Calculate the top speed a falling object reaches (terminal velocity) from its mass, cross-sectional area, drag coefficient and the fluid density.
Last updated: November 8, 2026
The speed where weight and drag balance
As a falling object speeds up, air resistance grows. When the drag equals the weight, it stops accelerating and falls at a constant speed, its terminal velocity: • Weight = drag: m × g = ½ × ρ × v² × A × Cd • v = √(2 × m × g ÷ (ρ × A × Cd)) Example: an 80 kg skydiver with arms spread (A ≈ 0.7 m², Cd ≈ 1.0) in sea-level air (1.225 kg/m³) reaches √(2 × 80 × 9.81 ÷ (1.225 × 0.7 × 1.0)) ≈ 42.8 m/s, about 154 km/h or 96 mph. Higher up the air is thinner, so terminal velocity rises. Cd and area change a lot with body position, so treat the result as an estimate.
Common questions about terminal velocity
The constant speed a falling object reaches when air resistance equals its weight. At that speed it no longer accelerates.
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In kilograms.
Area facing the direction of travel.
Spread skydiver ≈ 1.0, sphere ≈ 0.47.
Air at sea level ≈ 1.225.