Escape Velocity Calculator — Breaking Free from Gravity
Calculate escape velocity for any planet or star using v = √(2GM/r). Covers Earth, Moon, Jupiter, and black holes, with orbital mechanics context.
Escape velocity is the minimum speed needed to break free from a body's gravitational pull without any further propulsion. Get to escape velocity and you'll coast forever away from the planet — gravity will slow you but never quite stop you. Fall short and gravity eventually pulls you back. It's a clean dividing line between orbiting and escaping.
The CalcHub escape velocity calculator computes escape velocity for any mass and radius combination.
The Formula
v_e = √(2GM/r)- v_e = escape velocity (m/s)
- G = gravitational constant = 6.674 × 10⁻¹¹ N·m²/kg²
- M = mass of the body (kg)
- r = distance from center (radius at surface, or orbital radius)
Escape Velocities in Our Solar System
| Body | Escape velocity |
|---|---|
| Moon | 2.38 km/s |
| Mars | 5.03 km/s |
| Earth | 11.19 km/s |
| Saturn | 35.5 km/s |
| Jupiter | 59.5 km/s |
| Sun | 617.7 km/s |
| Neutron star (typical) | ~100,000 km/s (0.33c) |
| Black hole event horizon | c (speed of light) |
Why Rockets Don't Need to Maintain Escape Velocity
Rockets don't need to instantly reach 11.2 km/s. They continuously burn fuel, gradually adding energy to the spacecraft. The escape velocity formula assumes a single impulse from the surface with no further thrust — a useful theoretical baseline.
Worked Example
What is the escape velocity from Earth's surface?
v_e = √(2 × 9.81 × 6.371 × 10⁶)
= √(124,993,620)
≈ 11,180 m/s ≈ 11.18 km/s
An object launched at 11.18 km/s from Earth's surface (straight up, no atmosphere) would escape Earth's gravity entirely. The Moon orbits at about 1.02 km/s — much slower, but circular orbit speed is always escape velocity / √2.
What's the difference between escape velocity and orbital velocity?
Orbital velocity v_o = √(GM/r) — circular orbit speed at radius r. Escape velocity v_e = √(2GM/r). So v_e = v_o × √2 ≈ 1.414 × v_o. To go from orbit to escape, you need to increase speed by 41.4%.
Does escape velocity depend on direction?
No — the formula gives the minimum speed regardless of direction (assuming no atmosphere). Even launching horizontally, you'll escape as long as you reach escape speed. Direction affects the shape of the departure trajectory but not the energy threshold.
What is a black hole, in terms of escape velocity?
A black hole forms when escape velocity exceeds the speed of light. The Schwarzschild radius r_s = 2GM/c² is where this happens. At or inside r_s, nothing — not even light — has escape velocity enough to escape. For Earth's mass, r_s ≈ 9 mm.