Escape velocity calculator
This escape velocity calculator works out the speed needed to leave a planet or moon from its mass and radius: 11.18 km/s for Earth. Pick a body and an altitude, or enter your own values.
Example: Celestial body: Earth · Altitude above the surface 0 km → Result: Escape velocity: 11.18 km/s (40,248 km/h). Source: Wikipedia – Kosmische Geschwindigkeit (Fluchtgeschwindigkeit, Kreisbahngeschwindigkeit). Updated: .
How it is calculated
Escape velocity v = √(2·G·M/r). For Earth it is 11.18 km/s (about 40,250 km/h), for the Moon 2.38 km/s and for Mars 5.02 km/s.
What escape velocity means
It is the speed at which an unpowered object leaves a gravitational field without ever falling back. It depends only on the mass M of the body and the distance r from its centre, not on the mass of the object. It drops with altitude because r grows.
Circular orbit and orbital period
The speed of a circular orbit is √(G·M/r), which is the escape velocity divided by √2. At 400 km above Earth that is 7.67 km/s and one lap takes about 92.6 minutes. The calculator also shows the gravitational acceleration at that altitude and the Schwarzschild radius, the radius to which a body would have to shrink for not even light to escape (about 9 mm for Earth).
- Rockets do not need to reach escape velocity in one go; it only describes unpowered ballistic paths.
- For gas giants the radius is taken at one bar of pressure.
Frequently asked questions
What is the escape velocity of Earth?
About 11.18 km/s, or roughly 40,250 km/h. You get it from v = √(2·G·M/r) with M = 5.972·10²⁴ kg and r = 6,378 km.
How do you calculate escape velocity?
With v = √(2·G·M/r). G is the gravitational constant 6.6743·10⁻¹¹ m³/(kg·s²), M the mass of the body and r the distance from its centre.
Why is the orbital speed lower?
A circular orbit needs only 1/√2 (about 71 %) of the escape velocity. Exceeding it by 41 % lets you leave the gravitational field.
Sources and legal basis
- Wikipedia – Kosmische Geschwindigkeit (Fluchtgeschwindigkeit, Kreisbahngeschwindigkeit)
- Wikipedia – Escape velocity
- NASA Planetary Fact Sheet – masses and equatorial radii of the celestial bodies
- Wikipedia – Schwarzschild-Radius
As of: · Editorial policy
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