Terminal Velocity Calculator

Terminal velocity occurs when the downward force of gravity acting on a falling object equals the upward aerodynamic drag force exerted by the surrounding fluid. At this point, the net force becomes zero, meaning acceleration stops and the object continues falling at a constant speed. The mathematical formula implemented by this calculator is:

v_t = √( (2 × m × g) / (ρ × A × C_d) )

Where: v_t is the terminal velocity, m is the mass of the object, g is the acceleration due to gravity, ρ (rho) is the fluid density, A is the projected cross-sectional area, and C_d is the drag coefficient.

Let us calculate the terminal velocity of a skydiver with equipment falling through standard air. Assume the following values: Mass (m) = 85 kg, Gravity (g) = 9.81 m/s², Fluid Density (ρ) = 1.225 kg/m³ (air at sea level), Projected Area (A) = 0.7 m² (in a belly-to-earth stable position), and Drag Coefficient (C_d) = 1.0.

Step 1: Multiply the numerator variables: 2 × 85 kg × 9.81 m/s² = 1667.7.

Step 2: Multiply the denominator variables: 1.225 kg/m³ × 0.7 m² × 1.0 = 0.8575.

Step 3: Divide the numerator by the denominator: 1667.7 / 0.8575 = 1944.84.

Step 4: Take the square root of the result: √(1944.84) ≈ 44.1 m/s (or about 158.8 km/h).

When using this calculator, ensure all input variables use consistent metric units (kilograms, meters, seconds) to avoid calculation errors. Remember that an object's drag coefficient is not a fixed constant; it changes depending on the object's orientation, surface roughness, and speed. For high-altitude calculations, always adjust the fluid density value because air becomes significantly less dense as altitude increases.