This orbital velocity calculator finds the speed a satellite needs for a circular orbit at any altitude — and its orbital period — around Earth or any other body.
Higher orbit = slower speed but longer period (Kepler’s third law in work clothes): a satellite at geostationary altitude (35,786 km) crawls at 3.07 km/s yet takes exactly one sidereal day — slow speed, vast circle.
v = √(µ ÷ r) — Falling Around a Planet
Gravity supplies exactly the centripetal force a circular orbit needs, and mass cancels again: speed depends only on the body’s gravitational parameter µ = GM and the orbital radius r (from the center — altitude plus body radius, the input error this page refuses to let you make quietly). The period follows from Kepler: T = 2π√(r³/µ). Leaving entirely costs √2× more: our Escape Velocity Calculator. Part of our Physics Calculators collection.
Worked Example (Verified)
- The ISS at 408 km (defaults): r = 6,779 km → v = √(398,600/6,779) = 7.67 km/s, period 92.6 minutes — ~15.6 orbits and 16 sunrises per crew day
- Geostationary (35,786 km): 3.07 km/s, 23 h 56 min — parked over one longitude by moving at exactly Earth’s rotation rate
- GPS constellation (~20,180 km): 3.87 km/s, ~11 h 58 min — half a sidereal day, by design, so ground tracks repeat
- Low lunar orbit (100 km over the Moon): 1.63 km/s, ~118 min — Apollo command modules’ stately pace
Reading an Orbit Like an Engineer
- Speed falls with altitude but energy rises: raising an orbit takes work even though the satellite slows down (potential gains beat kinetic losses).
- Real orbits are ellipses; the circular case here is the reference every elliptical vis-viva calculation (v² = µ(2/r − 1/a)) generalizes from.
- Below ~200 km, atmospheric drag makes orbits decay in days; the “edge of space” is an engineering gradient, not a line.
- Orbital velocity is horizontal velocity — rockets turn sideways as they climb (“gravity turn”) because orbit is a direction as much as a speed.
Related Tools
- Escape Velocity Calculator — the √2 door out
- Centripetal Force Calculator — the force bookkeeping
- Physics Calculators — the full collection
Frequently Asked Questions
How fast is the ISS moving?
About 7.67 km/s (27,600 km/h) at its ~408 km altitude, completing an orbit every 92.6 minutes. This calculator reproduces that from Earth’s µ (398,600 km³/s²) and orbital radius (6,371 + 408 km) — enter any altitude for its figures.
How do you calculate orbital velocity?
v = √(µ/r), where µ = GM of the central body and r is distance from its center (altitude + radius). Period: T = 2π√(r³/µ) — Kepler’s third law. Everything scales from these two: double r, and v falls by √2 while T grows by 2√2.
Why do higher satellites move slower but take longer?
Because gravity weakens with r² while the required centripetal force only needs v²/r: equilibrium settles at v ∝ 1/√r. The period grows twice over — longer circumference and slower speed — compounding to T ∝ r^1.5.
What altitude is geostationary orbit?
35,786 km above the equator, where this calculator’s period equals Earth’s rotation (23 h 56 min 4 s, the sidereal day) at 3.07 km/s. Only equatorial, circular orbits qualify — inclined ones trace figure-eights in the sky instead.
Does satellite mass affect orbital speed?
No (to superb approximation) — mass cancels between gravity’s pull and inertia. A bolt and a space station at the same altitude orbit identically, which is why rendezvous is a game of position and velocity matching, not mass allowances. (Strictly, µ uses the sum of both masses — irrelevant until moons and planets.)
Is this orbital velocity calculator free?
Yes — free, instant, no sign-up.