Terminal Velocity (Advanced) Calculator Formula

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

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Formulas Used

Terminal Velocity

terminal_v = sqrt(2 * mass * 9.80665 / (density * cd * area))

Terminal Velocity (km/h)

terminal_v_kmh = sqrt(2 * mass * 9.80665 / (density * cd * area)) * 3.6

Variables

VariableDescriptionDefault
massObject Mass(kg)80
cdDrag Coefficient1
densityAir Density(kg/m3)1.225
areaCross-Sectional Area(m2)0.7

How It Works

Terminal Velocity

When a falling object's drag force equals its weight, it stops accelerating and falls at a constant speed.

Formula

v_t = sqrt(2mg / (rho Cd A))

Derived from setting drag equal to weight: 0.5 Cd rho A v^2 = mg.

A skydiver in belly-down position has about 55 m/s (200 km/h); head-down is about 90 m/s (320 km/h).

Worked Example

80 kg skydiver, belly-down (Cd = 1.0, A = 0.7 m2), sea level.

mass = 80cd = 1density = 1.225area = 0.7
  1. 01v_t = sqrt(2 * 80 * 9.807 / (1.225 * 1.0 * 0.7))
  2. 02v_t = sqrt(1569 / 0.8575)
  3. 03v_t = sqrt(1830)
  4. 04v_t = 42.8 m/s = 154 km/h

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