Escape Velocity Calculator
Find the speed needed to escape a planet's gravity.
Earth ≈ 5.972e24 kg.
Earth ≈ 6.371e6 m.
Results update as you type.
How it works
Escape velocity is the minimum speed an object must reach to break free of a planet, moon, or star's gravitational pull and never fall back, without any additional thrust. This escape velocity calculator computes it from the celestial body's mass and radius using Newton's law of gravitation. For Earth this speed is about 11.2 kilometres per second, roughly 33 times the speed of sound, which is why launching into space demands such enormous rockets. This concept matters for spaceflight, astronomy, and planetary science. Mission planners use escape velocity to work out the energy a spacecraft needs to leave Earth or land on and depart from another world. It also explains why small bodies like the Moon cannot hold onto an atmosphere, since gas molecules easily exceed the low escape speed, while massive planets like Jupiter retain thick atmospheres. A black hole, in the extreme, has an escape velocity exceeding the speed of light. The formula works by balancing kinetic energy against gravitational potential energy, so escape velocity rises with the body's mass and falls as the launch radius increases. Remarkably, it does not depend on the mass of the escaping object, so a pebble and a spacecraft need the same speed. Astronomers, engineers, and physics students rely on an escape velocity calculator to compare worlds and plan the energy budgets of space missions.
vₑ = √( 2·G·M ÷ r ), G = 6.674×10⁻¹¹
Escape velocity is the minimum speed an object needs to break free of a body's gravity without further propulsion, and it comes from setting the object's kinetic energy equal to the gravitational potential energy binding it. Solving that energy balance gives the square root of twice the gravitational constant times the body's mass divided by its radius. The formula works because a more massive body pulls harder and requires more speed, while starting farther from the centre, at a larger radius, weakens the pull and lowers the escape speed. Notably it does not depend on the escaping object's own mass.
Source:Standard physics (Newtonian gravitation)
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter mass of body and radius.
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Escape velocity updates instantly as you type — no button to press.
Frequently asked questions
Does escape velocity depend on the object's mass?
No, and this surprises many people. The escaping object's own mass cancels out of the equation because both its kinetic energy and its gravitational potential energy scale with that mass in the same way. This means a tiny pebble and a massive spacecraft need exactly the same speed to escape a given body. Only the mass and radius of the body being escaped from determine the required velocity.
Why is Earth's escape velocity about 11.2 km/s?
Plugging Earth's mass of roughly 5.972×10²⁴ kilograms and radius of about 6,371 kilometres into the formula yields around 11,186 metres per second, or 11.2 kilometres per second. This is the speed an object launched straight up would need to coast away forever without further power. It reflects the balance between Earth's substantial mass, which pulls objects back, and its radius, which sets the starting distance from the centre.
Do rockets actually reach escape velocity at launch?
Not instantly. Escape velocity is the speed needed to coast away with no further thrust from the surface, but rockets burn fuel continuously, so they can leave more gradually by maintaining thrust. Most launches first reach orbital velocity, about 7.9 kilometres per second, to circle Earth, and only missions leaving Earth entirely build up to escape velocity. Continuous propulsion means a rocket never has to hit that full speed in one sudden burst.
How does radius affect escape velocity?
Escape velocity is inversely proportional to the square root of the radius, so starting farther from a body's centre lowers the speed required to escape. Launching from a mountaintop or from orbit needs slightly less than launching from the surface. This also means that for two bodies of equal mass, the more compact one with the smaller radius has the higher escape velocity, because its surface sits deeper in the gravity well.
What is the connection to black holes?
A black hole is an object so compact that its escape velocity at the event horizon reaches the speed of light. Because nothing can travel faster than light, nothing, not even light itself, can escape once it crosses that boundary. Applying the same formula with an extremely large mass packed into a tiny radius drives the escape velocity up to and beyond light speed, which is the defining feature of a black hole.