Calculate escape velocity for any celestial body using v_e = √(2GM/r). Includes solar system presets, altitude analysis, orbital velocity, and Schwarzschild radius.
Escape velocity is the minimum speed an object needs to break free from a celestial body's gravitational pull without further propulsion. Given by v_e = √(2GM/r), it depends only on the body's mass M and the distance r from its center — not on the mass of the escaping object. Earth's escape velocity at the surface is about 11.2 km/s (roughly 25,000 mph).
Understanding escape velocity is essential for space mission design, planetary science, and astrophysics. It determines whether a planet can retain an atmosphere (gas molecules moving faster than escape velocity leave), how much fuel rockets need, and at what radius an object becomes a black hole (when escape velocity exceeds the speed of light).
This calculator computes escape velocity for any celestial body, with presets for all major solar system objects. It also provides orbital velocity, surface gravity, gravity at altitude, and the Schwarzschild radius. Comparison charts and altitude tables help visualize how these quantities change across the solar system and with distance from a body's center.
Escape velocity calculations require the gravitational constant G = 6.674 × 10⁻¹¹ N·m²/kg² and planetary data that most people do not have memorized. This calculator includes accurate mass and radius data for all major solar system bodies, handles altitude corrections, and provides related quantities like orbital velocity and surface gravity that are usually needed alongside escape velocity.
Escape Velocity: v_e = √(2GM/r) Orbital Velocity: v_o = √(GM/r) = v_e/√2 Surface Gravity: g = GM/R² Schwarzschild Radius: r_s = 2GM/c² Where: G = 6.674 × 10⁻¹¹ N·m²/kg² M = mass of the body (kg) r = distance from center (m) R = surface radius (m) c = speed of light
Result: 11,186 m/s (11.19 km/s)
Earth's surface escape velocity: v_e = √(2 × 6.674×10⁻¹¹ × 5.972×10²⁴ / 6.371×10⁶) = 11,186 m/s ≈ 11.2 km/s. Orbital velocity at the surface would be 7,910 m/s (7.91 km/s).
Escape velocity comes from energy conservation. An object at distance r from a mass M has gravitational potential energy U = -GMm/r and kinetic energy K = ½mv². For escape, the total energy must be at least zero (the object reaches infinity with zero speed): ½mv² - GMm/r ≥ 0. Solving for v gives v_e = √(2GM/r).
Notice the escaping mass m cancels — this is a deep consequence of the equivalence principle, which states that gravitational and inertial mass are identical. This principle is the foundation of Einstein's general relativity.
A planet's ability to retain an atmosphere depends critically on its escape velocity relative to the thermal speed of gas molecules. The thermal speed is v_th = √(3kT/m_mol), where T is temperature and m_mol is molecular mass. Lighter molecules (hydrogen, helium) move faster and are more easily lost.
This explains why Earth has lost most of its primordial hydrogen and helium but retains heavier gases like nitrogen and oxygen. Mars, with only 5 km/s escape velocity and lower gravity, has lost most of its atmosphere over billions of years. Jupiter, with 59.5 km/s, retains even hydrogen easily.
When the escape velocity at some radius equals the speed of light c, we get the Schwarzschild radius r_s = 2GM/c². Inside this radius, not even light can escape. For Earth, r_s ≈ 8.9 mm; for the Sun, r_s ≈ 3 km. Stellar-mass black holes have Schwarzschild radii of kilometers, while supermassive black holes at galaxy centers have radii comparable to our solar system.
No. Escape velocity is a scalar speed, not a velocity vector. An object launched at escape speed in any direction (except straight down) will eventually escape, though its trajectory will differ.
Because both gravitational force and kinetic energy are proportional to the escaping mass. When you set ½mv² = GMm/r and solve for v, the mass m cancels out.
Not instantaneously. Rockets provide continuous thrust, so they can escape at any speed — even slowly — as long as they maintain thrust long enough. Escape velocity applies to objects launched with no further propulsion (like a cannonball).
It is the radius at which escape velocity equals the speed of light. If an object's mass were compressed within its Schwarzschild radius, it would become a black hole. Earth's Schwarzschild radius is about 8.9 mm.
Gas molecules have thermal velocities. If a significant fraction of molecules move faster than escape velocity, the atmosphere gradually leaks into space. This is why the Moon (v_e = 2.4 km/s) has no atmosphere while Earth (v_e = 11.2 km/s) retains one.
Escape velocity is always √2 times the circular orbital velocity at the same altitude. An orbiting spacecraft needs only 41% more speed to escape.