How much power does a wind turbine make?

What the number means

The result is the electrical-side power a rotor of the given size could take from a steady wind of the given speed, before the losses of the generator, controller and wiring. It is a snapshot at one wind speed. What you actually pay for or save is energy over a year, which depends on how often the wind blows at each speed, so the calculator also gives a yearly estimate from the average wind speed.

The formula

Power = Cp × ½ × ρ × A × V³, as in the DOE Small Wind Guidebook. V is the wind speed in meters per second. A is the swept area, π × D² ÷ 4 for a rotor of diameter D. ρ is the air density: the calculator takes the pressure from the standard atmosphere at your altitude and divides by R × T, with R = 287.05 J/(kg·K) for dry air. Cp is the share of the wind's power the rotor captures, at most 16/27 = 0.593. For the yearly figure, the average of V³ for a Rayleigh wind distribution is 6/π ≈ 1.91 times the cube of the mean speed, so energy = ½ ρ A Cp × 1.91 × V̄³ × 8,760 hours.

Worked example

A 10-foot rotor (3.05 m) has a swept area of 7.3 m². At sea level and 59 °F the air density is 1.225 kg/m³. In a 15 mph wind (6.71 m/s) the wind carries ½ × 1.225 × 7.3 × 6.71³ = 1,348 W through the rotor. The Betz limit allows 799 W; with Cp = 0.35 the turbine yields 472 W. For a 10 mph annual average the Rayleigh estimate is 2,338 kWh a year. The DOE rule of thumb, 0.01328 × 10² × 10³, gives 1,328 kWh.

Limits of this method

One wind speed is not a year. A turbine starts only above its cut-in speed and stops producing more at its rated speed, so the cubic law holds only in between. The yearly estimate here ignores cut-in, the rated-power ceiling and all losses, so it tends to run higher than real output; the DOE rule of thumb is more conservative. The average wind speed must be measured where the rotor will be. The DOE guide says rotors should be 30 feet above any obstacle within 300 feet, and recommends getting a better estimate from the manufacturer, dealer or a site assessor. The capacity factor is only as good as the inputs. A value above about 50 percent is a warning sign that the rated power or the Cp is wrong. Cp is not a constant. It changes with wind speed and with the pitch and rpm of the rotor, so a single Cp is an average.

Common mistakes

Using the blade length instead of the diameter (the area is then four times too small); entering mph in the meters-per-second box (the cube makes the error large); using the rated power of the generator as the output at an ordinary wind speed; and comparing a power in watts with a yearly energy in kWh without multiplying by hours.

Questions

How is wind turbine power calculated?

The DOE Small Wind Guidebook gives Power = Cp × ½ × ρ × A × V³: the power coefficient Cp, the air density ρ in kg/m³, the rotor's swept area A in m², and the wind speed V in m/s, cubed. A 10-foot rotor (swept area 7.3 m²) in a 15 mph wind at sea level, with Cp 0.35, gives 472 watts.

What is the Betz limit?

No turbine can extract all the kinetic energy of the wind, because the air has to keep moving past the rotor. The theoretical maximum fraction is 16/27, or 59.3 percent, called the Betz limit; the DOE guidebook quotes it as 0.59. Real rotors reach a power coefficient Cp of about 0.25 to 0.45, according to the same guidebook, and the calculator does not accept a Cp above the limit.

Why does wind speed matter so much?

Power rises with the cube of the speed. Doubling the wind from 15 to 30 mph multiplies the output by eight, from 472 W to 3,773 W for the same rotor. A small difference in wind speed at your site is therefore a big difference in energy, and a turbine placed in a slower, turbulent wind near trees or buildings gives far less than the brochure suggests.

How much does altitude or temperature change the power?

Through air density. The standard atmosphere gives 1.225 kg/m³ at sea level and 15 °C, 1.019 kg/m³ at 5,000 feet (the same wind then yields 83 percent of the sea-level power) and 1.146 kg/m³ at sea level and 35 °C. The NREL consumer guides advise correcting for elevation, and note that a temperature correction is typically unnecessary for long-term performance estimates.

How many kWh does a small turbine produce in a year?

It depends on the average wind speed and the rotor size far more than on the rated power on the box. The DOE guidebook gives a preliminary rule: annual energy in kWh is 0.01328 × D² × V³, with D the rotor diameter in feet and V the annual average wind speed in mph. For a 10-foot rotor at 10 mph average that is 1,328 kWh. The calculator's Rayleigh estimate, with Cp 0.35 and a 10 mph average, is 2,338 kWh before losses. The two differ because the DOE rule, put through the same calculation, works out like a Cp of about 0.2, so it is the more conservative number and the better one for a first budget.

What average wind speed do I need?

The DOE guidebook says to consider a grid-connected small system if your annual average wind speed is at least 10 mph (4.5 m/s), and a battery or off-grid hybrid system from 9 mph (4 m/s). It also advises mounting the rotor at least 30 feet (9 meters) above any obstacle within 300 feet (90 meters), because turbulence near the ground wastes energy and wears the machine. Measure the wind at hub height before buying.

Does a bigger rotor help more than a taller tower?

Both help. The swept area grows with the square of the diameter: doubling the diameter from 10 to 20 feet gives four times the power, 1,887 W against 472 W at 15 mph. A taller tower reaches faster, smoother wind, and because of the cube law even a modest speed gain counts. The guidebook says the higher the tower, the more power the system can produce.

Sources: U.S. Department of Energy, Wind Energy Technologies Office, Small Wind Guidebook (power formula, Cp range 0.25 to 0.45, theoretical maximum 0.59, preliminary annual energy 0.01328 D² V³, 10 mph and 9 mph minimum average wind speeds, 30 ft above obstacles within 300 ft), and the NREL consumer guides "Small Wind Electric Systems" (air density corrected for elevation, temperature correction typically not needed), energy.gov and docs.nrel.gov, read October 27, 2026. Air density follows the International Standard Atmosphere. Betz limit: Albert Betz, 16/27. Capacity factors for typical small turbines are not given because we could not verify a current DOE or NREL figure. Related: solar panel calculator, electricity cost calculator, kinetic energy calculator. How we check our calculators.