What this calculator does
Escape velocity is the speed at which an object has just enough kinetic energy to climb out of a gravitational field entirely, never falling back, assuming nothing pushes it further along the way. From Earth's surface that speed is about 11.2 kilometres per second.
It is a speed rather than a force, and it depends only on the mass of the body and how far out you start. Crucially it does not depend on the mass of the escaping object: a pebble and a spacecraft need exactly the same speed.
The formula
Take the square root of twice the gravitational constant times the body's mass, divided by the distance from its centre. The result comes out in metres per second and is converted to more readable units alongside.
| Term | Meaning |
|---|---|
| Escape velocity | The speed at which kinetic energy exactly balances gravitational potential energy, allowing escape without further thrust. |
| Gravitational constant (G) | The universal constant 6.6743 × 10⁻¹¹ m³/(kg·s²) that sets the strength of gravity. |
| Orbital velocity | The speed needed to circle at a given radius, which is always escape velocity divided by the square root of two. |
The inputs explained
| Field | What to enter |
|---|---|
| Mass of the body (kg) | The mass of the body being escaped, in kilograms. Earth is 5.972 × 10²⁴. |
| Distance from centre (km) | The distance from the centre of the body, in kilometres. For a surface launch this is the body's radius, 6,371 km for Earth. |
When to use it
Understanding launch requirements
Escape velocity sets the energy a mission needs to leave a body entirely rather than orbit it.
Comparing different worlds
Running the same calculation for the Moon or Mars shows why leaving them takes so much less energy than leaving Earth.
Seeing why altitude helps
Starting further from the centre lowers the escape speed, which is part of why launches aim to gain altitude early.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does escape velocity fall with distance from Earth?
Escape velocity at a range of distances from Earth's centre.
| Distance from centre | Escape velocity | Surface gravity |
|---|---|---|
| 6,371 km | 11.186 km/s | 9.820 m/s² |
| 10,000 km | 8.928 km/s | 3.986 m/s² |
| 20,000 km | 6.313 km/s | 0.996 m/s² |
| 42,164 km | 4.348 km/s | 0.224 m/s² |
Questions
Does a heavier rocket need a higher escape velocity?
No. The escaping object's mass cancels out of the equation completely, so the required speed is identical for any mass. What a heavier rocket needs is more energy to reach that speed, which is a different question.
Do rockets actually reach escape velocity?
Not usually all at once. Escape velocity assumes a single impulse with no further thrust. A rocket under continuous power can leave more gradually, which is why launch profiles do not simply accelerate to 11.2 km/s at ground level.
Why is orbital velocity lower?
Because staying in orbit only requires balancing gravity with curvature, not defeating it entirely. Circular orbital velocity is always escape velocity divided by the square root of two, about 71 per cent of it.
Does atmosphere affect the figure?
The calculation ignores drag entirely. In reality atmospheric resistance means a launch needs more energy than the bare figure suggests, which is why rockets climb steeply out of the dense lower atmosphere first.
For the speed needed to stay in orbit rather than leave, see the orbital velocity calculator. For the force behind it, see the Newton's law of gravitation calculator.