Terminal Velocity Calculator

Find the fastest a falling object can go, once air resistance balances the pull of gravity.

Terminal Velocity
42.78 m/s
or 154.02 km/h
or 95.7 mph
TimeVelocityv_t

Velocity over time approaching terminal velocity (asymptotic curve).

How it was calculated

Formula:v_t = √((2 × m × g) / (ρ × A × C_d))
Numerator (2mg):2 × 80 × 9.81 = 1,569.6
Denominator (ρAC_d):1.225 × 0.7 × 1 = 0.8575
Calculation:v_t = √(1,569.6 / 0.8575)
Result:42.78 m/s

About the Terminal Velocity Calculator

When an object falls, gravity pulls it down and air resistance pushes it up. As it falls faster, air resistance increases. Terminal velocity is the exact point where these two forces balance out, meaning the object stops accelerating and falls at a constant, maximum speed.

Mathematical Formula & Logic

Terminal Velocity Formula v_t = sqrt((2 * m * g) / (rho * A * C_d)) - v_t = Terminal Velocity (m/s) - m = Mass (kg) - g = Acceleration of Gravity (m/s^2) - rho = Fluid Density (kg/m^3) - A = Projected Cross-sectional Area (m^2) - C_d = Drag Coefficient (dimensionless)

Step-by-Step Example

A typical skydiver falling belly-to-earth (mass 80 kg, area 0.7 m², drag coefficient 1.0) through sea-level air reaches about 43 m/s (120 mph). If the same skydiver dives head-first, their cross-sectional area drops to ~0.18 m², and their terminal velocity skyrockets to over 100 m/s (220 mph).

Reference Data & Values

massgravitydensityareadrag coeffterminal velocity
809.811.2250.7142.784
809.811.2250.180.7100.835
0.0059.811.2250.00030.4723.83
10009.81100021.053.056
101.225110

Frequently Asked Questions

The formula is v_t = √(2mg / ρAC_d). It involves mass (m), gravity (g), fluid density (ρ), cross-sectional area (A), and drag coefficient (C_d).
A typical skydiver falling in a belly-to-earth position has a terminal velocity of about 120 mph (54 m/s). Diving headfirst can increase this to over 200 mph.
Yes. If you have two objects of the exact same size and shape, the heavier one will have a higher terminal velocity. It requires a faster fall to generate enough air resistance to balance its greater weight.
The drag coefficient (C_d) is a number that describes how aerodynamic an object's shape is. A smooth teardrop shape has a very low C_d (~0.04), while a flat box has a high C_d (~1.05).
For a human skydiver, it takes about 12 seconds and roughly 450 meters (1,500 feet) of freefall to reach 99% of terminal velocity.
Yes! The air gets thinner (lower density) at higher altitudes. Lower density means less air resistance, which means terminal velocity is higher at high altitudes.
Because a penny is light and has a flat shape that causes it to tumble, its terminal velocity is only about 30-50 mph. It would not be fatal if dropped from a skyscraper.
Not accurately for dense fluids. This formula ignores the buoyant force (upward lift). In water, an object's weight is significantly countered by buoyancy, requiring a modified formula.