Escape Energy Calculator

How it is calculated

Escape energy is E = G × M × m / r and escape velocity is v = √(2 × G × M / r). M is the mass of the body you leave, in kg; r is the distance from its centre in metres (for a launch from the surface, its radius); m is the mass of the escaping object, in kg; G is fixed at 6.674×10⁻¹¹ N·m²/kg². Energy is returned in joules and velocity in m/s, both to two decimals.

Note that velocity does not depend on the object's mass, only energy does. All three inputs must be greater than zero or the tool gives no result. It is a bare gravitational calculation: it ignores air drag, the planet's rotation, and the fuel needed to carry fuel, so real launches need much more.

Common mistakes

• Entering the altitude instead of the distance from the centre. Radius must include the body's own radius, so a 400 km orbit around Earth is r = 6,771,000 m, not 400,000.
• Using kilometres or tonnes. The tool expects metres and kilograms; 6371 for Earth's radius would give an answer far too large.
• Expecting escape velocity to change with the object's mass. It does not, only the energy changes, so a satellite and a coin leave at the same speed.
• Confusing escape velocity with orbital velocity. Reaching orbit needs about 1/√2 of the escape speed at the same distance, so this is not the speed to put a satellite in orbit.
• Reading the energy as the fuel needed. It is the theoretical minimum, with no drag, no staging and no efficiency losses.