Escape velocity calculator
Escape velocity is the minimum speed an object needs to break free from a body’s gravity with no further thrust — the threshold at which kinetic energy equals gravitational potential energy. Crucially it depends only on the body you’re leaving, not on the object leaving it. This tool computes it for any planet, moon or star.
How it works
The calculator uses the standard formula v = √(2GM / r), where G is the gravitational constant 6.6743×10⁻¹¹ m³·kg⁻¹·s⁻², M is the body’s mass in kilograms and r is its radius in metres. Pick a preset to load real figures, or type your own values (scientific notation like 5.972e24 works). The result is shown in m/s, km/s and km/h. Because mass is inside a square root, doubling a body’s mass raises escape velocity by only about 41%.
Worked example: Earth
For Earth (M = 5.972×10²⁴ kg, r = 6.371×10⁶ m):
v = √(2 × 6.6743×10⁻¹¹ × 5.972×10²⁴ / 6.371×10⁶)
= √(1.253×10⁸)
≈ 11,186 m/s
≈ 11.2 km/sPreset body comparison
| Body | Mass (kg) | Mean radius (m) | Escape velocity |
|---|---|---|---|
| Moon | 7.342×10²² | 1.737×10⁶ | ≈ 2.4 km/s |
| Mars | 6.39×10²³ | 3.39×10⁶ | ≈ 5.0 km/s |
| Earth | 5.972×10²⁴ | 6.371×10⁶ | ≈ 11.2 km/s |
| Jupiter | 1.898×10²⁷ | 7.149×10⁷ | ≈ 59.5 km/s |
| Sun | 1.989×10³⁰ | 6.96×10⁸ | ≈ 618 km/s |
The Moon’s escape velocity of about 2.4 km/s is why the Apollo missions needed relatively modest ascent stages to lift off from the surface — about one-fifth the speed needed to leave Earth. Jupiter’s enormous mass pushes its escape velocity to over 59 km/s despite its large radius.
What escape velocity tells you in practice
- Spacecraft design. To leave Earth without any subsequent thrust, a craft would need to reach approximately 11.2 km/s at the surface. In practice, rockets burn continuously over minutes rather than achieving this speed instantly, which is why the effective required velocity is lower — but the concept sets the energy budget for the mission.
- Atmospheric retention. Gas molecules in a planet’s atmosphere escape if they exceed the escape velocity. Lighter gases like hydrogen and helium have high thermal speeds and escape more easily from lower-gravity bodies, which is why small planets like Mars have thin atmospheres and the Moon has essentially none.
- Black holes. A black hole is a body where the escape velocity from the surface (the Schwarzschild radius) equals or exceeds the speed of light. Nothing — not even light — can escape, which is why it is black.
- Custom bodies. Enter your own mass and radius to find the escape velocity of hypothetical or exoplanetary bodies. For a neutron star (mass ≈ 2 solar masses, radius ≈ 10 km), the escape velocity approaches a significant fraction of the speed of light.
Common misunderstanding
Escape velocity is not the speed needed to reach orbit — that is a different and lower threshold. To remain in a stable low circular orbit around Earth you need about 7.9 km/s. Escape velocity (11.2 km/s) is the speed needed to leave entirely with no further thrust. Orbital velocity and escape velocity are related by a factor of √2.
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