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.
- 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
Frequently Asked Questions
Why does power depend on wind speed cubed?
The kinetic energy in wind is 0.5 m v^2. The mass flow rate through the rotor is rho A v. Power = energy x flow rate = 0.5 rho A v^3. So doubling wind speed increases power 8-fold. This is why site selection (average wind speed) is critical.
What is the Betz limit?
Albert Betz proved in 1919 that no turbine can extract more than 59.3% of the kinetic energy in the wind. This is because the wind must continue flowing downstream; extracting all energy would require stopping the wind entirely.
What wind speed is needed for viable wind power?
Annual average wind speed above 5-6 m/s is generally required for economic viability. Most utility-scale turbines are rated for 10-15 m/s wind and cut in at 3-4 m/s.
Ready to run the numbers?
Open Wind Turbine Power Calculator