How the Escape Velocity Calculator works
Escape velocity describes the ideal speed needed to leave a spherical body’s gravity without further propulsion, ignoring atmosphere and rotation. The core relationship used here is vₑ = √(2GM/r). Using Earth-unit mass and radius makes comparison between worlds straightforward. If you are building a complete observing or imaging setup, use the Orbital Velocity Calculator alongside this page rather than treating one number in isolation.
Worked example and interpretation
Earth’s surface escape velocity is about 11.2 km/s, while the Moon’s is about 2.4 km/s.
For broader physical context, the NASA Planetary Fact Sheet is a useful external reference.
When this calculator is useful
Use it to compare planets and moons, understand gravity wells and distinguish escape speed from circular orbital speed.
When the result involves angular size, field, observing conditions or a current target, continue with Weight on Planets Calculator. For a different but related perspective, Orbital Period Calculator can connect the formula to an actual observing, telescope or Solar System context.
Diagrams
Assumptions, accuracy and practical limits
A real rocket does not need to instantaneously reach this speed. Mission delta-v depends on thrust, staging, trajectory, atmosphere, rotation and where propulsion is applied.
A second external cross-check is available from NASA Solar System. Not for operational or published work.
Reference table: escape and circular speeds at the surface
| Body | Escape velocity | Circular speed at surface |
|---|---|---|
| Earth | 11.19 km/s | 7.91 km/s |
| Moon | 2.38 km/s | 1.68 km/s |
| Mars | 5.03 km/s | 3.55 km/s |
| Jupiter | 59.53 km/s | 42.10 km/s |
| Sun | 617.67 km/s | 436.76 km/s |
The Moon’s 2.38 km/s explains why lunar landers need far less propellant than Earth launchers, and why its thin exosphere cannot be retained.
Related SpaceTracker.live tools
Continue with Orbital Velocity Calculator, Weight on Planets Calculator and Orbital Period Calculator.
Worked scenarios: escaping from orbit instead of the ground
Escape velocity is √2 (about 1.414) times the circular speed at the same radius. At 400 km altitude the circular speed is 7.67 km/s and the escape speed is 10.85 km/s, so a spacecraft already in low orbit needs about 3.18 km/s extra to leave Earth’s gravity.
Using v = √(2gR), Earth gives 353.49 km/s and Mars (g = 3.71 m/s², R = 3,389.5 km) gives 158.59 km/s. A gas molecule can escape if its speed exceeds this, which is why the Moon (2.38 km/s) has almost no atmosphere.
Common mistakes and body comparison
- Confusing escape with orbital speed. Escape speed is √2 times the circular speed at the same distance.
- Using the wrong radius. Use the distance from the body’s centre, not its altitude.
- Thinking escape needs a constant push. The speed is a one-time value for a ballistic path; a rocket with continuous thrust can escape at any speed.
| Body | Escape velocity |
|---|---|
| Ceres | 0.51 km/s |
| Moon | 2.38 km/s |
| Pluto | 1.21 km/s |
| Mars | 5.03 km/s |
| Earth | 11.19 km/s |
| Neptune | 23.5 km/s |
| Jupiter | 59.5 km/s |
| Sun | 617.5 km/s |
More questions answered
Why can the Moon not hold an atmosphere?
Its escape velocity is only 2.38 km/s, so light gases escape into space; Earth’s 11.19 km/s retains most gases.
Do rockets reach escape velocity at launch?
No. Rockets climb gradually and reach it only high above the surface, at the end of a continued burn.
Frequently asked questions
Does escape velocity depend on the mass of my spacecraft?
No. It depends on the body’s mass and the starting radius only.
Does a rocket need to reach escape velocity in one burn?
No. Rockets climb continuously, so escape velocity is a theoretical energy threshold, not a speed they must reach instantly.
Why is the Sun’s value so large?
Escape velocity from the Sun’s surface is about 617 km/s because of its enormous mass; from Earth’s orbit it is only about 42 km/s.