Terminal Velocity Calculator Formula

Understand the math behind the terminal velocity calculator. Each variable explained with a worked example.

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Formulas Used

Terminal Velocity

terminal_vel = sqrt(2 * mass * gravity / (rho * area * cd))

Terminal Velocity (km/h)

terminal_vel_kmh = sqrt(2 * mass * gravity / (rho * area * cd)) * 3.6

Variables

VariableDescriptionDefault
massMass(kg)80
gravityGravitational Acceleration(m/s²)9.81
rhoAir Density(kg/m³)1.225
areaCross-Sectional Area(m²)0.7
cdDrag Coefficient1

How It Works

Terminal Velocity

Terminal velocity is reached when air drag equals gravitational force, producing zero net acceleration.

Derivation

Setting weight equal to drag: m*g = (1/2)*rho*v²*Cd*A

Solving: vt = sqrt(2*m*g / (rho*A*Cd))

Worked Example

A skydiver (80 kg, belly-down, A = 0.7 m², Cd = 1.0) in standard atmosphere.

mass = 80gravity = 9.81rho = 1.225area = 0.7cd = 1
  1. 01vt = sqrt(2 * m * g / (rho * A * Cd))
  2. 02vt = sqrt(2 * 80 * 9.81 / (1.225 * 0.7 * 1.0))
  3. 03vt = sqrt(1569.6 / 0.8575)
  4. 04vt = sqrt(1830.6)
  5. 05vt ≈ 42.8 m/s ≈ 154 km/h

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