By Zencalcy Editorial TeamLast reviewed About us
Air drag grows with the square of speed, so a falling object approaches a terminal velocity instead of accelerating forever. This calculator uses the standard quadratic drag model to give terminal velocity, speed at a chosen time and distance fallen.
Speed and distance when drag grows with the square of speed.
v_t = √(2mg / (ρ A C_d)) v(t) = v_t · tanh(g t / v_t) s(t) = (v_t² / g) · ln(cosh(g t / v_t))
This is the quadratic drag model with a constant drag coefficient. It is accurate for compact objects at speeds well below the speed of sound.
| Symbol | Meaning |
|---|---|
| m | Object mass, in kilograms. |
| A | Frontal area, in square metres. |
| C_d | Drag coefficient (dimensionless). |
| ρ | Air density, in kilograms per cubic metre. |
| v_t | Terminal velocity, in metres per second. |
At sea-level density the terminal velocity is about 42.8 m/s. After 5 s the object has reached roughly 34.9 m/s and fallen about 103 m.
Continue with the Friction Calculator, Ground Speed Calculator, or the Horizontal Projectile Motion Calculator — or browse more kinematics tools and all physics calculators.
The drag force is proportional to v², which makes the equation of motion nonlinear. Its closed-form solution is a hyperbolic tangent for speed and a log-cosh for distance.
Results are computed from the standard equations of classical mechanics. Unit conversions use the SI definitions published by NIST. Air resistance is ignored unless the calculator names a drag model.
Reference material used to build and check this calculator:
Last reviewed: September 2026. See how we build and check every tool on the about page.
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Content updated: September 2026