Terminal Velocity Calculator
Terminal velocity is the maximum speed a falling object reaches when the drag force from air resistance equals the gravitational force pulling it down. At terminal velocity, the net force is zero and the object falls at a constant speed. This calculator uses the formula vt = sqrt(2mg / (ρCdA)) to find that speed.
When an object falls through a fluid (like air), two forces act on it: gravity pulling it down and drag pushing it up. As the object accelerates, drag increases with the square of velocity. Eventually drag equals gravity, acceleration drops to zero, and the object reaches terminal velocity.
The formula vt = √(2mg / (ρCdA)) shows that terminal velocity depends on mass (m), gravitational acceleration (g = 9.81 m/s²), air density (ρ), drag coefficient (Cd), and cross-sectional area (A). Heavier objects or those with smaller frontal areas fall faster, while larger drag coefficients or denser air slow the fall.
A skydiver in a belly-to-earth position (Cd ≈ 1.0, A ≈ 0.7 m²) reaches about 55 m/s (200 km/h). In a head-down dive (smaller A), terminal velocity can exceed 80 m/s (290 km/h). A golf ball (Cd ≈ 0.47, small A, low mass) has a terminal velocity of about 32 m/s. Understanding terminal velocity is essential in skydiving, aerospace engineering, meteorology, and sedimentation analysis.