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Mechanics
Mechanics

Terminal Velocity

vt=2mgCDρAv_t = \sqrt{\frac{2mg}{C_D \rho A}}

Maximum velocity when drag equals weight.

Variables

v_t
Terminal velocity
Maximum falling speed
m/s
m
Mass
Object mass
kg
g
Gravitational acceleration
≈ 9.8 m/s²
m/s²
C_D
Drag coefficient
Shape-dependent constant
unitless
ρ
Fluid density
Density of fluid
kg/m³
A
Cross-sectional area
Projected area
m²

Derivation

Set drag force equal to weight and solve for v.

Your notes

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Common questions

What is the Terminal Velocity formula?

Terminal Velocity is written vₜ = √(2mg/C_D ρA). Maximum velocity when drag equals weight. It belongs to Mechanics, under Dynamics.

What are the units in vₜ = √(2mg/C_D ρA)?

In SI units, v_t is terminal velocity, measured in m/s; m is mass, measured in kg; g is gravitational acceleration, measured in m/s²; C_D is drag coefficient (dimensionless); ρ is fluid density, measured in kg/m³; A is cross-sectional area, measured in m².

How is the Terminal Velocity formula derived?

Set drag force equal to weight and solve for v. The result is vₜ = √(2mg/C_D ρA).