Wind Turbine Power Calculator
A wind turbine’s power at one wind speed, from its rotor size and power coefficient, with the Betz limit.
Result
Enter power coefficient, cp to see the result.
https://calcgallery.com/energy-utilities/wind-turbine-power-calculator/
Results are estimates based on the ratings, usage and prices you enter. Actual consumption, losses, tariffs and equipment performance vary. Check your bill, meter and manufacturer information before relying on the result. Read the full disclaimer
How to use the Wind Turbine Power Calculator
- Enter the rotor diameter, tip to tip.
- Enter the wind speed at the height of the hub.
- Enter the turbine's power coefficient at that speed, from its power curve or as an assumption.
- Read the turbine's power, the power in the wind and the Betz limit.
How it is calculated
swept area A = π × diameter² ÷ 4power in the wind = ½ × air density × A × speed³turbine power = Cp × power in the windBetz limit = 16/27 × power in the windThe power coefficient Cp is defined by the second and third lines: the share of the wind’s power that comes out of the turbine. It cannot be more than 16/27 ≈ 0.593, the Betz limit from momentum theory, and the page refuses a larger one.
Air density
Air density starts at 1.225 kg per cubic metre, the sea-level value at 15 °C in the U.S. Standard Atmosphere, 1976. Change it under More options for your site: air at higher altitude, at higher temperature or with more moisture is less dense, and power falls in the same proportion.
What the diagram shows
The rotor face on, with the circle its blades sweep and the wind arriving from the left. Faster wind is drawn with longer arrows.
With your numbers
- Swept area = π × diameter² ÷ 4 = 78.54 ft²
- Power in the wind = ½ × air density × area × speed³ = 689.9 W
- Turbine power = 0.35 × 689.9 W = 241.5 W
Quick reference
At one steady wind speed. A year’s energy depends on how often each speed blows, which this does not model.
| Example | Turbine power |
|---|---|
| 10 ft rotor, 12 mph, Cp 0.35 | 0.2415 kW |
| 10 ft rotor, 24 mph, Cp 0.35 | 1.932 kW |
| 6 ft rotor, 15 mph, Cp 0.3 | 0.1455 kW |
| 20 ft rotor, 18 mph, Cp 0.4 | 3.726 kW |
| 3 m rotor, 5 m/s, Cp 0.35 | 0.1894 kW |
| 10 m rotor, 10 m/s, Cp 0.4 | 19.24 kW |
| 82 m rotor, 12 m/s, Cp 0.45 | 2,515 kW |
Where the numbers come from
The fixed figures this calculator relies on, and the published source each one was checked against. How the calculators are built and checked
1 source
U.S. Standard Atmosphere, 1976, NOAA-S/T 76-1562, NASA-TM-X-74335, Table I "Geometric Altitude, Metric Units", p. 53, Z = 0 m: T 288.150 K, P 1.01325E+3 mb, ρ 1.2250 kg/m³. https://ntrs.nasa.gov/citations/19770009539
Used for
- Density of air at sea level in the standard atmosphere, at 15 °C and 1013.25 hPa: 1.2250 kg/m³. Warmer, higher or more humid air is less dense.
Common questions about the Wind Turbine Power Calculator
- How much power does a wind turbine produce?
- It depends most on the wind speed, because power goes with the cube of speed: twice the wind gives eight times the power. A rotor 10 feet across in a 12 mph wind has about 690 watts of wind passing through it; at a power coefficient of 0.35 the turbine makes about 240 watts. At 24 mph the same turbine would make about 1,930 watts, if it is rated for that much.
- What is the Betz limit?
- The most power any open rotor can take out of the wind: 16/27 of it, about 59.3%. It is named after Albert Betz. A rotor that took all of the wind’s energy would stop the air behind it, so no more could flow through; momentum theory shows the best a rotor can do is slow the wind to a third of its speed far behind it, which gives 16/27. Real turbines reach less, because of drag on the blades, the wake’s spin and losses in the gearbox and generator.
- Where do I find the power coefficient?
- Divide the power on the maker’s power curve at a given wind speed by the power in the wind at that speed, which this page shows. The coefficient changes with wind speed, so use the one for the speed you enter. The page does not assume one for you.
- Can I use an average wind speed to estimate yearly energy?
- Not with this formula. Because power rises with the cube of speed, the power at the average wind speed is below the average power over a year of gusts and calms. A yearly estimate needs how often each speed blows and the turbine’s power curve across all of them.