Escape Velocity Calculator
How fast must you go to leave a world for good? Pick a planet or enter any mass and radius, at the surface or high above it.
By Manzoor Ahmad, pharmacist · Updated What is the escape velocity formula?
ve = √(2GM ÷ r). For Earth, GM = 3.986 × 10¹⁴ m³/s² and r = 6,371 km, so ve = 11.19 km/s (about 40,270 km/h or 25,000 mph). The Moon’s escape velocity is 2.38 km/s and Jupiter’s about 60 km/s. Circular orbital speed is ve ÷ √2.
Escape velocity of the planets, Moon and Sun
Surface values from mean radius; orbital velocity is for a circular orbit skimming the surface.
| Body | Escape velocity | Orbital velocity | Surface gravity |
|---|
Escape vs orbital velocity
At any distance, vescape = √2 × vorbit. A spacecraft in a 408 km orbit is already moving at 7.67 km/s; it needs only about 3.2 km/s more to reach the local escape speed of 10.84 km/s. To compare gravity itself, see the weight on other planets calculator.
Escape velocity FAQs
v_e = √(2GM ÷ r), where G = 6.6743 × 10⁻¹¹ N·m²/kg², M is the body's mass and r is the distance from its center. It is the launch speed needed to coast to infinity with no further thrust and no air resistance.
About 11.19 km/s (40,270 km/h or 25,000 mph) from the surface, using Earth's mean radius of 6,371 km.
About 2.38 km/s, roughly a fifth of Earth's, which is why the Apollo lunar modules needed far smaller engines to leave the Moon.
No. The rocket's mass cancels out of the energy balance, so a pebble and a spacecraft need the same escape speed. Heavier rockets just need more energy to reach it.
Circular orbital velocity is v = √(GM ÷ r); escape velocity is √2 (about 1.414) times larger. At the International Space Station's altitude, orbital speed is about 7.67 km/s and escape speed about 10.84 km/s.
Yes. It falls with distance from the center as 1/√r. At 400 km above Earth it is about 10.85 km/s instead of 11.19 km/s.
Not necessarily at launch. Rockets burn for minutes, climbing and accelerating gradually; escape velocity is the speed an unpowered object would need. Missions to the Moon and planets do reach roughly 11 km/s after their final burn.
About 618 km/s from its surface. From Earth's orbit, escaping the Sun's gravity needs 42.1 km/s, though Earth's own orbital speed of 29.8 km/s helps.
The radius at which an object's escape velocity equals the speed of light, r_s = 2GM ÷ c². Squeezed inside it, a mass becomes a black hole: about 9 mm for Earth and 2.95 km for the Sun.
Its low escape velocity (2.38 km/s) lets fast-moving gas molecules escape over time, especially when heated by sunlight. Earth's higher escape speed keeps nitrogen and oxygen, though hydrogen and helium still leak away.
Jupiter, at about 60 km/s from its cloud tops, more than five times Earth's.
Set kinetic energy equal to the gravitational energy needed to reach infinity: ½mv² = GMm/r. Solving gives v = √(2GM/r).
Sources
- NASA Planetary Fact Sheet (masses, radii, escape velocities)
- NIST CODATA: Newtonian constant of gravitation
- OpenStax University Physics Volume 1, Section 13.3: Gravitational Potential Energy and Total Energy
- NASA: Sun Fact Sheet
- IAU: Nominal values for selected solar and planetary quantities (Resolution B3, 2015)
Escape velocity ignores air resistance, planetary rotation and the gravity of other bodies. Values use NASA gravitational parameters (GM) and mean radii.