Planetary Escape Velocity Calculator

Escape velocity is the minimum speed an object needs to escape a body’s gravitational pull without additional propulsion — it assumes an instant initial velocity (like a cannon shot, not a rocket).

Formula:

v_esc = √(2GM / R)

Where:

• G = 6.674 × 10⁻¹¹ N·m²/kg²
• M = mass of the body (kg)
• R = radius of the body (m)

Planetary escape velocities:

Key points:

• Escape velocity does not depend on the direction of launch (any direction works, ignoring atmosphere)
• Rockets don’t need to achieve escape velocity instantly — they thrust continuously, which is actually more efficient
• The Moon’s low escape velocity (2.38 km/s) explains why it has no significant atmosphere
• A black hole’s escape velocity equals or exceeds c (speed of light)
• Earth’s escape velocity (11.19 km/s) equals about Mach 32.6 at sea level conditions

What escape velocity does not mean. It is not a speed limit you must reach to leave. It is the speed needed to escape on a single unpowered coast, with no further thrust. A rocket that keeps its engines running can leave at any speed it likes, and in practice none of them ever travel at 11.2 km/s near the ground, because pushing that fast through thick air would tear the vehicle apart. Escape velocity is the right number for a cannonball and the wrong intuition for a rocket.

Why it explains which worlds keep an atmosphere. Gas molecules move at a range of speeds set by temperature, and the fast tail of that distribution slowly leaks away. The rough rule is that a world holds a gas over billions of years if its escape velocity is at least six times the average molecular speed of that gas. That single ratio explains a lot: the Moon at 2.38 km/s holds nothing, Mars at 5.03 km/s holds carbon dioxide but lost most of its water, Earth at 11.19 km/s holds nitrogen and oxygen while steadily leaking hydrogen and helium, and Jupiter at 59.5 km/s holds onto everything including the lightest element there is.