Wind Turbine Power Output Calculator Formula
Understand the math behind the wind turbine power output calculator. Each variable explained with a worked example.
Formulas Used
Power Output
power_output_kw = wind_power * efficiency / 100 / 1000Power Output
power_output_mw = wind_power * efficiency / 100 / 1000000Rotor Swept Area
swept_area_m2 = swept_areaBetz Limit Power
betz_max_kw = wind_power * 0.593 / 1000Variables
| Variable | Description | Default |
|---|---|---|
wind_speed | Wind Speed(m/s) | 12 |
rotor_diameter | Rotor Diameter(m) | 80 |
air_density | Air Density(kg/m³) | 1.225 |
efficiency | Overall Efficiency(%) | 40 |
swept_area | Derived value= pi * pow(rotor_diameter / 2, 2) | calculated |
wind_power | Derived value= 0.5 * air_density * swept_area * pow(wind_speed, 3) | calculated |
How It Works
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.
Worked Example
A turbine with 80 m rotor diameter operates in 12 m/s wind at 40% efficiency.
wind_speed = 12rotor_diameter = 80air_density = 1.225efficiency = 40
- 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
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