Escape Velocity Calculator
Calculate escape velocity v = √(2GM/r) for any planet, moon, or custom body. Compare orbital velocity and cosmic velocities.
Quick Presets
Select a planet or enter custom M and R, then see escape and orbital velocities instantly.
Escape Velocity
km/s
Orbital Velocity
km/s
Surface Gravity
m/s²
Escape (m/s)
m/s
Escape (mph)
mph
Fraction of c
× speed of light
Three Cosmic Velocities (Earth)
What Is Escape Velocity?
Escape velocity is the minimum speed an object must reach to break free from a gravitational field without any further propulsion. Once an object exceeds this speed, it has enough kinetic energy to overcome the gravitational potential energy binding it to the planet — it will never fall back, even without engines.
Crucially, escape velocity does not depend on the direction of launch (ignoring atmosphere) or on the mass of the escaping object — only on the mass of the body being escaped and the launch radius.
Deriving v = √(2GM/r) from Energy Conservation
At escape velocity the total mechanical energy is exactly zero — kinetic energy equals gravitational potential energy:
Cancel mass m (explaining mass-independence), rearrange:
G = 6.6743×10⁻¹¹ N·m²/kg², M = planet mass (kg), r = distance from center (m). At the surface r = R (planet radius). Adding altitude h gives r = R + h.
Escape Velocity for Every Planet
| Body | v_esc (km/s) | v_orb (km/s) | g (m/s²) |
|---|---|---|---|
| Sun | 617.7 | 436.8 | 274.0 |
| Mercury | 4.25 | 3.01 | 3.70 |
| Venus | 10.36 | 7.33 | 8.87 |
| Earth | 11.19 | 7.91 | 9.81 |
| Moon | 2.38 | 1.68 | 1.62 |
| Mars | 5.03 | 3.55 | 3.72 |
| Jupiter | 59.54 | 42.10 | 24.79 |
| Saturn | 35.49 | 25.10 | 10.44 |
| Pluto | 1.22 | 0.86 | 0.62 |
Orbital vs Escape Velocity
Orbital velocity at radius r is v_orb = √(GM/r). Escape velocity is always √2 ≈ 1.414 times the orbital velocity at the same radius. This means a spacecraft already in orbit at 400 km altitude needs only a 41.4% increase in speed to escape Earth entirely.
Earth Low Orbit (400 km)
Earth Surface
The Three Cosmic Velocities
First Cosmic Velocity — 7.91 km/s
The minimum speed to orbit Earth at its surface. Derived from v = √(GM/R). Any orbital satellite must travel at or above this speed.
Second Cosmic Velocity — 11.19 km/s
Earth's escape velocity. A spacecraft launched at this speed (with no further propulsion) will escape Earth's gravity and continue into interplanetary space.
Third Cosmic Velocity — 16.62 km/s
The speed needed (from Earth's surface, accounting for Earth's orbital velocity around the Sun) to escape the Solar System entirely. Pioneer and Voyager probes exceeded this velocity.
Black Holes and the Schwarzschild Radius
A black hole forms when matter is compressed so densely that the escape velocity exceeds the speed of light c. The Schwarzschild radius is found by setting v_esc = c in the escape velocity formula:
For Earth, r_s ≈ 8.9 mm. For the Sun, r_s ≈ 3 km. At radii smaller than r_s (the event horizon), not even light can escape — hence "black" hole.
Worked Examples
Example 1 — Earth surface
Example 2 — Moon surface
Example 3 — Mars surface
Example 4 — ISS altitude (400 km)