Estimate how much electricity a wind turbine makes. Enter the rotor diameter, wind speed, air density and power coefficient to get the power output with P = ½ ρ A v³ Cp, plus an annual energy estimate based on a realistic spread of wind speeds, the capacity factor and a full power curve.
Last updated:
Turbine
Blade tip to blade tip (twice the blade length plus hub).
Share of wind power the rotor captures. Betz limit 0.593; small turbines ~0.25–0.35, large ~0.40–0.50.
%
kW
Output is capped here. Leave empty for no cap.
m/s
m/s
Wind
Used for instant power and as the annual mean for the energy estimate.
m
m
1/7 ≈ 0.143 for open land; 0.10 over water, 0.2–0.3 near trees or buildings.
Air density
Air density from
kg/m³
Enter your values to see the result.
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How to use the Wind Turbine Power Calculator
Enter the rotor diameter and the turbine's power coefficient and generator efficiency (defaults suit a small turbine).
Add the rated power and cut-in / cut-out speeds from the spec sheet, or leave the rated power empty for no cap.
Type your site's average wind speed and, if it was measured lower than the hub, turn on the hub-height adjustment.
Choose the air density: standard, from your elevation and temperature, or a custom value.
Read the power output and annual kWh, then check the power curve table to see which wind speeds produce the most energy.
The wind power equation
Swept area: A = π × D² ÷ 4 (a 7 m rotor sweeps 38.5 m²)
Power in the wind: Pwind = ½ × ρ × A × v³
Electrical output: P = Pwind × Cp × η, capped at the turbine's rated power
Betz limit: Cp ≤ 16/27 ≈ 0.593
Air density: ρ = p ÷ (287.05 × T), with pressure p = 101,325 × (1 − 2.25577×10⁻⁵ × h)5.25588 Pa at elevation h meters and T in kelvin
Hub height: vhub = vref × (hhub ÷ href)α, with α ≈ 1/7 over open ground
Example: a 7 m rotor at 6 m/s in sea-level air: ½ × 1.225 × 38.48 × 216 = 5.09 kW in the wind; × 0.35 × 0.90 = 1.60 kW of electricity.
Wind power by wind speed (sea level, ρ = 1.225 kg/m³)
Wind speed
Power in the wind (W/m²)
Electrical, Cp 0.35 × 90% (W/m²)
7 m rotor output (kW)
3 m/s (6.7 mph)
17
5
0.20
4 m/s (8.9 mph)
39
12
0.48
5 m/s (11.2 mph)
77
24
0.93
6 m/s (13.4 mph)
132
42
1.60
7 m/s (15.7 mph)
210
66
2.55
8 m/s (17.9 mph)
314
99
3.80
10 m/s (22.4 mph)
612
193
7.43
12 m/s (26.8 mph)
1,058
333
12.83
Notice how output climbs steeply: 12 m/s carries 64 times the power of 3 m/s. Real turbines limit output above their rated wind speed and shut down at cut-out speed to protect themselves.
Tips for a realistic estimate
Use measured or mapped wind data at your hub height. Average speeds from airports or weather apps are often measured at 10 m and can be lower than at a 30 m tower.
Height beats size near obstacles. Trees and buildings create turbulence; a common guideline is to put the rotor well above anything within a few hundred feet.
Check the manufacturer's power curve. If it is published, enter values so your curve matches it, or compare their annual energy figure at the same average wind speed.
Allow for losses: wiring, inverter, availability and icing typically shave another 5–15% off real-world output.
Frequently asked questions
What is the formula for wind turbine power?
P = ½ × ρ × A × v³ × Cp × η, where ρ is air density (about 1.225 kg/m³ at sea level), A is the swept area π × D² ÷ 4, v is the wind speed in m/s, Cp is the rotor power coefficient and η is the generator and electrical efficiency. The result is in watts.
How much power does a wind turbine produce?
It depends mostly on rotor size and wind speed. A 7 m rotor with Cp 0.35 and 90% efficiency makes about 1.6 kW in a steady 6 m/s wind at sea level, and about 7.4 kW at 10 m/s. A modern utility turbine with a 130 m rotor produces several megawatts at its rated wind speed.
What is the Betz limit?
The Betz limit says no turbine can capture more than 16/27, about 59.3%, of the kinetic energy in the wind passing through its rotor, because the air must keep moving to leave the rotor. Real large turbines reach a Cp of roughly 0.45 to 0.50 at best; small turbines are typically 0.25 to 0.35.
Why does wind speed matter so much?
Power rises with the cube of wind speed. Doubling the wind from 5 to 10 m/s gives eight times the power. That is why a site's average wind speed and the hub height are the most important factors, and why a small error in the wind estimate causes a large error in energy.
How is the annual energy estimated?
Wind is not steady, so the calculator assumes the common Rayleigh distribution (a Weibull distribution with shape factor 2) around your average wind speed. It multiplies the turbine's power at each speed by the share of hours at that speed and adds up 8,760 hours. Because power follows v³, this gives more energy than a constant average wind would.
What is a good capacity factor for a wind turbine?
Capacity factor is the average output divided by the rated power. Modern onshore wind farms in the US commonly average roughly 30% to 40%, while small turbines on homes often achieve much less, frequently below 20%, because of lower hub heights and turbulent wind near buildings and trees.
How does altitude affect wind turbine output?
Thinner air carries less energy. Air density falls by roughly 10% for every 1,000 m of elevation, and warm air is less dense than cold air. Power is directly proportional to density, so a turbine at 1,500 m produces about 14% less than the same turbine at sea level in the same wind.
Are all the tools on FreeToolCabin tested for quality and accuracy?
Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.