Satellite Orbital Altitude Calculator
A circular satellite orbit has a fixed relationship between its period and its altitude, set by Kepler's third law. Give the orbital period and the calculator finds the orbit radius, then subtracts the planet's radius to give the altitude above the surface. It also returns the circular orbital speed. The gravitational parameter and planet radius are user-editable inputs, defaulting to Earth values, so you can model orbits around any body. Enter the period in seconds to see the matching altitude and speed for a circular orbit.
Orbital altitude formula
orbit radius a = cube root( mu * T^2 / (4 * pi^2) )
altitude = a - planet radius
orbital speed = sqrt( mu / a )
T = orbital period in seconds
This is Kepler's third law rearranged for the semi-major axis. For a circular orbit the semi-major axis equals the orbit radius, and the orbital speed follows from the vis-viva relation.
Orbit notes
- The default period 5,400 seconds is a typical low Earth orbit.
- A lower orbit has a shorter period and a higher speed.
- Use km cubed per second squared for mu and km for the radius.
- Outputs assume a circular orbit; elliptical orbits vary in altitude.
- Edit mu and radius to model orbits around other bodies.
Satellite orbit: frequently asked questions
How is orbital altitude found from the period?
Kepler's third law links the orbital period and the orbit radius: the radius equals the cube root of the gravitational parameter times the period squared, divided by four pi squared. Subtracting the planet's radius gives the altitude above the surface. This calculator does both steps for a circular orbit.
What gravitational parameter and radius should I use?
For Earth, the standard gravitational parameter is about 398,600 cubic kilometers per second squared, and the mean radius is about 6,371 kilometers. Both are user-editable inputs so you can model orbits around other bodies using their published values.
What is the orbital speed output?
For a circular orbit the speed equals the square root of the gravitational parameter divided by the orbit radius. The calculator reports this in kilometers per second. A lower orbit is faster; a higher orbit is slower.
Does this assume a circular orbit?
Yes. The altitude and speed outputs are for a circular orbit of the given period. Elliptical orbits have a varying altitude and speed, so for those the period still gives the semi-major axis but not a single altitude.
What period gives a low Earth orbit?
A typical low Earth orbit at a few hundred kilometers altitude has a period of roughly 90 minutes (about 5,400 seconds). Enter your target period in seconds and the calculator returns the matching circular altitude and speed.
Official sources
- NASA Glenn Beginner's Guide to Aeronautics: orbital motion and Kepler's laws.
- NASA NSSDCA: planetary radii and constants.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.