Escape Velocity Calculator
Pick a world or choose custom and enter a mass and radius. Add an altitude to get the speeds at that height above the surface.
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Formula
- Escape velocity:
v_esc = √(2 G M ÷ r) - Circular orbital velocity:
v_orb = √(G M ÷ r), sov_esc = √2 × v_orb - Orbital period:
T = 2π √(r³ ÷ (G M)); gravity there:g = G M ÷ r²
r is the body's radius plus the altitude. G = 6.67430 × 10⁻¹¹ m³ kg⁻¹ s⁻² (CODATA 2018). Masses and mean radii come from the NASA Planetary Fact Sheet (Earth mass 5.9722 × 10²⁴ kg, mean radius 6371.0 km).
Worked example
Earth at the surface: v_esc = √(2 × 6.6743e-11 × 5.9722e24 ÷ 6.371e6) = 11 186 m/s = 11.19 km/s, which is 40,270 km/h or 25,023 mph. The circular orbital velocity is 7.91 km/s and gravity is 9.82 m/s².
At 400 km altitude (r = 6771 km): escape 10.85 km/s, orbital 7.67 km/s, period 92.4 minutes.
Frequently asked questions
What is escape velocity?
It is the speed an object needs, with no further propulsion, to move away from a body's gravity for good: v = √(2GM ÷ r). For Earth (5.9722 × 10²⁴ kg, 6371 km) that is 11.19 km/s, about 40,270 km/h.
What is the difference between escape velocity and orbital velocity?
A circular orbit needs v = √(GM ÷ r), which is the escape velocity divided by √2. Just above Earth's surface that is 7.91 km/s against 11.19 km/s. At 400 km altitude the orbital speed is 7.67 km/s and the orbit takes 92.4 minutes.
Does escape velocity depend on the mass of the object?
No. The object's mass cancels out of the formula, so a marble and a spacecraft have the same escape velocity from the same place. Only the mass and radius of the body being left matter, plus the distance from its centre.
Do rockets need to reach escape velocity to leave Earth?
Not at launch. The figure applies to an object coasting without thrust. A rocket under continuous thrust can climb slowly, and the formula ignores air drag and the pull of other bodies. For the Moon (7.346 × 10²² kg, 1737.4 km) the escape velocity is only 2.38 km/s.