Wind Turbine Power Calculator Formula
Understand the math behind the wind turbine power calculator. Each variable explained with a worked example.
Formulas Used
Wind Power Available
available_power = 0.5 * air_density * swept_area * pow(wind_speed, 3) / 1000Turbine Power Output
output_power = 0.5 * air_density * swept_area * pow(wind_speed, 3) * cp / 1000Swept Area
swept_area_out = swept_areaVariables
| Variable | Description | Default |
|---|---|---|
wind_speed | Wind Speed(m/s) | 8 |
rotor_dia | Rotor Diameter(m) | 80 |
air_density | Air Density(kg/m^3) | 1.225 |
efficiency | Overall Efficiency (Cp)(%) | 40 |
swept_area | Derived value= pi * pow(rotor_dia / 2, 2) | calculated |
cp | Derived value= efficiency / 100 | calculated |
How It Works
Wind Turbine Power
Wind power depends on the cube of wind speed and the swept area of the rotor.
Formula
P_available = 0.5 rho A V^3 (total wind power)
P_output = 0.5 rho A V^3 Cp (extracted power)
where rho is air density, A is the swept area (pi D^2/4), V is wind speed, and Cp is the power coefficient. The Betz limit states maximum Cp = 16/27 = 59.3%. Practical turbines achieve 35-45%.
Worked Example
An 80 m rotor diameter turbine in 8 m/s wind, Cp = 0.40.
wind_speed = 8rotor_dia = 80air_density = 1.225efficiency = 40
- 01Swept area = pi x 40^2 = 5,027 m^2
- 02Available power = 0.5 x 1.225 x 5027 x 8^3 = 0.5 x 1.225 x 5027 x 512
- 03Available = 1,576,461 W = 1,576 kW
- 04Output = 1,576 x 0.40 = 630.6 kW
Ready to run the numbers?
Open Wind Turbine Power Calculator