Last updated: 2026-06-15

Terminal Velocity

Drop something in air and it does not speed up forever. As it falls faster, air resistance grows until it exactly cancels the pull of gravity; from then on the object falls at a steady speed called its terminal velocity. This is why a skydiver settles at a roughly constant rate, why hailstones do not arrive at lethal speeds, and why a parachute works at all. This calculator finds the terminal velocity from the object's mass, frontal area, drag coefficient and the density of the fluid it falls through.

Where the formula comes from

At high speed, drag rises with the square of velocity: $F_d = \tfrac{1}{2}\rho v^2 C_d A$. An object reaches terminal velocity when this drag equals its weight $mg$. Setting them equal and solving for $v$ gives the result below — the one speed at which the net force, and therefore the acceleration, is zero.

Formula

Everything that resists the fall — density, drag coefficient and area — sits under the square root in the denominator, while mass sits on top. Because of the square root, a quantity must change fourfold to double or halve the terminal velocity.

Worked example

Take a 75 kg skydiver presenting 0.7 m² of frontal area with a drag coefficient of about 1.0, falling through sea-level air ($\rho = 1.225\ \text{kg/m}^3$):

Real skydivers usually fall a little faster, around 50–55 m/s, because their effective drag coefficient and posture differ. Opening a parachute multiplies the area and drag coefficient by a large factor, dropping terminal velocity to a survivable few metres per second.

What changes terminal velocity

A heavier object of the same shape falls faster, since mass is on top of the fraction. Anything that increases drag lowers terminal velocity: a bigger area, a blunter shape (higher $C_d$), or a denser fluid. This explains a feather versus a hammer in air — the feather's huge area-to-mass ratio gives it a tiny terminal velocity — and why both hit the ground together on the airless Moon.

Limitations

The formula assumes quadratic (high-speed) drag with a constant drag coefficient and a constant fluid density, which is a good model for everyday falling objects in air but not for very small or very slow ones, where drag is instead proportional to speed. It gives the final steady speed, not how long the object takes to reach it. Real drag coefficients also vary with speed and orientation, and air density falls with altitude, so high-altitude terminal velocities are higher than this sea-level estimate.