What is escape velocity?

The minimum speed an object needs at a distance r from the centre of a mass M to reach infinity with zero remaining kinetic energy, v_esc = √(2GM/r). It is independent of the object's mass.

What is Earth's escape velocity?

About 11.2 km/s from Earth's surface. The Moon's is about 2.4 km/s; the Sun's is about 618 km/s from its surface.

Is escape velocity the same as orbital velocity?

No. Escape velocity is √2 times the circular orbital velocity at the same radius. A satellite in circular orbit has E = -GMm/(2r); an escaping object has E ≥ 0.

Why does escape velocity decrease with altitude?

Escape velocity depends on the depth of the gravitational well at that point. Higher altitude means the well is shallower (|U| is smaller), so less kinetic energy is needed to reach zero total energy.

← HSC Physics calculators

NSW · HSCModule 5

Escape velocity calculator

Pick a body or enter a custom mass and radius. Get the escape velocity at the surface or any altitude, plus the circular orbital velocity at the same radius for comparison.

Inputs

Body presetBody mass M (kg)Body radius R (m)Altitude h (m)0 for the body's surface

Result

Escape velocity v_esc

1.119e+4m/s

≈

11.19km/s

Orbital velocity at same r

7910m/s

Surface gravity

9.820m/s²

v_esc = √(2GM/r). Independent of the escaping object's mass.

How this calculator works

Setting total mechanical energy to zero (½mv² − GMm/r = 0) and solving for v gives v_esc = √(2GM/r). The calculator adds altitude h to the body's radius R to get r, then applies the formula. Circular orbital velocity at the same r is √(GM/r), exactly v_esc / √2.

For the derivation and worked example, read our gravitational potential energy dot point answer.

Common questions

What is escape velocity?: The minimum speed an object needs at a distance r from the centre of a mass M to reach infinity with zero remaining kinetic energy, v_esc = √(2GM/r). It is independent of the object's mass.
What is Earth's escape velocity?: About 11.2 km/s from Earth's surface. The Moon's is about 2.4 km/s; the Sun's is about 618 km/s from its surface.
Is escape velocity the same as orbital velocity?: No. Escape velocity is √2 times the circular orbital velocity at the same radius. A satellite in circular orbit has E = -GMm/(2r); an escaping object has E ≥ 0.
Why does escape velocity decrease with altitude?: Escape velocity depends on the depth of the gravitational well at that point. Higher altitude means the well is shallower (|U| is smaller), so less kinetic energy is needed to reach zero total energy.