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Wind turbine power output calculator.
Watts from rotor size and wind speed. Doubling the wind speed gives eight times the power.
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Power output
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How do you calculate wind turbine power output?
The U.S. DOE's Small Wind Guidebook gives Power = Cp x 1/2 x rho x A x V³, where Cp is the power coefficient (0.25 to 0.45 in practice, theoretical maximum 0.59), rho is air density, A is the swept area of the rotor and V is wind speed. Wind speed carries an exponent of 3, so small gains in wind speed bring large gains in power. Air density comes from NASA's formula rho = p / [0.2869 x (T + 273.1)] with p in kPa and T in °C, about 1.225 kg/m³ at sea level and 15 °C. The Betz limit, 16/27 or 59.3%, is the most any rotor can capture.
Worked example. A 3 m rotor has 7.07 m² of swept area. In an 8 m/s wind at 15 °C and 101.3 kPa (1.225 kg/m³) with Cp 0.35: 0.35 x 0.5 x 1.225 x 7.07 x 512 = 776 W. At 16 m/s the same rotor would produce 8 times as much, about 6.2 kW, if the generator could take it.
Frequently asked questions
How much power does a wind turbine produce?
Power = Cp x 1/2 x air density x swept area x wind speed cubed. A 3 m rotor in an 8 m/s wind with Cp 0.35 gives about 776 W. Real output is capped by the generator's rated power.
What is the Betz limit?
No rotor can extract more than 16/27 (59.3%) of the wind's kinetic energy. DOE quotes 0.59 as the theoretical maximum Cp and 0.25 to 0.45 for real turbines.
Why does wind speed matter so much?
Power depends on the cube of wind speed. Doubling the speed gives 8 times the power; a 10% faster wind gives about 33% more.
Is this the same as annual energy?
No. This is instantaneous power at one wind speed. For yearly kWh use the small wind turbine annual energy calculator.
Sources
Checked
- U.S. Department of Energy WINDExchange: Small Wind Guidebook
- NASA Glenn: Earth Atmosphere Model (air density formula)
The power equation and the 0.25 to 0.45 Cp range are from the DOE Small Wind Guidebook; the Betz limit is 16/27. Air density uses NASA's formula. Real turbines also have cut-in speeds and rated power that this tool does not model. Runs entirely in your browser. Nothing you type is sent or stored.
Scope
Planning estimate only. Manufacturer power curves, turbulence and tower height determine real output. Wind turbines need a professionally engineered tower and electrical connection.