Calculate the escape velocity of any planet, moon, or star from its mass and radius, or solve for the mass or radius needed to produce a given escape speed.
Escape Velocity Formula
- v_e is the escape velocity (m/s)
- G is the universal gravitational constant, 6.674 x 10^-11 N*m^2/kg^2
- M is the mass of the celestial body (kg)
- r is the distance from the body’s center (m), equal to the radius for a launch from the surface
The calculator rearranges the same equation for its other two modes. Solving for mass gives:
Solving for radius gives:
In the escape velocity mode, you enter the mass and radius of a body, or pick a preset planet, moon, or the Sun, and the calculator returns the minimum speed needed to escape its gravity. The advanced altitude option replaces r with R + h, where h is the launch height above the surface, so you can see how escape velocity drops as you start higher. The mass mode tells you how heavy a body of a given radius must be to produce a given escape velocity, and the radius mode tells you how small a given mass must be squeezed to produce one. Notice that the mass of the escaping object never appears in the formula: escape velocity is a property of the body being escaped, not of the rocket.
Escape Velocities in the Solar System
The table below lists the surface escape velocity for the major bodies of the solar system. You can reproduce any row with the calculator’s presets.
| Body | Escape velocity (km/s) | Escape velocity (mph) |
|---|---|---|
| Moon | 2.38 | 5,320 |
| Mercury | 4.25 | 9,510 |
| Mars | 5.03 | 11,250 |
| Venus | 10.36 | 23,180 |
| Earth | 11.19 | 25,030 |
| Uranus | 21.3 | 47,650 |
| Neptune | 23.5 | 52,570 |
| Saturn | 35.5 | 79,410 |
| Jupiter | 59.5 | 133,100 |
| Sun | 617.5 | 1,381,300 |
Escape velocity also falls as you move away from a body, which is why real missions burn their escape stages from orbit rather than from the ground. The next table shows Earth’s escape velocity at increasing altitudes, alongside the circular orbital velocity at the same distance. The two are always related by a factor of the square root of 2, so a spacecraft already in orbit only needs about 41% more speed to escape.
| Altitude above Earth | Escape velocity (km/s) | Circular orbital velocity (km/s) |
|---|---|---|
| Surface (0 km) | 11.19 | 7.91 |
| ISS orbit (400 km) | 10.85 | 7.67 |
| 1,000 km | 10.40 | 7.35 |
| Geostationary orbit (35,786 km) | 4.35 | 3.07 |
| Lunar distance (384,400 km) | 1.43 | 1.01 |
Example Problems
Example 1: Escape velocity of Earth. Earth has a mass of 5.972 x 10^24 kg and a radius of 6,371 km (6.371 x 10^6 m). Plugging into the formula: v_e = sqrt(2 * 6.674 x 10^-11 * 5.972 x 10^24 / 6.371 x 10^6) = sqrt(1.2512 x 10^8) = 11,186 m/s, or about 11.19 km/s (roughly 25,000 mph). Any object launched straight up at this speed, ignoring air resistance, would coast away from Earth and never fall back.
Example 2: Escape velocity of Mars. Mars has a mass of 6.417 x 10^23 kg and a radius of 3,389.5 km. v_e = sqrt(2 * 6.674 x 10^-11 * 6.417 x 10^23 / 3.3895 x 10^6) = sqrt(2.527 x 10^7) = 5,027 m/s, or about 5.03 km/s. This is less than half of Earth’s escape velocity, which is one reason a Mars ascent vehicle can be far smaller than the rockets needed to leave Earth.
Frequently Asked Questions
Does escape velocity depend on the mass of the rocket?
No. The mass of the escaping object cancels out of the energy equation, so a pebble and a spacecraft need the same speed to escape. What changes with the object’s mass is the energy and fuel required to reach that speed, not the speed itself.
Why don’t real rockets need to reach escape velocity?
The formula gives the speed needed by an unpowered projectile launched from the surface. A rocket that keeps burning its engines can leave Earth at any speed, as long as it keeps adding energy. In practice, missions first enter orbit at about 7.8 km/s and then perform an escape burn, because escape velocity at orbital altitude is lower and only about 41% more speed is needed from a circular orbit.
How is escape velocity related to black holes?
If you compress a mass into a small enough radius, the escape velocity at its surface reaches the speed of light. That radius is the Schwarzschild radius, r = 2GM/c^2, and any object smaller than it is a black hole. You can explore this with the calculator’s radius mode: enter a mass and an escape velocity near 299,792 km/s to see how tiny the body would have to be.