Wind Power Potential Calculator
Calculate theoretical wind power output based on wind speed, rotor diameter, and air density.
Includes Betz limit for practical maximum.
Wind Power Potential estimates how much energy can be extracted from moving air using a wind turbine or similar device.
The fundamental formula is:
P = 0.5 × ρ × A × v³
Where:
- P = power in watts (W)
- ρ (rho) = air density in kg/m³ (standard sea level value is 1.225 kg/m³)
- A = swept area of the rotor in m² (calculated from rotor diameter: A = π × (d/2)²)
- v = wind speed in meters per second (m/s)
The Betz Limit: In 1919, German physicist Albert Betz proved that no wind turbine can capture more than 59.3% of the kinetic energy in wind. This is known as the Betz limit. Real-world turbines typically achieve 35-45% efficiency due to mechanical losses, generator inefficiency, and blade design limitations.
Wind Speed Units: Wind speed can be measured in different units. For this calculation, all speeds are converted to meters per second internally.
- 1 mph = 0.44704 m/s
- 1 km/h = 0.27778 m/s
- 1 m/s = 1 m/s
Rotor Diameter: The rotor diameter determines the swept area, which is the circular area through which the blades pass. A small residential turbine might have a 3-5 meter (10-16 foot) rotor diameter. Large commercial turbines can have rotors exceeding 150 meters (490 feet) in diameter. Doubling the rotor diameter quadruples the swept area and therefore the power output.
Why wind speed cubed matters: The cubic relationship between wind speed and power is critical. If wind speed doubles, the available power increases by a factor of eight (2³ = 8). This means that even small increases in average wind speed at a site dramatically increase energy potential.
Practical examples:
- A small 3-meter rotor in 5 m/s (11 mph) wind produces roughly 57 watts (theoretical) or about 34 watts at Betz limit.
- A large 80-meter commercial turbine in 12 m/s (27 mph) wind can produce over 5 megawatts theoretically.
Air density considerations: Air density decreases with altitude and increases with colder temperatures. At sea level on a standard day, air density is 1.225 kg/m³. At 1,500 meters (5,000 feet) elevation, it drops to about 1.06 kg/m³, reducing power output by roughly 13%.
Tips:
- Ideal wind turbine sites have average speeds above 6 m/s (13 mph or 22 km/h).
- Turbulence from trees and buildings reduces effective power. Mount turbines well above obstacles.
- Annual energy production depends on the wind speed distribution, not just the average.