Escape Velocity Calculator

The Escape Velocity Calculator works out how fast an object must travel to break free from the gravity of any planet, moon, star, or custom celestial body — and never fall back. Pick a body from the Solar System or beyond, or enter your own mass and radius, and the tool computes the escape velocity with the formula \(v_{esc} = \sqrt{2GM/r}\), shows it in km/s, mph and Mach, and places it on a visual ladder from a sprinter all the way up to the speed of light.

What Is Escape Velocity?

Escape velocity is the minimum speed an object needs to escape a body's gravitational pull without any further push. Launch something slower and gravity eventually drags it back; launch it at escape velocity and it coasts outward forever, ever slowing but never quite stopping. Because it is a speed rather than a direction, escape velocity is the same whether you fire straight up or at an angle (ignoring air resistance and rotation).

Crucially, escape velocity does not depend on the mass of the object that is escaping. A grain of sand and a rocket must both reach the same speed to leave Earth — about 11.2 km/s. The rocket simply needs far more energy and fuel to get there.

Escape Velocity Formula

Escape velocity comes directly from equating kinetic energy with gravitational potential energy. The result is a compact formula that needs only the body's mass and radius:

where:

• \(v_{esc}\) — escape velocity (metres per second)
• \(G\) — the gravitational constant, \(6.674 \times 10^{-11}\ \text{m}^3\,\text{kg}^{-1}\,\text{s}^{-2}\)
• \(M\) — the mass of the body (kilograms)
• \(r\) — the distance from the body's centre, usually its radius (metres)

If you know the surface gravity \(g\) instead of the mass, an equivalent form is \(v_{esc} = \sqrt{2gr}\), since \(g = GM/r^2\).

Escape Velocities of the Solar System

Why Jupiter Beats the Sun's Planets and the Moon Is So Easy

Escape velocity rises with mass and falls with radius. Jupiter is over 300 times Earth's mass, and even though its radius is 11 times larger, the mass wins out — giving it the highest planetary escape velocity at about 60 km/s. The Moon sits at the other end: with barely 1% of Earth's mass, its escape velocity is only 2.4 km/s. That gap is exactly why the compact Apollo Lunar Module could lift off the Moon, while leaving Earth demanded a giant Saturn V.

What Affects Escape Velocity?

When Escape Velocity Reaches the Speed of Light

Squeeze enough mass into a small enough radius and the Newtonian escape velocity reaches the speed of light, \(c \approx 299{,}792\ \text{km/s}\). At that point not even light can escape and the object is a black hole. The radius where this happens is the Schwarzschild radius:

For the Sun that radius is just about 3 km; for Earth it is under a centimetre. This calculator watches for that limit: if the escape velocity you compute reaches light speed, it flags a black hole and reports the Schwarzschild radius. (Near that regime the Newtonian formula is only an approximation — general relativity gives the exact picture — but the crossover point is correct.)

How to Use This Calculator

1. Choose a body: Select a planet, moon, star or exotic object, or choose "Custom Body" to enter your own.
2. Enter mass and radius: For a custom body, type its mass and radius and pick the units — kilograms and kilometres, or Earth/Jupiter/solar masses and Earth/solar radii.
3. Click Calculate: The tool applies \(v_{esc} = \sqrt{2GM/r}\) and shows the result instantly.
4. Explore the result: Read the escape velocity in km/s, mph, miles per second and Mach, watch the launch animation, see how far it sits from light speed, compare it on the velocity ladder, and follow the step-by-step working.

Frequently Asked Questions

What is escape velocity?

Escape velocity is the minimum speed an object needs to break free from a celestial body's gravity and never fall back, without any further propulsion. At exactly escape velocity an object would coast outward forever, slowing but never stopping. Earth's escape velocity is about 11.2 kilometres per second.

How is escape velocity calculated?

Escape velocity equals the square root of (2 × the gravitational constant G × the body's mass M, divided by the distance r from the centre): \(v_{esc} = \sqrt{2GM/r}\). G is \(6.674 \times 10^{-11}\). It depends only on the body's mass and radius, not on the mass of the object escaping.

What is Earth's escape velocity?

Earth's escape velocity at the surface is about 11.2 kilometres per second, which is roughly 25,000 miles per hour or Mach 33. The Moon's is only about 2.4 km/s, which is why the Apollo missions could leave it with a much smaller rocket.

Does escape velocity depend on the mass of the rocket?

No. Escape velocity is the same for a pebble and a spaceship because the mass of the escaping object cancels out of the physics. A more massive rocket needs more energy and fuel to reach that speed, but the target speed itself is identical.

What happens when escape velocity equals the speed of light?

When a body is so dense that its escape velocity reaches the speed of light, not even light can escape and the object is a black hole. The radius at which this happens is the Schwarzschild radius, \(r_s = 2GM/c^2\). This calculator flags that case and shows the Schwarzschild radius.

Why is Jupiter's escape velocity so high?

Jupiter's escape velocity is about 60 km/s, more than five times Earth's, because it is over 300 times more massive. Even though it is much larger in radius, which lowers escape velocity, its enormous mass dominates, giving it the highest escape velocity of any planet in the Solar System.

Additional Resources

• Escape Velocity - Wikipedia
• Schwarzschild Radius - Wikipedia