Math
Escape Velocity Calculator
Compute escape velocity v = sqrt(2 G M / r) for any celestial body. Includes presets for Earth, Moon, Mars, Sun, Jupiter, plus orbital velocity.
Escape Velocity Calculator
Given mass and radius, compute v = sqrt(2 G M / r).
Pick a body to auto-fill mass and radius. Edit either field to switch back to custom values.
Total mass of the body in kilograms. Earth is 5.972e24 kg.
Distance from the center of mass in meters. Earth surface is about 6.371e6 m.
Escape velocity
11.185978 km/s
Escape velocity (m/s)
11,185.977892 m/s
Escape velocity (km/s)
11.185978 km/s
Circular orbital velocity
7,909.680822 m/s
Gravitational parameter mu
3.9859e+14 m^3/s^2
Body mass
5.9720e+24 kg
Radius
6.3710e+6 m
Frequently Asked Questions about the Escape Velocity Calculator
What is escape velocity?
Escape velocity is the minimum speed an object needs at the surface of a body to escape its gravity without further propulsion. For Earth's surface it is about 11.18 km/s; for the Moon, 2.38 km/s; for the Sun's surface, about 617 km/s.
What is the formula for escape velocity?
v_escape = sqrt(2 x G x M / r), where G is the gravitational constant (6.674 x 10^-11 N m^2 / kg^2), M is the body's mass, and r is the distance from the body's center.
Does escape velocity depend on the launching object's mass?
No. Escape velocity is independent of the escaping object's mass. A grain of sand and a battleship both need exactly the same launch speed to escape Earth's gravity, ignoring air drag.
What is the orbital velocity shown alongside?
Circular orbital velocity at radius r is sqrt(G x M / r), which is the escape velocity divided by sqrt(2). It is the speed needed to maintain a circular orbit at that radius. For low Earth orbit it is about 7.9 km/s.
What happens at the Schwarzschild radius?
When you shrink a mass below its Schwarzschild radius r_s = 2 G M / c^2, the escape velocity equals or exceeds the speed of light, and a black hole forms. The calculator flags this case rather than returning a super-luminal escape velocity.