What Is Escape Velocity and How Is It Calculated?
Escape velocity is the minimum speed an object must reach to break free from the gravitational pull of a body without further propulsion, ignoring air resistance. At Earth's surface it is about 11.186 km/s (40,270 km/h), and it depends only on the body's mass and the distance from its center, not on the escaping object's mass.
The escape velocity formula, derived from Newton's law of universal gravitation and conservation of energy, is: v = √(2 × G × M ÷ r), where v is escape velocity in m/s, G is the gravitational constant (6.6743 × 10⁻¹¹ N·m²/kg², CODATA 2018), M is the mass of the body in kg, and r is the distance from the body's center in metres. It is exactly √2 times the circular orbital speed at the same distance.
According to NASA, the Moon's escape velocity is only 2.38 km/s, about one fifth of Earth's, which is why the Apollo lunar module needed far less propellant to leave the Moon than the Saturn V needed to leave Earth. The Soviet Luna 1 probe became the first spacecraft to exceed Earth's escape velocity in January 1959.
How to Use This Escape Velocity Calculator
Choose a body or enter your own values; results update instantly:
- Celestial body: Select a planet, the Moon, Pluto or the Sun to fill in its mass and mean radius automatically. Editing mass or radius switches to "Custom body".
- Mass (kg): Accepts scientific notation such as 5.972e24 for Earth.
- Radius (km): The mean radius of the body, measured from its center to the surface.
- Altitude (km): Height above the surface. Escape velocity falls as you climb, because r grows. At the ISS altitude of about 420 km, it is roughly 10.8 km/s.
All inputs use SI-based units (kg and km), which are the standard in physics and astronomy worldwide. Results are shown in km/s, m/s, km/h and mph so they suit both metric and US readers.
Escape Velocity of Planets and Other Bodies
The table below lists surface escape velocities calculated with this escape velocity calculator, using mean radii from NASA planetary fact sheets.
| Body | Escape velocity (km/s) | vs Earth |
|---|---|---|
| Pluto | 1.21 | 0.11× |
| Moon | 2.38 | 0.21× |
| Mercury | 4.25 | 0.38× |
| Mars | 5.03 | 0.45× |
| Venus | 10.36 | 0.93× |
| Earth | 11.19 | 1.00× |
| Uranus | 21.4 | 1.91× |
| Neptune | 23.6 | 2.11× |
| Saturn | 36.1 | 3.23× |
| Jupiter | 60.2 | 5.38× |
| Sun | 617.8 | 55.2× |
A black hole is an object whose escape velocity at the event horizon equals the speed of light, 299,792 km/s. Setting v = c in the formula gives the Schwarzschild radius r = 2GM/c², which this calculator also reports for your chosen mass (about 8.9 mm for Earth).
Frequently Asked Questions
What is the escape velocity of Earth?
The escape velocity of Earth at sea level is 11.186 km/s, which is about 40,270 km/h or 25,020 mph. It decreases with altitude, falling to roughly 10.8 km/s at the altitude of the International Space Station.
What is the difference between escape velocity and orbital velocity?
Orbital velocity is the speed needed to stay in a circular orbit, while escape velocity is the speed needed to leave the body's gravity entirely. Escape velocity is always exactly √2 (about 1.414) times the circular orbital velocity at the same distance.
Does escape velocity depend on the mass of the object?
No. Escape velocity depends only on the mass of the body being escaped and the distance from its center. A feather and a spacecraft need the same speed in a vacuum, although the spacecraft needs far more energy and fuel to reach it.
Why do rockets not need to reach escape velocity to leave Earth?
Escape velocity applies to an unpowered object launched once, like a cannonball. A rocket keeps firing its engines and can climb slowly while gaining altitude, so it can leave Earth's gravity at any speed, though real missions still reach about 11 km/s to escape on a direct trajectory.