Wind Energy Power Calculator
Wind turbine power output is governed by the wind power equation: P = 0.5 * rho * A * v^3 * Cp. This formula captures the kinetic energy of air flowing through the turbine's rotor swept area. The critical insight is that power scales with the cube of wind speed: a 10 percent increase in wind speed increases power output by about 33 percent. This is why wind turbine siting to maximize wind speed is so important. The theoretical maximum power coefficient (Betz limit) is 0.593, but real turbines achieve 0.35 to 0.50. Enter your turbine parameters to estimate power output in watts and energy in kWh per day.
Wind power formula
A = pi * (D/2)^2 (rotor swept area, m2)
P = 0.5 * rho * A * v^3 * Cp (power in watts)
Daily energy (kWh) = P / 1000 * 24
Where rho is air density (kg/m3), A is rotor swept area (m2), v is wind speed (m/s), and Cp is the dimensionless power coefficient. The daily energy output assumes the turbine operates at the given wind speed continuously for 24 hours, which is an idealization. Real capacity factors for onshore wind turbines are typically 25 to 45 percent.
Wind energy context
- Wind power is the largest source of renewable electricity in the US, generating over 380 TWh per year (DOE 2023).
- A modern 3 MW utility-scale turbine with a 130 m rotor diameter can power about 1,000 homes per year.
- The US wind capacity factor averages about 35 percent, meaning turbines produce 35 percent of their theoretical maximum output.
- The best US onshore wind resources are in the Great Plains, with average wind speeds above 8 m/s at 80 m hub height.
- NREL's Wind Prospector tool provides US wind resource maps and data at hub heights relevant to wind development.
Frequently asked questions
What is the wind power equation?
The wind power equation is P = 0.5 * rho * A * v^3 * Cp, where P is power in watts, rho is air density (kg/m3), A is rotor swept area (m2), v is wind speed (m/s), and Cp is the power coefficient (Betz limit max 0.593). This equation is derived from the kinetic energy of the air mass passing through the rotor.
What is the Betz limit?
The Betz limit (0.593) is the theoretical maximum fraction of wind energy that a turbine can extract, derived by Albert Betz in 1919 using conservation of momentum. Real turbines achieve Cp values of 0.35 to 0.50, depending on design, wind speed, and tip-speed ratio.
Why does power increase with the cube of wind speed?
Wind power is proportional to v^3 because power equals kinetic energy per second. Kinetic energy is 0.5 * m * v^2, and the mass flow rate through the rotor (m/s) is proportional to v, giving P proportional to v^3. Doubling wind speed increases power eightfold.
What air density should I use?
Sea-level air density is approximately 1.225 kg/m3 at 15 degrees C (standard atmosphere, ICAO). At higher altitudes or warmer temperatures, density decreases. At 1,000 m elevation and 25 degrees C, density is about 1.07 kg/m3. Use the ideal gas law or NOAA atmospheric tables for accurate local values.
How is rotor swept area calculated?
The rotor swept area A = pi * r^2, where r is the rotor radius (half the rotor diameter). A 100-meter diameter turbine (typical utility-scale) has a swept area of about 7,854 m2. A 3-meter small wind turbine has a swept area of about 7 m2.
Official sources
- DOE: Wind Energy Technologies Office.
- NREL: NREL Wind Energy Research.
- NOAA: NOAA Atmospheric Data.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.