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Physics

Escape Velocity Calculator

Minimum speed an object needs to escape a celestial body's gravity, ignoring atmospheric drag.

Result

Escape Velocity

11185.7265 m/s

In km/s

11.1857 km/s

Mass used

5.972e+24 kg

Radius used

6.371e+6 m

Concept

Escape velocity is the minimum speed a body must have to escape a planet's gravitational pull without any further propulsion. At this speed, the body's kinetic energy equals the gravitational potential energy binding it to the planet.

Derivation: set KE = GPE → ½mv² = GMm/R → v = √(2GM/R). Note that mass m cancels — escape velocity is independent of the escaping object's mass.

Earth's escape velocity is ~11.2 km/s. For a black hole, the escape velocity exceeds c (speed of light), which is why nothing escapes a black hole.

Formula

ve=2GMR
Also expressed as=2gR (when g = GM/R² is known)

Variables

vₑm/s or km/s
Escape velocity.
G6.674 × 10⁻¹¹ N·m²/kg²
Universal gravitational constant.
Mkg
Mass of the planet or body.
Rm
Radius of the planet — from centre to surface.
gm/s²
Surface gravitational acceleration = GM/R².