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. A belly-to-earth skydiver (~0.7 m², Cd ≈ 1) tops out near 195 km/h; head-down, area shrinks and speed rises past 250 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 — 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.
Frequently asked questions
What is a skydiver's terminal velocity?
About 190–200 km/h belly-to-earth, and 250–300+ km/h head-down. The world speed-skydiving record exceeds 500 km/h using minimal area and optimized suits.
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.