Terminal Velocity Calculator Formula
Understand the math behind the terminal velocity calculator. Each variable explained with a worked example.
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)) * 3.6Variables
| Variable | Description | Default |
|---|---|---|
mass | Mass(kg) | 80 |
gravity | Gravitational Acceleration(m/s²) | 9.81 |
rho | Air Density(kg/m³) | 1.225 |
area | Cross-Sectional Area(m²) | 0.7 |
cd | Drag Coefficient | 1 |
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.
- 01vt = sqrt(2 * m * g / (rho * A * Cd))
- 02vt = sqrt(2 * 80 * 9.81 / (1.225 * 0.7 * 1.0))
- 03vt = sqrt(1569.6 / 0.8575)
- 04vt = sqrt(1830.6)
- 05vt ≈ 42.8 m/s ≈ 154 km/h
Frequently Asked Questions
What is a typical terminal velocity for a skydiver?
About 55 m/s (200 km/h) in a belly-down position, or up to 90 m/s (320 km/h) in a head-down dive.
Does mass affect terminal velocity?
Yes. Heavier objects (with the same shape) reach higher terminal velocities because more gravitational force is needed to balance drag.
What is the drag coefficient?
A dimensionless number that characterizes the aerodynamic drag of an object. A sphere has Cd around 0.47; a flat plate perpendicular to flow is about 1.28.
Ready to run the numbers?
Open Terminal Velocity Calculator