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, 6.67430 x 10^-11 N*m^2/kg^2 (CODATA 2022)
- 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 gives ideal surface escape speeds using the calculator’s rounded mass and mean-radius presets. Rotation and atmosphere are ignored; the displayed speeds are rounded.
| Body | Escape velocity (km/s) | Escape velocity (mph) |
|---|---|---|
| Moon | 2.38 | 5,313 |
| Mercury | 4.25 | 9,507 |
| Mars | 5.03 | 11,245 |
| Venus | 10.36 | 23,177 |
| Earth | 11.19 | 25,022 |
| Uranus | 21.38 | 47,815 |
| Neptune | 23.56 | 52,706 |
| Saturn | 36.09 | 80,738 |
| Jupiter | 60.20 | 134,663 |
| Sun | 617.48 | 1,381,269 |
The next table compares Earth’s ideal escape and circular orbital speeds at the same distance. In this isolated-body model, escape speed is √2 times circular speed. An ideal impulsive prograde burn from a circular orbit therefore adds about 41.4% of that orbital speed. Actual mission design also depends on energy, burn location and other constraints.
| 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 (378,029 km altitude) | 1.44 | 1.02 |
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 * 6.67430 x 10^-11 * 5.972 x 10^24 / 6.371 x 10^6) ≈ sqrt(1.251261 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 * 6.67430 x 10^-11 * 6.417 x 10^23 / 3.3895 x 10^6) ≈ sqrt(2.527157 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, with an ideal impulsive prograde burn adding about 41.4% of the circular speed at that same radius. This ideal comparison does not by itself determine the most efficient real mission trajectory.
How is escape velocity related to black holes?
Setting the Newtonian expression equal to light speed gives the Schwarzschild scale r = 2GM/c² for a nonrotating, uncharged black hole. The calculator can show this formal radius, but Newtonian mechanics does not describe motion near or inside the horizon. A value at or above light speed is not a physically attainable launch speed; compact objects require general relativity.
