Wind turbine power calculator
Wind power goes as the cube of wind speed and the square of rotor diameter. No turbine can extract more than 59.3% of it.
m/s
kg/m3
%
Power output
775.8W
- Power in the wind
- 2216.7
- Betz limit
- 1313.6
- Swept area
- 7.069
- Annual generation
- 1700 kWh
- Output at twice the wind speed
- 6207
- Wind power density
- 313.6 W/m2
Show the working
- Rotor diameter = 3
- Wind speed = 8
- Air density = 1.225
- Power coefficient = 0.35
- Capacity factor = 25
- Swept area = pi * (3/2)^2 = 7.068 58
- Power in the wind = 0.5 * 1.225 * 7.068 58 * 8^3 = 2216.71
- Betz limit = 2216.71 * 0.5925925925925926 = 1313.6
- Power output = 2216.71 * 0.35 = 775.848
- Annual generation = 775.848 / 1000 * 8766 * 25/100 = 1700.27
- Output at twice the wind speed = 2216.71 * 8 * 0.35 = 6206.78
- Wind power density = 7.068 58 > 0 ? 2216.71/7.068 58 : 0 = 313.6
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- power in the wind = (1/2) rho A v^3
- Betz limit: no turbine can extract more than 16/27 = 59.26% of it
Doubling wind speed multiplies available power by eight. Siting matters far more than turbine quality.
Small roof-mounted turbines rarely justify themselves: turbulent, slow air near buildings cubes down to almost nothing.