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Orbital Velocity Calculator

Find the orbital velocity.

How it is calculated

For a circular orbit the pull of gravity supplies the centripetal force, which gives v = √(G·M ÷ r). Here G = 6.674×10−11 m³·kg−1·s−2 is fixed inside the tool, M is the mass of the body being orbited in kilograms, and r is the orbital radius in metres.

The radius is measured from the centre of the central body, so it equals the body's own radius plus the altitude. Scientific notation such as 5.972e24 is accepted. The speed is shown in m/s rounded to a whole number and in km/s with two decimals. The radius must be above zero. The mass of the orbiting object does not appear in the formula and is assumed to be negligible compared with M.

Worked example

A satellite orbits Earth (M = 5.972×1024 kg) about 400 km above the surface. Earth's radius is roughly 6,371 km, so r = 6,371,000 + 400,000 = 6,771,000 m.

G·M = 6.674×10−11 × 5.972×1024 ≈ 3.986×1014. Divide by r: 3.986×1014 ÷ 6.771×106 ≈ 5.886×107. The square root is about 7,672 m/s, or 7.67 km/s.

Try this example →

Common mistakes

  • Entering the altitude as the radius. Typing 400 gives nearly 1,000 km/s; add the central body's radius first.
  • Entering the radius in kilometres. The field is in metres, so 6,771 km must be typed as 6771000.
  • Entering the mass in tonnes or in Earth masses. It must be in kilograms.
  • Putting the satellite's own mass in the mass field. Only the mass of the body being orbited counts.
  • Using the result for an elliptical orbit. It is the speed of a perfectly circular orbit at that radius only.

About this calculator

This calculator finds circular orbital velocity using v = √(GM/r), where G is the gravitational constant, M is the mass of the body being orbited, and r is the orbital radius. The result is the exact speed needed to maintain a stable circular orbit at that distance.

Aerospace engineers use it when planning satellite orbits, astronomy students use it to work out how fast planets or moons move, and space enthusiasts use it to check how orbital speed changes with altitude — the higher the orbit, the slower the required velocity.

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