Physics
Terminal velocity from the force balance
Weight equals quadratic drag, solved for speed.
The Formula
v = sqrt(2 x m x g / (rho x Cd x A))
Weight equals quadratic drag, solved for speed.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| v | Terminal velocity | metres per second | The steady falling speed. |
| m | Mass | kilograms | The mass of the falling object. |
| rho | Air density | kg per cubic metre | The density of the fluid being fallen through. |
| Cd | Drag coefficient | unitless | A shape factor, about 1 for a human body. |
| A | Presented area | square metres | The cross sectional area facing the flow. |
What Each Symbol Means
vmetres per second
Terminal velocity
The steady falling speed.
mkilograms
Mass
The mass of the falling object.
rhokg per cubic metre
Air density
The density of the fluid being fallen through.
Cdunitless
Drag coefficient
A shape factor, about 1 for a human body.
Asquare metres
Presented area
The cross sectional area facing the flow.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate terminal velocity page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate Terminal Velocity, filed under Science. Every number the guide produces comes from substituting into this one line.