What this calculator does
A falling object does not accelerate forever. Drag grows with the square of speed, so it rises rapidly until it exactly balances weight, at which point acceleration stops and the speed holds constant. That speed is the terminal velocity.
Because drag depends on frontal area, posture matters enormously. A skydiver falling flat presents far more area than one diving head-down, which is why the same person can fall at very different speeds by changing shape alone.
The formula
Terminal velocity is the square root of twice the mass times gravity, divided by the product of fluid density, cross-sectional area and drag coefficient. At that speed the drag force exactly equals the object's weight.
| Term | Meaning |
|---|---|
| Drag coefficient (Cd) | A dimensionless number describing how streamlined a shape is. A flat plate is around 1.2; a sphere about 0.5. |
| Cross-sectional area | The frontal area presented to the airflow, which changes with orientation. |
| Terminal velocity | The constant speed reached when drag balances weight and net acceleration falls to zero. |
The inputs explained
| Field | What to enter |
|---|---|
| Mass (kg) | The mass of the falling object, in kilograms. |
| Fluid density (air ≈ 1.225) (kg/m³) | The density of the fluid it falls through. Air at sea level is about 1.225 kg/m³. |
| Cross-sectional area (m²) | The frontal area presented to the airflow, in square metres. |
| Drag coefficient | The drag coefficient for the shape and orientation. |
When to use it
Understanding skydiving speeds
Changing body position changes frontal area, which changes terminal velocity substantially without any change in mass.
Sizing a parachute
A parachute works by hugely increasing area and drag coefficient, which drops terminal velocity to something survivable.
Estimating settling rates
The same relationship governs how fast particles settle through a fluid, which matters in filtration and sedimentation.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does body position change a skydiver's terminal velocity?
The same mass presenting a range of frontal areas.
| Frontal area | Terminal velocity | In km/h |
|---|---|---|
| 0.3 m² | 65.34 m/s | 235.2 km/h |
| 0.7 m² | 42.78 m/s | 154.0 km/h |
| 1.5 m² | 29.22 m/s | 105.2 km/h |
Questions
Why does a heavier object fall faster in air?
Because weight grows with mass while drag depends only on size and shape. A heavier object of the same size needs more drag to balance its weight, and more drag requires more speed. In a vacuum, with no drag at all, everything falls identically.
How long does it take to reach terminal velocity?
For a skydiver, roughly 10 to 15 seconds and several hundred metres. The approach is asymptotic, so the last few per cent of speed takes disproportionately long.
Why can small creatures survive any fall?
Because terminal velocity scales with the ratio of mass to area, and small bodies have far more surface area relative to their mass. An insect reaches a terminal velocity low enough to be harmless.
Does altitude change terminal velocity?
Yes. Air density falls with altitude, so terminal velocity is higher up high. This is how extreme high-altitude jumps have reached speeds far above ordinary skydiving.
For the drag force itself at any speed, see the drag force calculator. For the same balance in a liquid, see the buoyancy calculator.