What this calculator does
The power in the wind rises with the cube of its speed. That single fact dominates everything about wind energy: doubling the wind speed multiplies the available power by eight, so a site with 8 m/s average wind is worth vastly more than one with 4 m/s, not twice as much.
No turbine captures all of it, and none can. Extracting all the energy would mean bringing the air to a standstill behind the rotor, which would stop any more air arriving. The theoretical maximum, the Betz limit, is 59.3%, and real turbines reach somewhere around 35 to 45% of the available wind power in practice.
The formula
The swept area is the circle described by the rotor, π times the square of half the diameter. The power in the wind through that area is half the air density times the area times the cube of the wind speed. The output is that figure multiplied by the coefficient of performance Cp, which bundles aerodynamic, mechanical and electrical losses into one number and cannot physically exceed the Betz limit.
| Term | Meaning |
|---|---|
| Swept area | The area the rotor sweeps, which scales with the square of the diameter. |
| Cp | Coefficient of performance: the share of the available wind power actually converted. Typically 0.35 to 0.45. |
| Betz limit | 0.593, the theoretical maximum any open-flow turbine can extract, derived from the flow having to keep moving. |
| Air density | 1.225 kg/m³ at sea level and 15°C. Falls with altitude and with temperature. |
The inputs explained
| Field | What to enter |
|---|---|
| Rotor diameter (m) | Rotor diameter in metres, tip to tip. |
| Wind speed (m/s) | Wind speed at hub height in metres per second. Use the site average rather than a rated speed, and note that wind is faster higher up. |
| Air density (kg/m³) | Air density in kg/m³. Lower it for high altitude sites, where thinner air carries proportionally less energy. |
| Turbine efficiency coefficient Cp | The coefficient of performance. Anything above 0.593 is physically impossible and the calculator will say so. |
When to use it
Estimating output at a site
Rotor size and average wind speed give a first indication of what a site could produce, which is enough to rule out poor sites before any detailed assessment.
Seeing how much wind speed matters
The cubic relationship is easier to believe once seen. Comparing two speeds at the same rotor size shows why turbine siting is dominated by wind resource rather than by equipment choice.
Checking a manufacturer claim
Any claimed output implying a Cp above 0.593 is impossible regardless of the technology, and the calculator flags that directly.
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 much does wind speed change the output?
A fixed 80 metre rotor across a range of wind speeds.
| Wind speed | Power output | Available wind power | Swept rotor area |
|---|---|---|---|
| 4 m/s | 69 kW | 197 kW | 5,026.5 m² |
| 6 m/s | 233 kW | 665 kW | 5,026.5 m² |
| 8 m/s | 552 kW | 1,576 kW | 5,026.5 m² |
| 10 m/s | 1,078 kW | 3,079 kW | 5,026.5 m² |
| 12 m/s | 1,862 kW | 5,320 kW | 5,026.5 m² |
Questions
Why does power depend on the cube of wind speed?
Two of the three factors come from speed. Faster wind carries more kinetic energy per unit of air, which goes as the square of the speed, and it also delivers more air per second, which goes as the speed itself. Multiplying the two gives a cube.
What is the Betz limit?
The maximum fraction of the wind energy any open turbine can extract, 16/27 or about 59.3%. It follows from the air needing to keep moving: taking all the energy would halt the flow behind the rotor and block anything more from passing through. It applies to every design, not just to conventional turbines.
Why do real turbines only reach 35 to 45%?
Because the Betz limit is an ideal that ignores all real losses. Blade drag, tip vortices, the wake rotation imparted to the air, gearbox friction and generator losses all take a share. Modern large turbines get close to 0.45 at their best wind speed and less at others.
Does air density make much difference?
A real one at altitude. Power is directly proportional to density, so a site 2,000 m above sea level with air around 20% thinner produces about 20% less from the same rotor and wind speed. Temperature matters too, with cold dense winter air carrying more energy than warm summer air at the same speed.
For power from falling water rather than moving air, see the hydroelectric power calculator. For where energy supply sits in total emissions, see the Kaya identity calculator.