Escape Velocity Calculator
Calculate the minimum speed needed to escape an object's gravity, with a clear formula substitution and related orbital values.
For surface escape velocity, enter the object's radius as r.
Escape Velocity Diagram and Values
Step-by-Step Solution
Escape Velocity Calculator
Use this Escape Velocity Calculator to find the minimum speed required to leave the gravitational pull of a planet, moon, star, or other massive object. Enter the object's mass in kilograms and the distance from its centre in metres. For a surface calculation, use the object's radius. The calculator returns escape velocity in metres per second and kilometres per second with fully worked formula steps.
Escape velocity is a key idea in physics, astronomy, rocketry, and space exploration. An object moving at escape velocity can continue outward indefinitely in the ideal two-body model, gradually slowing as gravity acts on it but never falling back. It does not need to keep accelerating after launch if no other forces act on it.
Escape Velocity Formula
The escape velocity formula is vesc = square root of 2GM divided by r. In the equation, vesc is escape velocity, G is the gravitational constant 6.67430 x 10 to the power of negative 11, M is the mass of the central object, and r is the distance from that object's centre. The answer is measured in metres per second when SI units are used.
The formula shows that escape speed increases with the mass of the object and decreases farther away from its centre. A large, dense planet has a higher surface escape velocity than a small body. Earth's escape velocity is about 11.2 km/s, while the Moon's is only about 2.38 km/s. The Sun has a much greater escape velocity because of its enormous mass.
Earth Escape Velocity Example
For Earth, use a mass of about 5.972 x 10 to the power of 24 kg and a mean radius of 6,371,000 m. Substituting these values into vesc = square root of 2GM divided by r produces approximately 11,186 m/s, or 11.19 km/s. This is the commonly quoted Earth surface escape velocity when air resistance and Earth's rotation are ignored.
The worked solution also displays surface gravity and circular orbital velocity at the selected radius. Circular orbital velocity is lower than escape velocity by a factor of square root of 2. A spacecraft can reach space without instantly travelling at 11.2 km/s because rockets accelerate over time, and real missions use staged propulsion and carefully planned trajectories.
Important Units and Assumptions
Use kilograms for mass and metres for radius or distance. Convert kilometres to metres before entering a value. The distance must be measured from the centre of mass, not from the surface unless the object is assumed to start at the surface and you enter the radius. The model assumes a spherical object, no atmosphere, and no additional forces from other bodies.
Real launches must overcome atmospheric drag, account for the rotation of Earth, and follow a path rather than a simple straight-line calculation. Escape velocity is not a speed limit and does not mean an object instantly leaves all gravity behind. It is the threshold energy condition for escaping without further propulsion in the simplified Newtonian model.
Frequently Asked Questions
What is escape velocity?
It is the minimum speed needed to escape an object's gravity without further propulsion in an ideal model.
What is Earth's escape velocity?
Earth's surface escape velocity is approximately 11.2 km/s, ignoring air resistance and rotation.
Does a rocket need to reach escape velocity instantly?
No. A rocket gains speed over time while its engines provide thrust.
Why does escape velocity change with altitude?
Distance from the object's centre increases at higher altitude, so gravity and escape velocity decrease.