Orbital Velocity Calculator
Enter a central mass and an orbital radius to get the circular orbital velocity in m/s and km/s — the speed a satellite needs to stay in a stable orbit.
m/s and km/s at once
Enter the central mass and the orbital radius and the orbital velocity calculator returns the speed in metres per second and kilometres per second together.
Use SI units
Mass in kilograms and radius in metres give the velocity in metres per second — and measure the radius from the centre of the central body.
What is orbital velocity?
The speed that keeps an orbit stable
The orbital velocity calculator finds the speed a body must travel to hold a stable circular orbit around a central mass. At that speed, gravity supplies exactly the centripetal force needed to keep bending the path into a circle, so the body neither spirals inward nor flies off. It depends only on the central mass and the orbital radius — never on the orbiting body's own mass, which is why a tiny satellite and a heavy space station orbit at the same altitude at the same speed. This is the number behind satellite deployment, the speed of the International Space Station, and how fast a planet sweeps around its star.
Enter a central mass in kilograms and an orbital radius in metres to get the orbital velocity in m/s and km/s instantly.
The circular orbital velocity is the square root of the gravitational constant times the central mass, divided by the orbital radius.
v = √(G × M / r)Here G = 6.6743e-11 N·m²/kg² is the gravitational constant, M is the central mass in kilograms, and r is the orbital radius in metres measured from the centre of the central body. Because r sits in the denominator under the square root, the velocity falls as the orbit grows wider. Divide the m/s result by 1000 to read it in km/s.
Suppose a satellite orbits Earth (M = 5.972e24 kg) at a radius of 6.771e6 m — Earth's radius plus about 400 km, a typical low Earth orbit.
Multiply G by the central mass
6.6743e-11 × 5.972e24 ≈ 3.986e14 — the standard gravitational parameter.
Divide by the orbital radius
3.986e14 / 6.771e6 ≈ 5.887e7 — the squared orbital speed.
Take the square root
√(5.887e7) ≈ 7672 m/s — the orbital velocity, which is about 7.67 km/s.
The formula is exact for an idealised orbit, but a few practical points are worth keeping in mind.
Circular orbits, point masses, and consistent units
This calculator assumes a perfectly circular orbit around a single, much heavier central body treated as a point mass. Real orbits are usually elliptical, where the speed varies along the path, and it ignores atmospheric drag and the pull of other bodies. Measure the radius from the centre of the central body — not its surface — and keep units consistent: kilograms for the mass and metres for the radius, or the velocity will be wrong.