Terminal Velocity Calculator
Find terminal velocity v=√(2mg/(ρ·A·Cd)). Enter mass, gravity, air density, area and drag coefficient. Skydiver (~80 kg) ≈ 55 m/s.
Input Data
Results
At a glance:Terminal velocity is the constant speed reached when the downward force of gravity equals the upward drag force, so net force and acceleration become zero. Drag follows F_d=(1/2)ρ·A·Cd·v²; setting mg=F_d and solving gives v=√(2mg/(ρ·A·Cd)). Properties: (1) heavier or more compact (small A, low Cd) objects fall faster; (2) denser fluid (higher ρ) lowers terminal velocity; (3) a parachute raises A and Cd to slow the fall. Examples: (1) skydiver 80 kg, belly-to-earth, A≈0.7 m², Cd≈1.0, ρ≈1.225 → v≈√(2·80·9.81/(1.225·0.7·1.0))≈55 m/s (~198 km/h); (2) same head-down (A≈0.18) → v≈108 m/s (~390 km/h); (3) raindrop 5e-5 kg, A≈5e-5 m², Cd≈0.5 → v≈9.2 m/s — so rain is not lethal. Applications: (1) skydiving and BASE jumping; (2) parachute and capsule recovery; (3) free-fall and drop-test analysis; (4) ballistics and projectile motion; (5) sports (cycling, skiing, golf ball design).
Formula
Terminal velocity: v = √(2mg/(ρ·A·Cd))
Drag force: F_d = ½·ρ·A·Cd·v²
Equilibrium: mg = F_d
Sea-level air density ρ ≈ 1.225 kg/m³
$$v_t = \sqrt{\frac{2mg}{\rho A C_d}}, \quad F_d = \tfrac{1}{2}\rho A C_d v^2$$How to Use
- Enter mass m, gravity g, air density ρ, frontal area A and drag coefficient Cd.
- The tool computes v=√(2mg/(ρ·A·Cd)).
- Common: skydiver ≈55 m/s belly-to-earth; head-down doubles it; a parachute drops it to ~5–7 m/s.
Case Studies
Skydiver terminal velocity
m=80 kg, g=9.81, ρ=1.225 kg/m³, A=0.7 m², Cd=1.0.
v = √(2×80×9.81/(1.225×0.7×1.0)).
≈ 54.8 m/s ≈ 197 km/h (belly-to-earth, typical skydiver).
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.