Orbital Velocity Calculator
Compute the speed, period, and angular speed of an object in a circular orbit from the central mass and orbital radius.
kg
m
Speed needed to maintain a circular orbit
- 1
G × M
6.674 × 10⁻¹¹ × 5,972,000,000,000,000,000,000,000 = 398,571,280,000,000 - 2
G × M ÷ r
398,571,280,000,000 ÷ 6,771,000 = 58,864,463.1517 - 3
Orbital speed v = √(G × M ÷ r)
√58,864,463.1517 = 7,672.32The speed at which gravitational pull exactly provides the centripetal acceleration.
How does this calculator work?
Orbital velocity for a circular orbit is v = √(G·M/r), where G = 6.674×10⁻¹¹, M is the central mass in kg, and r is the orbital radius in meters. The period is T = 2π·√(r³/(G·M)) and angular speed is ω = v/r. The orbiting object's own mass does not affect the result.
Formula
How this is calculated
For a circular orbit, gravity supplies exactly the centripetal force needed to keep the orbiting body on its path. Setting G·M·m/r² equal to m·v²/r and cancelling the orbiting mass m gives the orbital speed v = √(G·M / r), where G = 6.674×10⁻¹¹ N·m²/kg² is the gravitational constant, M is the central mass in kilograms, and r is the orbital radius in meters measured from the center of the central body.
The orbital period follows from the circumference 2πr divided by v, which simplifies to T = 2π·√(r³ / (G·M)) — a statement of Kepler's third law. The angular speed is ω = v / r in radians per second. Speed is reported in both m/s and km/s, and the period in both seconds and hours for convenience.
This model assumes a perfectly circular orbit, a point-mass (or spherically symmetric) central body, and that the orbiting mass is negligible compared with M. It ignores atmospheric drag, oblateness, and the gravity of other bodies. Both M and r must be positive; r is measured from the center, so for a surface-skimming orbit use the central body's radius plus altitude.
Frequently asked questions
No. The orbiting mass cancels out of the equation, so a small satellite and a large one at the same radius around the same body travel at the same speed.
Use Earth's radius (~6.371×10⁶ m) plus the altitude. For example, a 400 km orbit uses r ≈ 6.771×10⁶ m.
It is the same physical time, just different units. The calculator shows both so you can quickly relate short orbits (minutes to hours) to longer ones.
Also known as
TG we-Calculate Editorial Team. (2026). Orbital Velocity Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/orbital-velocity-calculator
TG we-Calculate Editorial Team. "Orbital Velocity Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/orbital-velocity-calculator.
TG we-Calculate Editorial Team, "Orbital Velocity Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/orbital-velocity-calculator
@misc{wecalculate_orbital_velocity_calculator, title = {Orbital Velocity Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/orbital-velocity-calculator}}, year = {2026}, note = {TG we-Calculate} }
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