Gravitation
Escape Velocity Calculator
Calculate the minimum speed needed to escape the gravity of any planet or body. Earth, Moon, Mars, Jupiter, Sun or custom.
Escape Velocity
v = √(2GM/r)
Surface Gravity
—
m/s²
Speed (m/s)
—
m/s
Step-by-Step Solution
What is Escape Velocity?
Escape velocity is the minimum speed an object needs to break free from a planet's gravitational pull without any further propulsion. It is derived from setting kinetic energy equal to gravitational potential energy. The escape velocity depends only on the planet's mass and radius — not on the mass of the escaping object.
vₛₜ = √(2GM/r)
G = 6.674×10⁻¹¹ N·m²/kg² | M = planet mass (kg) | r = planet radius (m)
💡 Earth's escape velocity is 11.2 km/s (~40,000 km/h). The Moon's is only 2.38 km/s, which is why the Moon has almost no atmosphere — gas molecules easily escape its weak gravity.
Real-World Applications
Space Launches
Rockets must reach escape velocity to leave Earth. Multi-stage rockets are used because single-stage cannot carry enough fuel.
Moon's No Atmosphere
The Moon's low escape velocity (2.38 km/s) means atmospheric gases escaped into space over billions of years.
Black Holes
A black hole's escape velocity exceeds the speed of light (3×10⁸ m/s), so nothing — not even light — can escape.
Gas Giant Retention
Jupiter's high escape velocity (59.5 km/s) lets it retain light gases like hydrogen and helium in its atmosphere.
Frequently Asked Questions
Does escape velocity depend on the direction of launch?
No. Escape velocity is the same regardless of direction because gravitational potential energy is scalar (no direction). However, launching eastward (same direction as Earth's rotation) gives a free boost from Earth's rotational speed (~0.46 km/s at the equator).
Is escape velocity the same as orbital velocity?
No. Orbital velocity for low Earth orbit ≈ 7.9 km/s, while escape velocity ≈ 11.2 km/s. The ratio is always √2: escape velocity = √2 × circular orbital velocity at the same radius.
What is the escape velocity of the Sun?
About 617.7 km/s from the Sun's surface. This is why solar wind particles (which travel ~400–800 km/s) can barely escape, and why the Sun loses only a tiny fraction of its mass this way.