Escape Velocity Calculator Formula

Understand the math behind the escape velocity calculator. Each variable explained with a worked example.

Use the Escape Velocity Calculator

Formulas Used

Escape Velocity

escape_vel = sqrt(2 * 6.6743e-11 * mass_body / radius)

Escape Velocity (km/h)

escape_vel_kmh = sqrt(2 * 6.6743e-11 * mass_body / radius) * 3.6

Variables

VariableDescriptionDefault
mass_bodyMass of Celestial Body(kg)5.972e+24
radiusRadius from Center(m)6371000

How It Works

Escape Velocity

Escape velocity is the minimum speed an object must have to permanently leave a gravitational field without further propulsion.

Derivation from Energy Conservation

Setting kinetic energy equal to gravitational potential energy:

(1/2)mv² = GMm/r

Solving for v: v = sqrt(2GM/r)

Note that escape velocity is independent of the escaping object's mass.

Worked Example

Escape velocity from Earth's surface.

mass_body = 5.972e+24radius = 6371000
  1. 01v = sqrt(2 * G * M / r)
  2. 02v = sqrt(2 * 6.6743e-11 * 5.972e24 / 6.371e6)
  3. 03v = sqrt(1.251e8)
  4. 04v ≈ 11,186 m/s ≈ 40,270 km/h

Ready to run the numbers?

Open Escape Velocity Calculator