Planetary Escape Velocity Calculator

Escape velocity is the minimum speed an object needs to escape a body’s gravitational pull without any further propulsion. It assumes one instant push, like a cannon shot rather than 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:

Every figure in that table comes out of the calculator below, so the table, the dropdown and the chart all give the same answer. The rocky bodies use their mean radii, which is what everyone quotes for them. The four giant planets use equatorial radii at the one-bar level, because they have no surface and that is the published convention: Jupiter on its mean volumetric radius of 69,911 km would read 60.2 km/s instead of 59.5, and Saturn 36.1 instead of 35.5. You will also see the Sun quoted as 617.5, which uses a solar radius of 696,000 km rather than the 695,700 km the IAU settled on.

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.

Enter a temperature below and the calculator runs that test for eight common gases. Two warnings about reading the result, because the rule is crude and it is easy to get a confident wrong answer out of it.

First, the temperature that governs escape is not the surface temperature but the exosphere temperature, hundreds of kilometers up, where a molecule that gets moving has nothing left to collide with. Earth’s surface averages 288 K while its exosphere runs between roughly 600 and 1,000 K depending on solar activity. Feed the calculator 288 K and Earth appears to hold hydrogen comfortably; feed it 1,000 K and hydrogen falls below the line, which is the honest answer and the reason our atmosphere really does leak about 3 kg of hydrogen per second.

Second, the Moon is a good demonstration of the same trap. At 288 K the rule says the Moon should just barely hold carbon dioxide. Its dayside actually reaches about 390 K, and at that temperature even carbon dioxide clears the bar and leaves. Airless worlds are usually hot somewhere.