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Orbital Period Calculator

Calculate orbital period from semi-major axis using Kepler’s third law.

About Orbital Period Calculator

Kepler’s third law states that the square of the period is proportional to the cube of the semi-major axis. That relationship fixes the geostationary radius at about 42,164 km for Earth. The cube-root dependence means large changes in altitude produce modest changes in period, which is why geostationary orbit sits so far out.

Formula

Orbital Period

T = 2π √(a³ ÷ GM)

a
Semi-major axis of the orbit
GM
Standard gravitational parameter of the body

Worked example

With the default values below, Orbital Period Calculator returns Orbital Period of 92.418. Change any input above and every figure here is recalculated in your browser.

Inputs used

Mass of the central bodyminimum 1 kg
5,972,000,000,000,000,000,000,000 kg
Semi-major axisminimum 1 m
6,771,000 m

Results

Orbital Period
92.418 min
Orbital Period
1.5403 h
Orbital Period
5,545.1 s
Mean Orbital Velocity
7,672.32 m/s
Radius for a 24-Hour Orbit
42,163,112 m

Step by step

  1. 1Values used
  2. 2Orbital Period
  3. 3Orbital Period= 92.418 min
  4. 4Orbital Period= 1.5403 h
  5. 5Orbital Period= 5,545.1 s
  6. 6Mean Orbital Velocity= 7,672.32 m/s
  7. 7Radius for a 24-Hour Orbit= 42,163,112 m

Assumptions and limits

  • The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is Orbital Period calculated?

T = 2π √(a³ ÷ GM) Kepler’s third law states that the square of the period is proportional to the cube of the semi-major axis. That relationship fixes the geostationary radius at about 42,164 km for Earth.

Why does Orbital Period matter?

The cube-root dependence means large changes in altitude produce modest changes in period, which is why geostationary orbit sits so far out.

What values do I need to enter?

This calculator takes 2 inputs: Mass of the central body, Semi-major axis. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.

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