Terminal Velocity

Terminal velocity is the constant, maximum speed a falling object reaches when moving through a fluid such as air or water, occurring at the exact point where the upward drag force pushing against the object equals the downward force of gravity pulling it down. Before reaching this point, an object in free fall continuously accelerates; once drag force catches up to gravitational force, net acceleration drops to zero and the object continues falling at an unchanging speed.

The Terminal Velocity Calculator computes this maximum speed from an object's mass, cross-sectional area, drag coefficient, and the density of the air (or fluid) it's falling through. It complements the Free Fall Calculator, which models the earlier accelerating phase of a fall under gravity before drag becomes significant — together the two calculators describe the complete story of an object falling through a real, resistive atmosphere rather than the idealized vacuum assumed in basic gravity equations.

Terminal velocity explains everyday physical intuitions that pure gravitational acceleration cannot: why a feather drifts down gently while a bowling ball drops rapidly despite both experiencing identical gravitational acceleration, and why skydivers can control their fall speed by changing body position to alter their cross-sectional area and drag coefficient.

v = √(2mg / (ρ × A × Cd))

Where v is terminal velocity (in meters per second, m/s), m is the object's mass (kg), g is gravitational acceleration (9.81 m/s² on Earth), ρ (rho) is the density of the fluid being fallen through (kg/m³ — about 1.225 kg/m³ for air at sea level), A is the object's cross-sectional area facing the direction of fall (m²), and Cd is the dimensionless drag coefficient describing the shape's aerodynamics.

A skydiver with a mass of 75 kg falls in a standard belly-to-earth position with a cross-sectional area of 0.7 m² and a drag coefficient of about 1.0, through sea-level air with a density of 1.225 kg/m³. Their terminal velocity is:

v = √((2 × 75 kg × 9.81 m/s²) ÷ (1.225 kg/m³ × 0.7 m² × 1.0)) v = √(1471.5 ÷ 0.8575) = √1716.2 ≈ 41.4 m/s (about 149 km/h or 93 mph)

This is close to the commonly cited real-world figure of around 195 km/h for a spread-eagle skydiving position (which accounts for a somewhat larger effective drag area across the whole body), illustrating how small changes in body position materially change the resulting terminal velocity.

• Occurs when gravity and drag balance exactly: once the upward drag force grows to match the object's weight, net force reaches zero and acceleration stops, locking the object into a constant falling speed.
• Depends heavily on shape and orientation: a skydiver can roughly double their terminal velocity by switching from a spread-eagle position to a head-down dive, since a smaller cross-sectional area sharply reduces drag.
• Increases with mass, decreases with air resistance: heavier objects need more drag force to reach balance, so denser or more compact objects of the same shape have higher terminal velocities than lighter ones.
• Higher at altitude, lower near the ground: because air density increases closer to sea level, an object's terminal velocity actually decreases as it descends into thicker air.
• The endpoint of, not a replacement for, Velocity analysis in free fall: the Free Fall Calculator tracks the accelerating phase governed by gravity alone, while terminal velocity describes the steady-state speed a falling object settles into once air resistance fully cancels that acceleration.