Terminal Velocity Calculator
Find an object's terminal velocity in a fluid.
Terminal velocity is the steady speed reached when drag balances gravity.
How the Math Works
The terminal velocity formula vₜ = √(2mg ÷ (ρ·A·Cd)) calculates the constant speed a falling object reaches when drag force equals gravitational force. Here, m is mass, g is gravitational acceleration (9.8 m/s²), ρ is fluid density, A is cross-sectional area, and Cd is the drag coefficient. The formula balances downward gravitational force (2mg) against upward drag force (ρ·A·Cd), with the square root yielding the equilibrium velocity where forces cancel out.
Practical Applications
To use this calculator practically, input the object's mass in kilograms, fluid density in kg/m³ (air is ~1.225 kg/m³ at sea level), cross-sectional area perpendicular to motion in square meters, and the drag coefficient (0.5 for streamlined shapes, 1.0-2.0 for blunt objects). For example, calculating a skydiver's terminal velocity: a 70 kg person with 0.7 m² surface area and Cd=1.0 yields approximately 53 m/s (190 km/h).
Day-to-Day Use
Understanding terminal velocity helps explain everyday phenomena like why a feather falls slowly while a coin drops quickly, or why parachutes work by increasing air resistance. It's essential for safety in sports (skiing, BASE jumping), engineering (designing stable structures against wind loads), and even meteorology (predicting raindrop sizes). This knowledge also aids in selecting appropriate protective gear and understanding vehicle aerodynamics for fuel efficiency.
Worked example
80 kg skydiver (~0.7 m², Cd 1) → ~54 m/s (~195 km/h).
FAQ
Belly-to-earth?
Larger area lowers terminal velocity; head-down is much faster.