Wind Energy Calculator
Calculate wind turbine power output, swept area, and annual energy production based on wind speed, rotor diameter, and turbine efficiency. Includes Betz Limit validation.
Input Parameters
Results
P = 0.5 × ρ × A × v³ × Cp. The Betz Limit (Cp ≤ 0.593) is the theoretical maximum fraction of wind energy that can be extracted. Annual energy uses the capacity factor to account for real-world variable wind speeds.
Understanding Wind Energy Potential
Wind energy is one of the fastest-growing sources of renewable electricity worldwide. This calculator demonstrates the fundamental physics of wind power extraction using the kinetic energy equation and helps engineers, developers, and students estimate the energy potential of a given site and turbine configuration.
The Cubic Relationship
The most important concept in wind energy is the cubic relationship between wind speed and power. Because power is proportional to the cube of velocity (v³), doubling the wind speed increases available power by a factor of eight. This is why wind farm siting is so critical — even small differences in average wind speed between sites can dramatically affect annual energy production and project economics.
The Betz Limit
The Betz Limit, derived by German physicist Albert Betz in 1919, proves that no wind turbine can capture more than 59.3% (16/27) of the kinetic energy in the wind. This is because the air passing through the rotor must retain enough velocity to move away from the turbine. Modern commercial turbines typically achieve a coefficient of performance (Cp) between 0.35 and 0.45, which represents 60-76% of the theoretical maximum — a remarkable engineering achievement.
Capacity Factor and Real-World Performance
Wind does not blow at a constant speed. The capacity factor represents the ratio of actual annual energy production to the theoretical maximum if the turbine ran at full rated power 24/7. Onshore wind farms typically achieve capacity factors of 25-40%, while offshore wind farms can reach 40-55% due to stronger, more consistent winds. This calculator uses a user-defined capacity factor to estimate annual energy production from the rated power output.
Limitations
This is a simplified estimation tool. Real-world wind energy assessments use Weibull probability distributions to model variable wind speeds, account for hub height wind shear profiles, and consider turbine power curves that include cut-in speed, rated speed, and cut-out speed. For project development, a detailed wind resource assessment with at least one year of on-site anemometer data is standard practice.
Frequently Asked Questions
What wind speed is needed for a wind turbine to be economical?
Generally, a site needs an average annual wind speed of at least 5-6 m/s (11-13 mph) at hub height for a small turbine to be economically viable, and 6-7 m/s (13-16 mph) for large commercial turbines. However, economics depend heavily on local electricity prices, available incentives, and project costs. Sites below 5 m/s are rarely viable for wind energy production.
What is the Betz Limit and why does it matter?
The Betz Limit (59.3%) is the theoretical maximum efficiency for any wind turbine. It exists because if a turbine extracted all the wind's kinetic energy, the air would stop moving and block incoming wind. Modern turbines achieve Cp values of 0.35-0.45, which is 60-76% of this theoretical maximum. If your Cp input exceeds 0.593, this calculator will flag it as physically impossible.
How does rotor diameter affect power output?
Power output is proportional to swept area, which is proportional to the square of the rotor diameter. Doubling the rotor diameter quadruples the swept area and therefore quadruples the power output (all else being equal). This is why modern utility-scale turbines have grown to rotor diameters of 150+ meters — larger rotors capture significantly more energy.
What is a typical capacity factor for wind turbines?
Onshore wind turbines typically achieve capacity factors of 25-40%, depending on the wind resource. Offshore wind farms range from 40-55%. Small residential turbines may achieve only 10-25% due to lower hub heights and turbulent wind conditions. A capacity factor of 30% is a reasonable starting point for preliminary onshore estimates.