Physics
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
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
Where
- =
- Escape velocity(m/s)
- =
- Newton's gravitational constant(6.674 × 10^-11 N m^2 kg^-2)
- =
- Mass of the central body(kg)
- =
- Distance from the centre of the body (so r = R + h at altitude h above the surface)(m)
Set total mechanical energy to zero (½mv² − GMm/r = 0) and solve for v. The result is independent of the escaping object's mass.
The calculator adds the altitude h to the body's surface radius R to get r, then applies the formula. Circular orbital velocity at the same r is √(GM/r), exactly v_esc divided by √2.
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.