Earth Orbit Calculator — Orbital Velocity & Period
Enter an altitude above Earth's surface to instantly calculate the orbital velocity, period, revolutions per day, and escape velocity for a circular orbit. Useful for satellites, the ISS, GPS constellations, and geostationary orbit calculations.
km
Speed required to maintain a circular orbit at this altitude
- 1
Orbital radius r = R_Earth + altitude
6,371 + 400 km = 6,771R_Earth = 6,371 km (WGS-84 mean radius). - 2
Orbital velocity v = √(μ ÷ r)
√(3.986 × 10¹⁴ ÷ 6,771,000) ÷ 1000 = 7.673μ = G × M_Earth = 3.986 × 10¹⁴ m³/s²; divided by 1000 to convert m/s → km/s.
How does this calculator work?
For a circular orbit at altitude h: orbital radius r = R_Earth + h, orbital velocity v = √(μ/r) ≈ 7.9 km/s at the surface, and period T = 2π√(r³/μ). Higher orbits move slower and have longer periods. The ISS at 400 km completes ~15.5 orbits/day at 7.66 km/s. μ = 3.986 × 10¹⁴ m³/s² is Earth's gravitational parameter.
Formula
How this is calculated
A satellite in a circular orbit moves fast enough that Earth's gravitational pull continuously curves its path into a closed circle. The required speed is found by equating gravitational and centripetal acceleration: g = μ/r² = v²/r, giving orbital velocity v = √(μ/r). Here μ = G × M_Earth = 3.986 004 418 × 10¹⁴ m³/s² is Earth's standard gravitational parameter (IERS 2010) and r = R_Earth + altitude is the orbital radius from Earth's centre (using the WGS-84 mean radius of 6 371 km).
Orbital period T = 2π × r / v = 2π √(r³/μ) follows from the circumference divided by speed. This is a special case of Kepler's third law. At 400 km altitude (ISS), v ≈ 7.66 km/s and T ≈ 92 minutes. At geostationary altitude (35 786 km), T = 24 hours exactly — the satellite stays above a fixed point on the equator. GPS satellites orbit at about 20 200 km with a period of roughly 12 hours (completing exactly 2 orbits per sidereal day).
Escape velocity from any orbital radius is simply v × √2 — the speed needed to escape Earth's gravity well from that altitude rather than orbiting. This model assumes a perfectly circular, equatorial orbit in a vacuum with Earth as a perfect uniform sphere; atmospheric drag (significant below ~500 km), the Earth's oblateness (J2 perturbation), and lunar/solar perturbations are not included.
Frequently asked questions
Orbital velocity is v = √(μ/r) — it decreases with the square root of the orbital radius. Higher orbits are farther from Earth's centre, so gravity is weaker and less centripetal acceleration is needed to maintain the circular path. The ISS at 400 km travels at ~7.66 km/s; a geostationary satellite at 35 786 km travels at only ~3.07 km/s.
A geostationary orbit (GEO) is a circular equatorial orbit at exactly 35 786 km altitude, where the orbital period equals Earth's rotation period (~24 hours). A satellite there appears stationary over one point on the equator, making it ideal for communications, weather, and TV broadcasting. Enter 35 786 km in the calculator — you should get a period of exactly 24 hours.
Orbital velocity (v = √(μ/r)) is the speed for a stable circular orbit at altitude r. Escape velocity (v_esc = √(2μ/r) = v × √2) is the speed needed to escape Earth's gravity entirely from that altitude, asymptotically reaching infinite distance with zero residual speed. Escape velocity is always about 41.4% higher than orbital velocity at the same radius.
TG we-Calculate Editorial Team. (2026). Earth Orbit Calculator — Orbital Velocity & Period [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/earth-orbit-calculator
TG we-Calculate Editorial Team. "Earth Orbit Calculator — Orbital Velocity & Period." TG we-Calculate. 2026. https://we-calculate.com/calculator/earth-orbit-calculator.
TG we-Calculate Editorial Team, "Earth Orbit Calculator — Orbital Velocity & Period," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/earth-orbit-calculator
@misc{wecalculate_earth_orbit_calculator, title = {Earth Orbit Calculator — Orbital Velocity & Period}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/earth-orbit-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?