Escape Velocity Calculator
Calculate escape velocity for a given mass and radius.
What is the Escape Velocity Calculator?
An escape velocity calculator works out the minimum speed an object needs to permanently break free of a body's gravity without further propulsion, based on that body's mass and radius. It works using the formula v = √(2GM ÷ r), where G is the universal gravitational constant (6.674×10⁻¹¹ N·m²/kg²), M is the mass of the body in kilograms and r is the body's radius in metres — the tool defaults to Earth's mass and radius, giving the familiar figure of roughly 11.2 km/s. To calculate it manually for any planet or moon, multiply 2 by G and by the body's mass, divide by its radius, then take the square root — this simplified version ignores atmospheric drag, which would matter for a real launch from Earth's surface.
How it works
Escape velocity is the minimum speed an object needs to break free from a body's gravity permanently, without further propulsion, ignoring atmospheric drag. It's calculated from the body's mass and radius using the universal gravitational constant — a larger mass or a smaller radius (meaning you're closer to the centre of that mass) both increase the required escape velocity.
UK context
This is exactly why escape velocity differs so much between celestial bodies — the Moon's much lower mass and radius compared with Earth gives it a dramatically lower escape velocity, which is part of why leaving the Moon's surface takes far less energy than leaving Earth's.
Tips
- This calculates theoretical escape velocity ignoring atmospheric drag — a real rocket launched from Earth has to additionally overcome air resistance during ascent through the atmosphere.
- Escape velocity doesn't depend on the mass of the escaping object itself — only on the mass and radius of the body being escaped from.
Frequently asked questions
Does a heavier spacecraft need a higher escape velocity?
No — escape velocity depends only on the mass and radius of the body being escaped from (like Earth), not on the mass of the object trying to escape. A heavier spacecraft needs more total energy to reach that velocity, but the velocity itself is the same.
Why is the Moon's escape velocity so much lower than Earth's?
Because the Moon has both a much smaller mass and a smaller radius than Earth — since escape velocity depends on both factors together, the combined effect makes the Moon's escape velocity dramatically lower.
A quick note
Uses v = √(2GM/r) with the standard gravitational constant. Ignores atmospheric drag, which is relevant for real-world launches from bodies with an atmosphere.