Escape Velocity Calculator
Calculate the escape velocity from any planet or moon given mass and radius.
Escape Velocity from Conservation of Energy
Escape velocity is the minimum initial speed that gives an unpowered object enough mechanical energy to reach infinitely far away with zero speed remaining. At distance r from the center of a spherical body, gravitational potential energy is −GMm/r. Setting the object's initial kinetic energy equal to the magnitude of that binding energy gives the familiar square-root formula.
The escaping object's mass m cancels, which is why a small probe and a massive spacecraft have the same ideal escape speed from the same location. The central body's mass M and the starting distance r are what matter. A more massive body increases the required speed, while starting farther from its center lowers it. For a launch from altitude h above a body's surface, use r = R + h rather than the surface radius R alone.
| Symbol | Meaning | Units / role |
|---|---|---|
| vesc | Escape velocity | m/s or km/s |
| G | Gravitational constant | 6.674 × 10−11 N m2/kg2 |
| M | Mass of central body | kg; more mass means stronger gravitational binding |
| r | Distance from body's center | m; surface launch uses approximately the body's radius |
This ideal result assumes a spherical gravitating body, no atmosphere, no rotation, and no additional propulsion after the initial speed is given. Real rockets do not need to be moving at 11.2 km/s at the launch pad; engines add energy continuously during ascent, and atmospheric drag and gravity losses also matter. At the same radius, ideal escape speed is √2 times the circular-orbit speed.
Worked Examples
Common Mistakes
The formula needs distance from the center of the gravitating body. At altitude h, use r = R + h. Near Earth's surface, using 400 km instead of about 6771 km produces a major error.
The spacecraft mass appears in both kinetic and gravitational potential energy and cancels. Ideal escape velocity depends on the central body's M and the starting radius r, not the payload mass.
A circular orbit does not escape. At the same radius, vesc = √2 vorbit in the ideal two-body model, so escape speed is about 41.4% higher than circular-orbit speed.
The textbook value applies to an object given an initial speed and then allowed to coast without propulsion. A powered spacecraft can gain the required energy over time along its trajectory.
Frequently Asked Questions
Formula Explorer connections
Interpretation: This relationship connects motion, force, momentum, work or energy in a mechanical system. Assumption: Choose a consistent reference direction and unit system. The model may assume constant acceleration, rigid bodies, negligible losses or an isolated system.