Wind Turbine Power Output Calculator
Calculate the theoretical power output of a wind turbine from wind speed, rotor diameter, and air density using the Betz limit.
m/s
m
kg/m³
%
Power Output
2,128.0 kW
Power Output2.128 MW
Rotor Swept Area5,027 m²
Betz Limit Power3,154.8 kW
Power Output vs Wind Speed
Wind Turbine Power Physics
Wind turbines extract kinetic energy from moving air. The available power depends on the cube of wind speed, which is why small increases in wind speed produce large gains.
Formula
P = 0.5 x rho x A x V³ x Cp
Where rho is air density (kg/m³), A is the rotor swept area (pi x r²), V is wind speed (m/s), and Cp is the power coefficient (efficiency). The Betz limit states that no turbine can capture more than 59.3% of the available wind energy.
Example Calculation
A turbine with 80 m rotor diameter operates in 12 m/s wind at 40% efficiency.
- 01Swept area = pi x (80/2)² = pi x 1600 = 5,026.5 m²
- 02Wind power = 0.5 x 1.225 x 5,026.5 x 12³ = 5,316,045 W
- 03Turbine output = 5,316,045 x 0.40 = 2,126,418 W = 2,126.4 kW
- 04That is 2.126 MW of electrical output