The Physics of the Universe
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Escape Velocity Calculator

Find the escape velocity of a planet, moon, star or black hole from its mass and radius using v = √(2GM/r) — the minimum speed needed to break free of gravity without further propulsion.

 

Formula

$$ v_{esc} = \sqrt{\dfrac{2GM}{r}} \qquad M = \frac{v^{2} r}{2G} \qquad r = \frac{2GM}{v^{2}} $$
G = 6.674×10⁻¹¹ N·m²/kg²

Worked example

For Earth, M = 5.972×10²⁴ kg and r = 6.371×10⁶ m, so \( v=\sqrt{2(6.674\times10^{-11})(5.972\times10^{24})/6.371\times10^{6}} \approx 11{,}186\ \text{m/s} \) — about 11.2 km/s, or 25,000 mph. That is why rockets need so much fuel.

How it works

Escape velocity is the minimum speed an object needs to permanently escape a body's gravity, with no further thrust. It comes from setting kinetic energy equal to the gravitational potential energy binding the object: ½ m v² = GMm/r, which rearranges to v = √(2GM/r).

Notice the escaping object's own mass cancels out — a pebble and a spaceship need the same escape speed. Escape velocity depends only on the mass and radius of the body you are leaving. For a black hole, the radius at which this speed equals the speed of light is the Schwarzschild radius.

Frequently asked questions

What is the escape velocity of Earth?

About 11.2 km/s (11,186 m/s, or roughly 25,000 mph). This is the speed needed to leave Earth's gravity without further propulsion, ignoring air resistance.

How do you calculate escape velocity?

Use v = √(2GM/r), where G is the gravitational constant (6.674×10⁻¹¹), M is the body's mass in kilograms and r is its radius in metres. Enter M and r above to get v.

Does escape velocity depend on the mass of the object escaping?

No. The escaping object's mass cancels out of the equation, so a small probe and a large spacecraft have the same escape velocity from a given body.

What is the escape velocity of a black hole?

At the event horizon (the Schwarzschild radius), the escape velocity equals the speed of light, which is why not even light can escape from inside it.

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