Orbital Velocity Calculatorv = √(GM ÷ r) · T = 2πr ÷ v
A satellite in a circular orbit moves at v = √(GM ÷ r), where r is its distance from the planet’s centre, and completes one orbit in T = 2πr ÷ v. The ISS at 408 km travels at about 7.66 km/s and circles Earth every 92.7 minutes. Find the speed and period at any altitude, or the altitude needed for a period, such as a geostationary orbit, around Earth, the Moon, Mars or any body.
Formula verified against OpenStax — University Physics, Volume 1 · NASA NSSDC — Planetary Fact Sheet
By Manzoor Ahmad · Pharmacist & calculator developerReviewed & updated
Planet & orbit
Earth: M = 5.9722 × 10²⁴ kg, equatorial radius 6,378.137 km.
Step-by-step working
What is orbital velocity?
Orbital velocity is the speed a satellite needs to stay in a stable orbit, falling around a planet without hitting it or flying away. For a circular orbit, gravity provides exactly the centripetal force the curved path needs.
Newton pictured a cannon on a mountain firing faster and faster until its ball fell around the Earth. Today the same maths places space stations, GPS satellites and the geostationary communications belt.
Quick answers
How fast does the ISS travel?
About 7.66 km/s (27,600 km/h, 17,100 mph), circling Earth about 15.5 times a day.
What altitude is a geostationary orbit?
35,786 km above the equator, where the period matches Earth’s 23 h 56 min sidereal day, so the satellite hovers over one spot. Use the Altitude for a period tab.
How do you calculate an orbital period?
T = 2π√(r³ ÷ GM). Doubling the orbit radius increases the period by 2√2 ≈ 2.83×, which is Kepler’s third law.
What is the difference between orbital and escape velocity?
Escape velocity is √2 (≈ 1.414) times the circular orbital velocity at the same radius. Near Earth’s surface that is 7.9 km/s against 11.2 km/s. See our escape velocity calculator.
Orbital velocity formula
For circular orbits. r = planet radius + altitude. Earth’s GM = 3.986 × 10¹⁴ m³/s².
| Symbol | Meaning | SI unit |
|---|---|---|
| v | Orbital speed | m/s |
| G | Gravitational constant | N·m²/kg² |
| M | Mass of the central body | kg |
| r | Orbit radius (from the centre) | m |
| T | Orbital period | s |
| h | Altitude above the surface | m |
How to calculate orbital velocity
- Add the altitude to the planet’s radius to get r from the centre.
- Multiply G by the planet’s mass (GM).
- Divide GM by r and take the square root for the speed.
- Divide the circumference 2πr by v for the period.
Worked example: the International Space Station
The ISS orbits about 408 km above Earth’s equatorial radius of 6,378 km.
v = √(3.986 × 10¹⁴ ÷ 6.786 × 10⁶) = 7.664 km/s ≈ 27,590 km/h
T = 2π × 6.786 × 10⁶ ÷ 7,664 = 5,563 s ≈ 92.7 min
For a geostationary orbit (T = 1 sidereal day) r = 42,164 km, an altitude of 35,786 km, at just 3.07 km/s.
Orbital speeds and periods around Earth
| Orbit | Altitude | Speed | Period |
|---|---|---|---|
| ISS | ≈ 408 km | 7.66 km/s | 92.7 min |
| Starlink | ≈ 550 km | 7.59 km/s | 95.6 min |
| GPS | 20,200 km | 3.87 km/s | ≈ 11 h 58 min |
| Geostationary | 35,786 km | 3.07 km/s | 23 h 56 min |
| Moon | ≈ 378,000 km | ≈ 1.02 km/s | 27.3 days |
Common mistakes to avoid
- Using the altitude instead of the radius. r is measured from the planet’s centre.
- Thinking faster means higher. Lower orbits are faster; to climb, a spacecraft speeds up first, then ends up slower.
- Ignoring drag in very low orbits. Below about 300 km, thin air quickly decays the orbit.
Manzoor Ahmad
Pharmacist turned Web Developer & Calculator Engineer · 13+ years in web developmentI’m a pharmacist by training who turned into a full-time tech geek, and for 13+ years I’ve designed and coded web tools. My pharmacy degree included physical pharmacy and pharmaceutics — states of matter, heat, flow and reaction kinetics — so the physics behind these tools is familiar ground, not a new hobby.
I’m not a physicist, so I don’t ask you to take my word for it: every formula on this page is traced to an open university textbook or NIST reference data, and the calculator is tested against published worked examples before it goes live. Spot an error? Tell me and it will be fixed and dated on the next update.
Orbital Velocity Calculator: frequently asked questions
v = √(GM ÷ r) for a circular orbit of radius r around a body of mass M.
No. The satellite’s mass cancels out, so a pebble and the ISS at the same altitude move at the same speed.
About 7.9 km/s, called the first cosmic velocity.
Gravity weakens with distance, so less speed is needed to balance it.
The square of the orbital period is proportional to the cube of the orbit radius: T² = 4π²r³ ÷ GM.
References & sources
- OpenStax — University Physics, Volume 1 — Ch. 13.4, Satellite Orbits and Energy
- NASA NSSDC — Planetary Fact Sheet — planetary masses and radii
- NASA — International Space Station facts — ISS orbit parameters
Disclaimer: This calculator is an educational tool built on idealised textbook models. It is not a substitute for professional engineering or safety calculations.