What this calculator does
Drag rises with the square of speed, and the power needed to push through it rises with the cube. That is why a car that cruises comfortably at 100 km/h needs far more than double the power to reach 150.
Everything else in the equation is fixed once the vehicle is built: the frontal area, the drag coefficient of the shape, and the density of the air it moves through. Only speed is under the driver's control, and it dominates.
The formula
Multiply half the fluid density by the square of speed, by the frontal area and by the drag coefficient. The power required is that force multiplied by speed, which is why power goes as the cube.
| Term | Meaning |
|---|---|
| Drag coefficient (Cd) | A dimensionless measure of how streamlined a shape is. A modern car is around 0.3; a brick is far worse. |
| Frontal area | The cross-section presented to the airflow, in square metres. |
| Dynamic pressure | The half rho v squared term, which is the pressure the moving air represents. |
The inputs explained
| Field | What to enter |
|---|---|
| Fluid density (air ≈ 1.225) (kg/m³) | Fluid density in kilograms per cubic metre. Air at sea level is about 1.225; it falls with altitude. |
| Speed (m/s) | Speed relative to the fluid, in metres per second. |
| Reference (frontal) area (m²) | Frontal area in square metres. |
| Drag coefficient | The drag coefficient for the shape. |
When to use it
Understanding fuel consumption at speed
Because power rises with the cube of speed, highway cruising speed has an outsized effect on fuel use.
Comparing vehicle shapes
Drag coefficient and frontal area multiply together, so a sleek but large vehicle can be no better than a boxy small one.
Estimating cycling effort
Above roughly 20 km/h, aerodynamic drag dominates over rolling resistance for a cyclist.
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 steeply do drag and power rise with speed?
The same vehicle at a range of speeds.
| Speed | Drag force | Power needed to overcome drag |
|---|---|---|
| 10 m/s | 27.56 N | 275.6 W |
| 25 m/s | 172.27 N | 4,306.6 W |
| 50 m/s | 689.06 N | 34,453.1 W |
| 100 m/s | 2,756.25 N | 275,625.0 W |
Questions
Why does power rise with the cube of speed?
Because power is force times speed, and the force itself already rises with speed squared. Multiplying the two gives a cube, which is why small speed increases cost so much extra energy.
Does drag matter at low speed?
Much less. Below roughly 50 km/h in a car, rolling resistance and drivetrain losses dominate. Aerodynamic drag takes over as the main resistance at highway speeds.
Is a lower drag coefficient always better?
Only in combination with frontal area, since the two multiply. A large vehicle with an excellent coefficient can still have more total drag than a small one with a mediocre shape.
Why does altitude help?
Because air density falls with height, and drag is directly proportional to it. This is why aircraft cruise high and why records are often set at altitude.
For the speed at which drag balances gravity in a fall, see the terminal velocity calculator. For the flow regime around the object, see the Reynolds number calculator.