How to use the wind power output calculator
- Enter the rotor diameter and the wind speed, choosing the units.
- Check the air density, the power coefficient and the drivetrain efficiency. The defaults are examples; use your turbine data when you have it.
- Open the advanced options for the average wind speed, the rated power and the cut-in and cut-out speeds.
- Read the electrical output, the power in the wind, the swept area and the estimated energy per year, plus a table of power at other wind speeds.
Formula
swept area = pi x (diameter / 2)^2
power in the wind = 1/2 x air density x area x speed^3
electrical power = power in the wind x power coefficient x efficiency, limited to the rated power
yearly energy = average power over a Rayleigh spread of wind speeds x 8,760 hours
The power coefficient cannot exceed the Betz limit of 16/27, about 0.593. A Rayleigh distribution is a common simple model of how often each wind speed occurs, set by the average speed.
A 2 m rotor at 8 m/s
A rotor 2 m across sweeps 3.142 m2. At 8 m/s with an air density of 1.225 kg/m3 the wind carries 0.5 x 1.225 x 3.142 x 512 = 985.2 W through the rotor. With a power coefficient of 0.35 the rotor takes 344.8 W, and with 90 percent efficiency the output is 310.3 W.
If the wind speed doubles to 16 m/s, the output is 8 times as large, 2.48 kW. With an average wind of 5 m/s, a cut-in of 3 m/s and a cut-out of 25 m/s, the average power is 143.2 W and the energy is about 1,254 kWh per year. Limiting the generator to 300 W lowers that to 913 kWh.
The cube law
Power in the wind grows with the cube of the speed, so a small change in wind makes a big change in power. A site with an average of 6 m/s is not 20 percent better than one with 5 m/s; as far as the cubic term goes it has about 73 percent more power in the wind. That is also why a few gusty hours can produce much of a year's energy, and why siting matters more than almost anything else.
The yearly figure is a rough estimate that follows the shape of a standard wind distribution. Real sites differ, and the real output also depends on the turbine's power curve, height, turbulence and downtime.
Using the result
Use the maker's power curve for any purchase or siting decision. To price the energy, try the electricity cost calculator; to compare with sunlight, the solar payback calculator. Related radio and solar planning tools are the solar string sizing calculator and the dipole antenna length calculator.
Assumptions and limits
- Wind blows straight at the rotor at a steady speed, and the air density is the same at every speed.
- The power coefficient and efficiency are constant across wind speeds, which real turbines do not do.
- The yearly estimate uses a Rayleigh distribution of speeds, with the cut-in, cut-out and rated limits you give.
- Icing, wake effects from nearby buildings and trees, and downtime are not modeled.
Frequently asked questions
What is the Betz limit?
It is the largest share of the wind power that any rotor can capture, 16/27 or about 59.3 percent. Real rotors reach 30 to 50 percent. The page refuses a power coefficient above the limit.
What does cut-in mean?
It is the wind speed below which the turbine does not produce power. Below the cut-in speed, the output is zero, and above the cut-out speed the turbine shuts down for safety.
Why is my yearly energy smaller than the simple cube law suggests?
A real turbine is limited by its rated power and stops below the cut-in speed and above the cut-out speed. The page applies those limits when you set them.
How do I find the air density?
Sea level air at 15 C is about 1.225 kg/m3. It falls with altitude and rises when cold. The density altitude calculator shows the effect of height and heat.