Wind Energy Calculator Formula
Understand the math behind the wind energy calculator. Each variable explained with a worked example.
Formulas Used
Annual Energy Production
annual_mwh = power_watts * 8760 * capacity_factor / 100 / 1000000Theoretical Power
rated_power_kw = power_watts / 1000Homes Powered
homes_powered = power_watts * 8760 * capacity_factor / 100 / 1000000 / 10.5CO2 Avoided
co2_avoided = power_watts * 8760 * capacity_factor / 100 / 1000 * 0.92 / 2204.6Variables
| Variable | Description | Default |
|---|---|---|
rotor_diameter | Rotor Diameter(meters) | 80 |
wind_speed | Average Wind Speed(m/s) | 7 |
air_density | Air Density(kg/m3) | 1.225 |
capacity_factor | Capacity Factor(%) | 35 |
swept_area | Derived value= pi * pow(rotor_diameter / 2, 2) | calculated |
power_watts | Derived value= 0.5 * air_density * swept_area * pow(wind_speed, 3) * 0.4 | calculated |
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.
- 01Swept area: pi * (80/2)^2 = 5,027 m2
- 02Theoretical power: 0.5 * 1.225 * 5,027 * 7^3 * 0.4 = 423,096 W = 423 kW
- 03Annual energy: 423 * 8,760 * 0.35 = 1,296 MWh
- 04Homes powered: 1,296 / 10.5 = 123 homes
Frequently Asked Questions
What is capacity factor?
Capacity factor is the ratio of actual energy produced to theoretical maximum if the turbine ran at full power 24/7. Onshore wind averages 25-45%, offshore 40-55%.
Why does wind speed matter so much?
Power scales with the cube of wind speed (speed^3). Doubling wind speed increases power 8x. This is why turbine siting is critical.
How tall are modern wind turbines?
Modern onshore turbines have hub heights of 80-120 meters and rotor diameters of 80-170 meters. Offshore turbines can exceed 260m total height.
Ready to run the numbers?
Open Wind Energy Calculator