About the Orbital Velocity Calculator
This orbital velocity calculator finds the speed a satellite needs to stay in a circular orbit at a chosen altitude, using v = √(GM/r). Pick Earth, the Moon, another planet or the Sun — or enter the mass and radius of a custom body — then type the altitude above the surface. You get the speed in km/s, m/s, km/h and mph, the time for one full orbit, and the escape velocity at the same height for comparison.
It is handy for students checking homework on circular motion and gravitation, space fans wondering how fast the International Space Station really moves, and writers or game designers who want believable numbers for fictional missions. The chart shows how orbital speed falls as you climb higher, which is why geostationary satellites move far more slowly than those in low Earth orbit.
The calculation assumes a circular orbit around a spherical body, ignores atmospheric drag and the satellite’s own mass (which is negligible next to a planet), and uses NASA fact-sheet values for GM and mean radius. Elliptical orbits change speed along the path; use the vis-viva equation for those.
With the default inputs, the orbital velocity is 7.673 km/s. Change any value above to recalculate instantly.
How to use the orbital velocity calculator
- 1Choose the body you are orbiting, or pick Custom and enter its mass and radius.
- 2Enter the orbit altitude above the surface in kilometres.
- 3Read the circular orbital velocity in km/s, m/s, km/h and mph.
- 4Check the orbital period and the escape velocity at that altitude.
- 5Use the chart to see how speed drops as the orbit gets higher.
Formula and method
For a circular orbit, gravity supplies exactly the centripetal force needed to curve the satellite’s path: GMm/r² = mv²/r. The satellite mass m cancels, leaving v = √(GM/r), where r is the distance from the centre of the body (its radius plus the altitude). Higher orbits have larger r, so they are slower.
The period is the circumference divided by the speed, T = 2πr/v, which is equivalent to Kepler’s third law. GM values (km³/s²) and mean radii come from NASA planetary fact sheets; for a custom body GM is computed from the mass with G = 6.6743 × 10⁻¹¹ m³·kg⁻¹·s⁻². Escape velocity at the same distance is √2 times the circular speed.
- v
- Circular orbital velocity
- G
- Gravitational constant, 6.6743 × 10⁻¹¹ m³·kg⁻¹·s⁻²
- M
- Mass of the central body
- r
- Orbit radius from the body’s centre
- R, h
- Body radius and altitude above the surface
- T
- Orbital period
Worked examples
International Space Station (400 km above Earth)
r = 6,371 + 400 = 6,771 km, so v = √(398,600.44 ÷ 6,771) ≈ 7.673 km/s, about 27,600 km/h. One orbit takes 2π × 6,771 ÷ 7.673 ≈ 5,545 s, roughly 92.4 minutes — close to the ISS’s real period.
Geostationary orbit (35,786 km)
At r = 42,157 km the speed is √(398,600.44 ÷ 42,157) ≈ 3.075 km/s, and the period comes out at about 1,435.7 minutes — one sidereal day (23 h 56 min), which is why the satellite stays above one spot.
Low lunar orbit (100 km)
The Moon’s GM is only 4,902.8 km³/s². At r = 1,837.4 km a spacecraft needs about 1.63 km/s and takes just under two hours per lap, similar to the Apollo command module.
400 km above Mars
With GM = 42,828 km³/s² and r = 3,789.5 km, orbital speed is about 3.36 km/s — less than half of Earth’s at the same altitude.
Frequently asked questions
How fast does the ISS travel?+
About 7.66–7.67 km/s, or roughly 27,600 km/h (17,100 mph), completing an orbit about every 92 minutes at around 400–420 km altitude. That works out to about 15.5 orbits per day.
Why do higher orbits move more slowly?+
Gravity weakens with the square of distance, so less speed is needed to balance it. Orbital speed falls as 1/√r — a geostationary satellite moves at about 3.07 km/s versus 7.7 km/s in low Earth orbit.
What is the difference between orbital velocity and escape velocity?+
Orbital velocity √(GM/r) keeps an object circling at a fixed distance. Escape velocity √(2GM/r) is √2 ≈ 1.414 times higher and lets an unpowered object leave the body’s gravity for good.
Does the satellite’s mass affect orbital velocity?+
No. The satellite’s mass appears on both sides of the force balance and cancels. A small cubesat and the ISS at the same altitude travel at the same speed, ignoring differences in drag.
Is this the same as the speed needed to reach orbit?+
Not quite. Reaching low Earth orbit takes about 9.3–10 km/s of rocket delta-v, because the rocket must also climb, fight gravity during ascent and overcome air drag. Use the rocket equation calculator for that.