Wind Turbine Calculator

This wind turbine calculator (also called a wind power or wind energy calculator) estimates how much power a turbine produces at a given wind speed and how much energy it could generate in a year. Enter the rotor diameter, wind speed, power coefficient and air density. It uses the standard wind power formula and shows each step, so you can check a small home turbine’s claims before buying.

How wind turbine power is calculated

The wind power formula is:

P = ½ × ρ × A × v³ × Cp

• ρ (rho) is air density, 1.225 kg/m³ at sea level and 15 °C
• A is the swept area of the rotor, π × (diameter ÷ 2)²
• v is wind speed in meters per second
• Cp is the power coefficient, the share of the wind’s energy the turbine actually captures, capped at the Betz limit of 0.593

The power coefficient is a turbine’s aerodynamic efficiency. The Betz limit is the theoretical maximum of 16/27, about 59.3%, published by Albert Betz in 1920 (Betz, English translation 2013; ECE 333 notes).

For yearly energy, the calculator treats your speed as the site’s average and assumes a Rayleigh distribution of wind speeds. Then the average of v³ is 6/π (about 1.91) times the average speed cubed. Annual kWh = ½ × ρ × A × 1.91 × v³ × Cp × 8,760 ÷ 1,000.

Worked example with the default inputs

Defaults: 3 m rotor, 5 m/s wind, Cp 0.35, air density 1.225 kg/m³.

1. Swept area: π × 1.5² = 7.07 m²
2. Power in the wind: 0.5 × 1.225 × 7.07 × 5³ = 541 W
3. Turbine output: 541 × 0.35 = 189 W
4. Annual energy at a 5 m/s average: 3,169 kWh a year, about 264 kWh a month
5. 5 m/s = 11.2 mph

Wind turbine power by wind speed

All rows use a 3 m rotor, Cp 0.35 and sea-level air density.

Wind speed	mph	Power in wind	Turbine output	kWh/year (as average speed)
3 m/s	6.7	117 W	41 W	685
4 m/s	8.9	277 W	97 W	1,623
5 m/s	11.2	541 W	189 W	3,169
6 m/s	13.4	935 W	327 W	5,476
7 m/s	15.7	1,485 W	520 W	8,696
8 m/s	17.9	2,217 W	776 W	12,980

Going from 4 to 8 m/s multiplies output by 8, the cube law at work. Rotor size matters too: at 5 m/s a 1.5 m rotor gives 47 W and a 5 m rotor gives 526 W, because swept area grows with the square of diameter.

What affects the result

Wind speed. Because of the cube, a site 1 m/s windier can produce far more energy. Measure for a year if you can, at the planned hub height.

Height and obstacles. Wind is slower and more turbulent near the ground and around trees and buildings. Small turbines usually need tall towers well clear of obstacles.

Power coefficient. Small turbines rarely reach the efficiency of large ones. Use the manufacturer’s power curve rather than the rated wattage, which is often quoted at a high wind speed.

Rated power and cut-out. Real turbines stop increasing output above their rated speed and shut down in storms. The annual figure here ignores that cap, so treat it as an upper bound.

Air density. Thinner air at altitude or in heat lowers output. Output scales directly with density, so air 10% thinner gives 10% less power; enter a lower density for a high-altitude site to see the effect.

History of the Betz limit

The cap of 16/27 on the power coefficient is usually credited to the German physicist Albert Betz of Göttingen, who published “Das Maximum der theoretisch möglichen Ausnützung des Windes durch Windmotoren” in Zeitschrift für das gesamte Turbinenwesen in 1920. An English translation appeared in Wind Engineering in 2013 (Betz, 1920/2013).

Betz was not alone. The British engineer Frederick Lanchester had derived the same maximum in 1915, and Nikolai Joukowsky of the Russian aerodynamic school derived it in 1920, the same year as Betz. For that reason Gijs van Kuik argued in 2007 that it should be called the Lanchester–Betz–Joukowsky limit (van Kuik, 2007).

Year	Milestone	Source
1915	Lanchester derives the maximum for an ideal actuator disc	Wind Energy 10:289
1920	Betz and Joukowsky publish the 16/27 limit independently	Wind Energy 10:289
2013	Betz’s paper translated into English	Wind Engineering 37:441

Turning kWh into dollars

At the US residential average of 18.2¢/kWh (EIA, August 2026), 3,169 kWh a year is worth about $577. Check other loads and rates with the kWh calculator and the electricity cost calculator, and compare a rooftop array with the solar panel calculator.

References

• Betz, A. (1920). “Das Maximum der theoretisch möglichen Ausnützung des Windes durch Windmotoren.” Zeitschrift für das gesamte Turbinenwesen, 26, 307–309. English translation: Wind Engineering, 37(4), 441–446 (2013). doi:10.1260/0309-524X.37.4.441
• van Kuik, G. A. M. (2007). “The Lanchester–Betz–Joukowsky limit.” Wind Energy, 10(3), 289–291. doi:10.1002/we.218

Before buying, read our home wind turbine guide for siting, zoning and real-world output, or the broader wind energy guide. Both sit within our coverage of renewable energy sources.