How it works
Terminal velocity is the speed at which air drag exactly balances gravity, so a falling object stops accelerating. Drag grows with the square of speed, so every falling object eventually finds this equilibrium.
The formula reveals the levers: more mass raises terminal velocity; more area, more drag coefficient or denser air lowers it. Note that A and Cd only ever appear multiplied together, so it is the effective drag area A·Cd that fixes the answer — not either factor on its own. The defaults above (80 kg, Cd 1.0, 0.7 m², sea-level air) make A·Cd = 0.70 m² and give 42.78 m/s, or 154 km/h.
A real skydiver falls faster than that, and the gap is in the drag area rather than the equation. Stable belly-to-earth fall rates are well established near 190–200 km/h — the familiar "120 mph" is 193 km/h, or 53.6 m/s. Run this calculator backwards and that speed implies an effective drag area A·Cd of about 0.45 m² for an 80 kg jumper at sea level, well under the 0.70 m² that a full spread-eagle silhouette at Cd 1.0 assumes. Enter Cd 0.65 at 0.7 m² and the answer is 53.06 m/s (191 km/h); enter Cd 1.0 with A = 0.45 m² and it is 53.35 m/s (192.1 km/h).
So frontal area and drag coefficient are worth treating as a single quantity: neither is separately measurable for a person in a jumpsuit, and only the product can be inferred from an observed fall rate. That product also sets the scale of everything else — halve the effective drag area and terminal velocity rises by a factor of √2, about 41%, which is how head-down and tracking positions pass 270 km/h.
This is why cats survive high falls better than people (large area-to-mass ratio), why parachutes work (huge area), and why raindrops arrive at a gentle ~9 m/s instead of bullet speed.
Use it in real life
Skydiving: body position is a speed control — spreading out adds area and slows you; tucking accelerates you. Formation jumpers literally fly with this equation.
Hail and safety: a 4 cm hailstone lands around 100 km/h — enter 0.030 kg (a 4 cm sphere of ice at ~900 kg/m³), Cd 0.5 for a sphere and A = 0.0013 m² and this calculator returns 27.18 m/s, or 97.9 km/h. That is the physics reason hail dents cars while raindrops never could.
Engineering: parachute designers size canopy area to bring terminal velocity down to a survivable ~5 m/s landing speed. For an 80 kg jumper that needs an effective drag area A·Cd near 51 m² — over 100× the ~0.45 m² of the same body falling belly-to-earth.
Frequently asked questions
What is a skydiver's terminal velocity?
About 190–200 km/h belly-to-earth (the familiar 120 mph is 193 km/h), and 250–300+ km/h head-down. The world speed-skydiving record exceeds 500 km/h using minimal area and optimized suits. To reproduce the belly-to-earth figure here, an 80 kg jumper needs an effective drag area A·Cd of about 0.45 m²: Cd 0.65 at 0.7 m² returns 191 km/h. The defaults on this page — Cd 1.0 at 0.7 m² — are a bluff-body textbook estimate, so they return a slower 154 km/h; they assume a body catching more air than a real skydiver does.
Why don't small animals get hurt falling from height?
Terminal velocity scales with the square root of mass-to-area ratio. An ant's is so low (a few m/s) that no fall can exceed its safe landing speed.
What drag coefficient should I use?
Sphere ≈ 0.47, human belly-down ≈ 1.0, streamlined body ≈ 0.05–0.1, flat plate ≈ 1.3. It must be measured or estimated — it isn't derivable from geometry alone for complex shapes. For a falling human, treat Cd and area as one quantity: only the product A·Cd can be inferred from an observed fall rate, and a stable belly-to-earth fall implies about 0.45 m² — noticeably less than 0.7 m² at Cd 1.0.