Earth Orbit Calculator

Enter a satellite's altitude above Earth's surface to find its orbital radius, circular orbital velocity, orbital period, and orbits per day, using Newton's law of gravitation and Kepler's third law.

Quick Facts

Earth's mean radius
R⊕ ≈ 6,371 km (3,959 mi)
Volumetric mean radius; the equatorial radius is slightly larger (6,378.137 km) because Earth bulges at the equator.
Standard gravitational parameter
GM⊕ = 398,600.4418 km³/s²
Product of the gravitational constant G and Earth's mass — known far more precisely than G or M alone.
Circular orbital velocity
v = √(GM⊕ / r)
r is measured from Earth's center: altitude plus Earth's radius, not altitude alone.
Orbital period (Kepler's Third Law)
T = 2π√(r³ / GM⊕)
Depends only on orbital radius, not on the orbiting object's mass.

Your Results

Calculated
Orbital Radius
-
Distance from Earth's center (altitude + Earth's radius)
Orbital Velocity
-
Speed needed for a stable circular orbit
Orbital Period
-
Time for one full revolution
Orbits per Day
-
Revolutions completed in 24 hours

Ready

Enter an orbital altitude and press Calculate.

Formula and Method for Earth Orbit Calculations

A satellite, moon, or spacecraft in a stable circular orbit around Earth is held on its path by the balance between Earth's gravitational pull and the centripetal force needed to keep it moving in a circle. Setting Newton's law of gravitation equal to the centripetal force equation and solving for velocity gives the orbital speed required at any given distance from Earth's center. Combining that speed with the orbit's circumference gives the orbital period — the time for one full revolution. This calculator uses those two relationships, plus Earth's radius, to convert an altitude above the surface into orbital radius, orbital velocity, orbital period, and revolutions per day.

Deriving orbital velocity and period

For an object of mass m orbiting at radius r from Earth's center (mass M⊕), gravity supplies the centripetal force: GM⊕m / r² = mv² / r. The orbiting object's mass cancels out, leaving the circular orbital velocity v = √(GM⊕ / r). Since the orbit's circumference is 2πr, the orbital period is T = 2πr / v, which simplifies to T = 2π√(r³ / GM⊕) — a special case of Kepler's third law for a circular orbit. Here GM⊕ = 398,600.4418 km³/s² is Earth's standard gravitational parameter, and r is the orbital radius (altitude plus Earth's radius), not the altitude alone.

Working with altitude, radius, and units

  • Always add Earth's radius to the altitude before computing velocity or period — using the altitude alone as "r" is the most common mistake and gives badly wrong results.
  • Earth is not a perfect sphere: use the equatorial radius (6,378.137 km) for orbits referenced from the equator, the polar radius (6,356.752 km) for polar orbits, or the mean radius (6,371 km) for a general-purpose estimate.
  • This calculator assumes a circular orbit. For an elliptical orbit, replace r with the semi-major axis a to get the period (Kepler's third law still holds), but the instantaneous velocity varies with position and requires the vis-viva equation instead of v = √(GM⊕/r).

Real-world orbit examples

Low Earth Orbit (LEO) satellites, including the International Space Station near 400 km altitude, complete an orbit in roughly 90 minutes. GPS satellites fly in medium Earth orbit (MEO) near 20,200 km altitude with a period close to 12 hours. Geostationary satellites sit near 35,786 km altitude, where the orbital period matches Earth's 23-hour-56-minute sidereal rotation, so the satellite appears to hang fixed over one point on the equator.

Frequently Asked Questions

What formula does the Earth Orbit Calculator use?
It uses Newton's law of gravitation combined with the centripetal force equation to get the circular orbital velocity v = √(GM⊕ / r), and Kepler's third law to get the orbital period T = 2π√(r³ / GM⊕), where r is the orbital radius (Earth's radius plus altitude) and GM⊕ = 398,600.4418 km³/s² is Earth's standard gravitational parameter.
Why does the calculator add Earth's radius to the altitude?
The formulas require r, the distance from Earth's center to the orbiting object — not the altitude above the surface. A satellite at 400 km altitude orbits at a radius of about 6,771 km once Earth's roughly 6,371 km mean radius is included, and using altitude alone would understate the orbital radius by that amount.
Does this calculator work for elliptical orbits, like the Moon's?
No, it assumes a circular orbit. For an elliptical orbit, Kepler's third law still gives the period from the semi-major axis (T = 2π√(a³/GM⊕)), but the orbital speed changes continuously between perigee and apogee and must be found with the vis-viva equation, v² = GM⊕(2/r − 1/a).
How high does the ISS orbit, and how long does one orbit take?
The International Space Station orbits at roughly 400-420 km altitude, giving an orbital period of about 90-93 minutes and roughly 15.5 orbits per day — figures this calculator reproduces closely when you enter that altitude.

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