What wind power depends on
The available power in wind depends on air density, rotor swept area, and wind speed cubed. Doubling wind speed increases available power by eight times before turbine limits are considered. That is why average wind speed alone can be misleading; the full wind distribution matters.
A turbine cannot capture all available wind energy. The power coefficient, Cp, represents the fraction converted by the rotor and drivetrain at a particular operating point. The theoretical Betz limit is about 59.3 percent, and real turbines operate below that, with Cp varying across wind speeds.
- Developers use it for early feasibility checks.
- Owners use it to compare site assumptions and expected kWh.
- Students and engineers use it to understand rotor and wind-speed sensitivity.
How to calculate wind turbine power
The formula is: P = 0.5 x rho x A x v^3 x Cp. P is power in watts, rho is air density in kg/m3, A is swept area in m2, v is wind speed in m/s, and Cp is the power coefficient. Swept area for a horizontal-axis turbine is A = pi x r^2.
Example: rotor radius is 5 m, so A = pi x 5^2 = 78.5 m2. Use air density 1.225 kg/m3, wind speed 8 m/s, and Cp = 0.35. P = 0.5 x 1.225 x 78.5 x 8^3 x 0.35 = about 8,600 W, or 8.6 kW at that wind speed.
From power to annual energy
Instantaneous power is not annual energy. Annual energy depends on the site's wind-speed distribution, turbine cut-in speed, rated speed, cut-out speed, downtime, electrical losses, wake effects, and curtailment. For a quick estimate, annual kWh = rated power x 8,760 x capacity factor.
If a 10 kW turbine has a 25 percent capacity factor, annual energy is 10 x 8,760 x 0.25 = 21,900 kWh. Revenue or bill savings then depends on the value per kWh, net metering rules, demand charges, incentives, and whether energy is consumed on site.
- Use measured hub-height wind data when possible.
- Do not apply one Cp value across an entire year as a final production estimate.
- Compare calculated power with the manufacturer's power curve.
Common wind estimate mistakes
The most serious mistake is using wind speed measured too low or too far from the turbine location. Wind shear, terrain, buildings, trees, and turbulence can make the rotor-level wind very different from a nearby weather station.
Another mistake is ignoring turbine limits. The cubic formula may produce power above the generator rating at high wind speeds, but real turbines cap output near rated power and shut down above cut-out speed for protection.
Frequently asked questions
Why is wind speed cubed in the power formula?
Wind energy depends on moving air mass and velocity. Combining mass flow through the rotor with kinetic energy produces the v^3 term.
What air density should I use?
A common sea-level standard is about 1.225 kg/m3, but density changes with elevation, temperature, humidity, and pressure.
Is Cp the same as efficiency?
Cp is the rotor power coefficient. Overall system efficiency may also include drivetrain, generator, inverter, and electrical losses.
Can the formula predict exact annual kWh?
Not by itself. Annual production requires a wind distribution and turbine power curve, not only one wind speed.