keisoku

Wind Turbine Power & Energy

Estimate a wind turbine's power output (W/kW), swept area, and daily energy from rotor diameter, wind speed, and power coefficient. See the Betz limit too.

Input

m
m/s
kg/m³

Result

Power output (estimated)

631 kW

＝ 630,530 W

Swept area

5,027 m²

Theoretical max (Betz limit)

934 kW

Daily output (24h continuous)

15,133 kWh

There is an upper limit on how much of the wind's kinetic energy can be extracted (the Betz limit, about 59.3%), and a real turbine's Cp cannot exceed it. The figures shown are approximate.

How it works

  • Power output is calculated with P = 0.5 × air density ρ × swept area A × wind speed v³ × power coefficient Cp. The swept area A is π × radius², where the radius is half the rotor diameter.
  • Air density defaults to about 1.225 kg/m³ for standard atmosphere. Higher temperatures or higher altitudes lower the density, which also lowers the output.
  • The power coefficient Cp expresses how much of the wind's energy can be converted into electricity; the default here is 0.4. Real large turbines typically reach about 0.3 to 0.45.
  • Crucially, output is proportional to the cube of wind speed, so doubling the wind speed increases output roughly eightfold in theory. Small differences in wind speed have a large effect on energy production.
  • Because of the Betz limit, at most about 59.3% (16/27) of the wind's kinetic energy can be extracted. Cp cannot exceed this value.
  • The daily output assumes the power stays constant for 24 hours and is only an estimate. In reality it falls well short due to varying wind speeds and capacity factors (around 20-40%). Use it as a rough guide only.