Planet Escape Velocity Calculator

Escape velocity from a planet

Escape velocity is the slowest you can go and still break free of a body's gravity with no more thrust after the launch. Set kinetic energy equal to potential energy and you get v_e = √(2GM/r), where G ≈ 6.674·10⁻¹¹ N·m²·kg⁻², M is the body's mass and r is the launch radius. Some reference values to anchor your intuition: Earth ≈ 11.2 km/s, Moon ≈ 2.38 km/s, Mars ≈ 5.03 km/s, Jupiter ≈ 59.5 km/s, Sun ≈ 617.5 km/s. A black hole is the limiting case, where v_e equals the speed of light c at the event horizon (that is essentially what the horizon means). And the rocket equation from Konstantin Tsiolkovsky, Δv = v_e_motor · ln(m₀/m_f), tells you how much velocity change you actually get out of a given exhaust velocity and mass ratio.

Applications

This number sits at the heart of space-mission design. A trans-lunar injection has to get you close to Earth's v_e, and any interplanetary trajectory piles more Δv on top of that. The Saturn V of the Apollo program supplied the Δv to escape Earth and head for the Moon, while SpaceX Starship, the vehicle Elon Musk keeps pushing, is built around the Δv budget needed to get to Mars. There is also an atmospheric retention side to it. Low-gravity worlds such as the Moon and Mercury can't hold onto light gases, because the thermal speeds of their molecules creep up toward v_e.

FAQ

Does direction matter? Not really. Escape velocity is a scalar threshold, so in vacuum any direction above the horizon will do, once you set aside rotation and atmosphere.

Why is Jupiter's v_e so high? Its mass runs to 318 Earths. The radius is much larger too, but the ratio M/r still comes out on the side of a bigger v_e.

What about a black hole? Inside the Schwarzschild radius, v_e ≥ c, so not even light gets out. That is exactly how the horizon is defined.

Why don't rockets reach v_e instantly? Because they burn for a long stretch rather than in one kick. The rocket equation adds up thrust over time, so it's perfectly normal to see a lower instantaneous speed plus some gravity losses along the way.