Escape Velocity Calculator
Calculate the escape velocity for any celestial body from its mass and radius.
Includes presets for Earth, Moon, Mars, Jupiter, and the Sun for comparison.
Escape Velocity
How Escape Velocity Is Calculated
Escape velocity is the minimum speed an object needs to break free from a planet’s gravitational field without further propulsion.
Escape Velocity Formula:
v_esc = √(2GM / r)
Where:
- v_esc = escape velocity in m/s
- G = gravitational constant = 6.674 × 10⁻¹¹ N·m²/kg²
- M = mass of the planet/body in kg
- r = radius (distance from center) in meters
Worked Example — Earth:
- M = 5.972 × 10²⁴ kg
- r = 6.371 × 10⁶ m (mean radius)
- v_esc = √(2 × 6.674×10⁻¹¹ × 5.972×10²⁴ / 6.371×10⁶)
- v_esc = √(7.972×10⁷) = 11,186 m/s ≈ 11.2 km/s
Escape Velocity Comparison:
| Body | Escape Velocity |
|---|---|
| Moon | 2.38 km/s |
| Mars | 5.03 km/s |
| Earth | 11.19 km/s |
| Saturn | 35.5 km/s |
| Jupiter | 59.5 km/s |
| Sun | 617.5 km/s |
| Neutron star | ~200,000 km/s |
| Black hole | ≥ c (300,000 km/s) |
Key Facts:
- Direction doesn’t matter — escape velocity is the same straight up or at any angle
- It is the speed, not the acceleration, that determines escape
- SpaceX Falcon 9 reaches ~9.4 km/s in orbit (below escape velocity by design)
- The Moon has no atmosphere because light gases (H₂, He) exceed lunar escape velocity