Wind Energy Calculator Formula

Understand the math behind the wind energy calculator. Each variable explained with a worked example.

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Formulas Used

Annual Energy Production

annual_mwh = power_watts * 8760 * capacity_factor / 100 / 1000000

Theoretical Power

rated_power_kw = power_watts / 1000

Homes Powered

homes_powered = power_watts * 8760 * capacity_factor / 100 / 1000000 / 10.5

CO2 Avoided

co2_avoided = power_watts * 8760 * capacity_factor / 100 / 1000 * 0.92 / 2204.6

Variables

VariableDescriptionDefault
rotor_diameterRotor Diameter(meters)80
wind_speedAverage Wind Speed(m/s)7
air_densityAir Density(kg/m3)1.225
capacity_factorCapacity Factor(%)35
swept_areaDerived value= pi * pow(rotor_diameter / 2, 2)calculated
power_wattsDerived value= 0.5 * air_density * swept_area * pow(wind_speed, 3) * 0.4calculated

How It Works

How to Calculate Wind Energy Production

Wind turbine energy output depends on wind speed, rotor size, and efficiency.

Formula

Power (W) = 0.5 * Air Density * Swept Area * Wind Speed^3 * Efficiency

Swept Area = pi * (Diameter/2)^2

Annual Energy = Power * 8,760 hours * Capacity Factor

The Betz limit caps theoretical efficiency at 59.3%. Modern turbines achieve about 40% (Cp = 0.4). Capacity factor accounts for variable wind conditions.

Worked Example

An 80m rotor wind turbine in 7 m/s average wind with 35% capacity factor.

rotor_diameter = 80wind_speed = 7air_density = 1.225capacity_factor = 35
  1. 01Swept area: pi * (80/2)^2 = 5,027 m2
  2. 02Theoretical power: 0.5 * 1.225 * 5,027 * 7^3 * 0.4 = 423,096 W = 423 kW
  3. 03Annual energy: 423 * 8,760 * 0.35 = 1,296 MWh
  4. 04Homes powered: 1,296 / 10.5 = 123 homes

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