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Terminal Velocity Calculator

Calculate terminal velocity from mass, area, drag coefficient, and fluid density. Solve for any variable. Includes skydiver, sphere, and raindrop presets.

Terminal Velocity Calculator

Solve for

Given mass, area, drag coefficient, and fluid density, compute v_t = sqrt(2 m g / (rho A Cd)).

Picking a preset fills mass, area, and drag coefficient. Choose "Custom object" to edit freely.

Falling object pushes this fluid out of the way. Density of air at sea level is 1.225 kg/m^3; water is about 1000 kg/m^3.

Mass of the falling object. Must be greater than zero.

Area facing the direction of motion. Belly-down skydiver is roughly 0.7 m^2; a 10 cm radius sphere is about 0.0314 m^2.

Dimensionless. Sphere 0.47, cube 1.05, parachute 1.5, airfoil 0.04, flat plate 1.28, skydiver belly 1.0.

Terminal velocity

42.776305 m/s

Velocity (m/s)

42.776305 m/s

Velocity (km/h)

153.994697 km/h

Velocity (mph)

95.687868 mph

Velocity (ft/s)

140.342207 ft/s

Mass (kg)

80 kg

Mass (lb)

176.36981 lb

Cross-sectional area

0.7 m^2

Drag Cd

1

Fluid density

1.225 kg/m^3

Gravity used

9.80665 m/s^2

Fast fall: in the range of a belly-down skydiver (~53 m/s, ~190 km/h).

Terminal Velocity Scaling

ChangeTerminal Velocity EffectReason
Mass doublesIncreases by √2Velocity scales with square root of mass
Area doublesDecreases by √2More drag area
Drag coefficient quadruplesHalvesVelocity scales with inverse square root of drag
Air density doublesDecreases by √2Denser fluid creates more drag
Mass quadruplesDoublesVelocity scales with square root of mass

Frequently Asked Questions about the Terminal Velocity Calculator

What is terminal velocity?
Terminal velocity is the constant speed a falling object reaches when air drag balances gravity. From that point on, there is no net force, so no further acceleration. For a skydiver in a spread-eagle position, that is roughly 53 m/s (120 mph).
What is the terminal velocity formula?
v = sqrt(2 m g / (rho x C_d x A)), where m is mass, g is 9.81 m/s^2, rho is fluid density, C_d is drag coefficient, and A is cross-sectional area. Doubling mass increases v by only sqrt(2), so terminal velocity grows slowly with size.
Why does a heavier skydiver fall faster?
More mass means more gravity pulling down without much change in cross-section or drag, so the equilibrium speed is higher. A 100 kg skydiver tops out around 60 m/s belly-down; a 60 kg skydiver tops out around 47 m/s in the same posture.
What drag coefficient should I use?
The presets use about 1.0 for a belly-down skydiver, 0.7 for a head-down skydiver, 0.47 for a sphere, and 0.5 for a large raindrop. Drag coefficient changes with shape, orientation, surface, and flow conditions. For engineering work, use data or testing for your specific geometry.
Does terminal velocity exist in vacuum?
No. Without a fluid there is no drag force to balance gravity, so this terminal-velocity model does not apply. In a uniform-field approximation acceleration is treated as constant, but a real gravitational field changes with position. The Moon demonstration showed that objects fall together when air resistance is negligible.

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