The Physics of the Universe
HomeCalculators › Terminal Velocity

Terminal Velocity Calculator

Find the terminal velocity of a falling object — the constant speed reached when air drag balances gravity — using v = √(2mg / ρ·A·C_d).

 

Formula

$$ v_{t} = \sqrt{\dfrac{2mg}{\rho\,A\,C_d}} $$

Worked example

An 80 kg skydiver, belly-down (C_d ≈ 1.0, A ≈ 0.7 m²) in sea-level air (ρ = 1.225) reaches \( v=\sqrt{2(80)(9.81)/(1.225 \times 0.7 \times 1.0)}\approx 43\ \text{m/s} \), about 154 km/h. A smaller frontal area (head-down) gives a higher terminal speed.

How it works

As an object falls, air resistance grows with speed until it exactly cancels gravity. At that point the net force is zero and the object stops accelerating — it has reached terminal velocity, v = √(2mg / ρ·A·C_d).

Heavier or more compact objects (small area, low drag coefficient) fall faster; thinner air (high altitude) raises terminal velocity. The drag coefficient C_d depends on shape — roughly 0.47 for a sphere and near 1.0 for a spread-eagled skydiver.

Frequently asked questions

What is terminal velocity?

It is the constant maximum speed a falling object reaches when the upward drag force equals the downward force of gravity, so acceleration becomes zero.

What is the terminal velocity of a human?

About 53 m/s (195 km/h) belly-to-earth, or up to ~90 m/s in a head-down dive. It depends on body position, which changes area and drag.

How do you calculate terminal velocity?

Use v = √(2mg / ρACd), where m is mass, g gravity, ρ air density, A cross-sectional area and Cd the drag coefficient.

Does a heavier object have a higher terminal velocity?

Yes, for the same shape and area. Terminal velocity rises with the square root of mass, which is why a heavy object falls faster than a light one of identical size in air.

Related calculators