes and everything else stays at the example values above:

Semi-major axis (from centre) (m)Orbital period (min)3,385,50032.675,078,25060.036,771,00092.428,463,750129.1510,156,500169.7813,542,000261.39

## Worked example

Inputs — Central body mass: 5.972e+24 kg; Semi-major axis (from centre): 6,771,000 m.

Results — **Orbital period = 92.42 min**; Mean orbital speed = 7.67 km/s.

## FAQ

**Why use distance from the centre?**
Kepler’s law uses the distance from the centre of the central body, not altitude.

**How long does the ISS take to orbit?**
About 92 minutes at roughly 400 km altitude.

**What formula does the Orbital Period Calculator use?**
T = 2π √(a³ ÷ GM).

**Can I work backwards from the result?**
Yes. Type the result you want into Orbital period and the calculator finds the matching semi-major axis (from centre).