Escape Velocity Calculator
Find the launch speed needed to break free of any body with v = √(2GM ÷ r).
That is 11,186 m/s. G = 6.674×10⁻¹¹ N·m²/kg²; enter M in kg and r in metres (use e-notation, e.g. 5.972e24).
Escape velocity is the minimum speed to leave a body’s gravity without further thrust: v = √(2GM ÷ r), with G = 6.674×10⁻¹¹ N·m²/kg². For Earth (M = 5.972×10²⁴ kg, r = 6.371×10⁶ m) it works out to about 11.2 km/s — roughly 40,000 km/h.
What escape velocity means
Escape velocity is the speed an object needs at a body’s surface so that its kinetic energy exactly cancels the gravitational potential binding it — after which it coasts away and never falls back, assuming no air drag and no extra propulsion. Setting ½mv² equal to GMm ÷ r and cancelling the object’s mass m gives v = √(2GM ÷ r). It is a scalar: direction does not matter, only speed, because gravity is conservative.
G = 6.674×10⁻¹¹ N·m²/kg², M is the body’s mass in kg, r its radius in metres, v in m/s
Worked example
What is Earth’s escape velocity? Use M = 5.972×10²⁴ kg and r = 6.371×10⁶ m (Earth’s mean radius).
- 1 Write the formula. v = √(2GM ÷ r), with G = 6.674×10⁻¹¹ N·m²/kg².
- 2 Substitute the values. v = √(2 × 6.674×10⁻¹¹ × 5.972×10²⁴ ÷ 6.371×10⁶).
- 3 Evaluate inside the root. 2GM ÷ r ≈ 1.251×10⁸ m²/s².
- 4 Take the square root. v ≈ 11,187 m/s ≈ 11.19 km/s — the speed to escape Earth from its surface.
Escape velocity of common bodies
Computed from each body’s mass and mean radius with v = √(2GM ÷ r).
| Body | Escape velocity (km/s) | Escape velocity (m/s) |
|---|---|---|
| Moon | 2.38 | 2,375 |
| Mars | 5.03 | 5,027 |
| Earth | 11.19 | 11,186 |
| Jupiter | 59.5 | 59,500 |
| Sun | 617.5 | 617,500 |
Why the numbers look the way they do
It does not depend on the escaping object’s mass. Because the object’s mass m cancels out of ½mv² = GMm ÷ r, a pebble and a spacecraft need the same escape speed from the same body. Only the central body’s mass M and radius r matter.
Bigger and denser bodies demand more. Escape velocity rises with √M and falls with √r. More mass deepens the gravity well; a smaller radius puts the surface closer to the centre, where the pull is stronger. That is why the Sun — enormous mass despite its large radius — needs about 617 km/s, while the small, low-mass Moon needs only 2.4 km/s.