Escape Velocity
Minimum speed to escape a body's gravity.
Formula
Live Calculator
MembersVariables
Example
Earth ≈ 11.2 km/s
How it works
This formula gives the minimum launch speed needed for an object to reach infinitely far away from a spherical body without any more propulsion. It comes from setting the object's initial kinetic energy equal to the gravitational potential energy it must gain as it climbs out of the body's gravity well, assuming no air resistance and no extra forces. The larger the mass of the body, or the closer you start to its center, the larger the escape speed must be.
When to use it
Use this when you need the speed required for a rocket, probe, or projectile to leave a planet, moon, or star without falling back. It is also useful in astrophysics for comparing how strongly different astronomical bodies hold onto gas, dust, or spacecraft.
Worked example, step by step
Find the escape velocity from the Moon. Given: G = 6.674 × 10^-11 N·m^2/kg^2, M = 7.35 × 10^22 kg, r = 1.74 × 10^6 m Step 1: Substitute into the formula: v_e = sqrt((2GM)/r) Step 2: Calculate the numerator: 2 × 6.674 × 10^-11 × 7.35 × 10^22 = 9.81009 × 10^12 Step 3: Divide by r: (9.81009 × 10^12) / (1.74 × 10^6) = 5.64028 × 10^6 Step 4: Take the square root: v_e = sqrt(5.64028 × 10^6) ≈ 2.37 × 10^3 m/s Final answer: v_e ≈ 2.37 km/s
Common mistakes to avoid
- Using the body's surface radius in the wrong units, or forgetting to convert kilometres to metres
- Confusing escape velocity with orbital speed, which is lower because the object stays bound in orbit
- Using mass of the object escaping instead of the mass of the body being escaped from
Did You Know?
Earth's escape velocity is about 11.2 km/s — roughly 40,000 km/h, no matter the object's mass.
Share this formula
More in Astronomy & Space
View allOrbital Velocity
IntermediateSpeed of a circular orbit.
Kepler's Third Law
AdvancedRelates orbital period to semi-major axis.
Schwarzschild Radius
AdvancedEvent horizon radius of a black hole.
Hubble's Law
AdvancedRecession velocity of galaxies with distance.
Stefan–Boltzmann Law
AdvancedLuminosity of a star from radius and temperature.
Redshift
AdvancedFractional wavelength shift of light.