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Escape Energy Calculator

Find the energy needed to escape gravity.

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.

Worked example

Earth: M = 5972000000000000000000000 kg (5.972×10²⁴), r = 6371000 m, and a 1000 kg object. First G × M / r = 6.674×10⁻¹¹ × 5.972×10²⁴ / 6.371×10⁶, about 62,560,239 J per kg. Times 1000 kg gives an energy of 62,560,238,581.07 J. For velocity, double the per-kg figure and take the square root: √(125,120,477) gives 11,185.73 m/s.

Try this example →

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.

About this calculator

This calculator finds the gravitational escape energy, E = G·M·m/r, the minimum energy an object of mass m needs to break free from a celestial body of mass M and radius r without any further propulsion, derived by setting the object's kinetic energy equal to the gravitational potential energy well it must climb out of. This is directly related to escape velocity, v = √(2GM/r), the speed at which that energy is entirely kinetic.

Aerospace engineers use this to calculate the minimum energy — and therefore fuel — a rocket needs to leave Earth's or another planet's gravity well, mission planners use it when comparing launch requirements from different bodies (the Moon needs far less escape energy than Earth), and astrophysicists use the underlying concept when discussing black holes and gravitational binding energy. Physics students and spaceflight enthusiasts use this calculator to see just how much energy gravity demands before something can leave for good.

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Comments (1)

  • Editorial team

    The radius field is the distance from the body's centre, so you can evaluate any point, not only a surface. Scientific notation works for the big masses: the Sun's mass of 1.989e30 kg at Earth's distance of 1.496e11 m gives about 42,127 m/s, the speed needed to leave the Sun's pull from there, ignoring Earth's own gravity and motion. Which body and starting distance are you checking, and what object mass are you using?

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