MotionLab

Terminal Velocity Calculator

The speed limit gravity hits once drag catches up — why a feather and a bowling ball don't fall at the same real-world rate.

Mass (kg)

Drag coefficient (Cd)

Air density (kg/m³)

Cross-sectional area (m²)

Terminal velocity (m/s)

42.784

v = √(2mg / (ρACd))

What you entered

Mass (kg): 80Drag coefficient (Cd): 1Air density (kg/m³): 1.225Cross-sectional area (m²): 0.7

1
v = √(2mg ÷ (ρACd))
√(2×80×9.81 ÷ (1.225×0.7×1))= 42.7836 m/s

Result

Terminal velocity (m/s): 42.784

An object with these properties reaches a terminal velocity of about 42.78 m/s.

Terminal velocity for falling objects

Terminal velocity is reached when drag balances weight. These use air at 1.225 kg/m3 and g at 9.81.

Mass (kg)	Drag coefficient	Area (m2)	Terminal velocity (m/s)	Object
80	1.3	1.0	31.395	Skydiver, belly-to-earth
70	1	0.7	40.020	Person, less spread
0.145	0.35	0.004	40.729	Baseball
1	0.47	0.01	58.376	Sphere, 1 kg
70	0.3	0.2	136.696	Skydiver, head-down

The first and last rows are the same skydiver in two body positions: spread flat gives about 31 m/s, while diving head-down cuts the area and drag coefficient enough to reach 137 m/s. That control is what makes formation skydiving possible. Terminal velocity rises with the square root of mass and falls with the square root of area, so heavy compact objects fall fastest. Once reached, acceleration stops entirely - the object continues at constant speed no matter how much further it falls, which is why the free fall calculator's figures become wrong beyond a few seconds.

Why falling speed eventually stops increasing

As a falling object speeds up, air resistance (drag) grows with the square of velocity — eventually drag force exactly balances gravity, and the object stops accelerating, settling into a constant 'terminal' velocity.

Shape and orientation change everything

A skydiver's terminal velocity is roughly 3x faster belly-down than in a vertical dive position — since drag coefficient and cross-sectional area both change dramatically with body orientation, this is a real, controllable factor in skydiving.

Frequently asked questions

A skydiver weighs 80 kg. What's their terminal velocity belly-down vs. headfirst?

Belly-down (Cd ≈ 1.0, A ≈ 0.7 m²): v_t ≈ √(2mg/(ρCdA)) = √(2×784.8/(1.225×1.0×0.7)) ≈ 42.8 m/s (154 km/h). Headfirst (Cd ≈ 0.4, A ≈ 0.15 m²): v_t ≈ 130 m/s (468 km/h) — 3× faster.

Why do raindrops not hurt when they hit you?

Raindrops are small (1-5 mm) and reach terminal velocity quickly — about 2-9 m/s depending on size. Their low mass and moderate speed mean minimal kinetic energy on impact. Hailstones are larger and denser, reaching higher terminal velocities, which is why they can cause damage.

How is terminal velocity related to the drag force calculator?

At terminal velocity, drag force exactly equals weight: ½ρv²CdA = mg. The drag force calculator computes drag at any speed; terminal velocity is the specific speed where drag perfectly balances gravity. See the drag force calculator for general drag calculations.

Does a feather really fall at the same rate as a bowling ball in a vacuum?

Yes — without air resistance, all objects fall at g = 9.81 m/s² regardless of mass. Apollo 15 astronaut David Scott demonstrated this on the Moon in 1971 by dropping a hammer and feather simultaneously — they hit the lunar surface at the same time.