Wind Turbine Power Output Calculator
The power output of a wind turbine is governed by the kinetic energy of moving air. The standard formula (IEC 61400-12) is P = 0.5 x rho x A x v^3 x Cp, where rho is air density, A is the rotor swept area, v is wind speed, and Cp is the power coefficient. The Betz Law limit caps Cp at 59.3%. Enter your turbine specifications and local wind conditions to compute theoretical maximum power (Betz limit) and estimated actual power output. Annual energy production (AEP) is estimated assuming an average wind speed and a capacity factor appropriate to the site.
Wind turbine power formula (IEC 61400-12)
Swept Area A = pi x (D/2)^2
Betz Limit Power = 0.5 x rho x A x v^3 x 0.593
Actual Power P = 0.5 x rho x A x v^3 x Cp
Annual Energy (kWh) = P(W) x 8,760 hours x Capacity Factor / 1,000
The formula derives from the kinetic energy equation: KE = 0.5 x m x v^2. For a column of air moving at velocity v through swept area A, mass flow rate = rho x A x v. Power = 0.5 x rho x A x v^3. The Betz coefficient (16/27 = 0.5926) is the theoretical maximum fraction of wind power extractable per actuator disk theory (Betz 1926, translated by NREL).
Wind resource and siting considerations
- Wind speed is the most critical variable. Power scales with the cube of wind speed: a 10% increase in wind speed yields 33% more power.
- Hub height matters significantly. Wind speed increases with height following the wind shear power law (typically v2/v1 = (h2/h1)^0.14 for open terrain per NREL).
- NREL's Wind Prospector tool (windprospector.nrel.gov) provides annual average wind speed at 80 m and 100 m hub height for the entire US.
- Small wind turbines are certified under AWEA/IEC 61400-2 and rated at 11 m/s (24.6 mph) reference wind speed.
- The US DOE defines a viable small wind site as having at least 4.0 m/s (8.9 mph) average annual wind speed.
Wind turbine power output: frequently asked questions
What is the Betz Law limit for wind turbines?
Betz Law, derived by German physicist Albert Betz in 1919, states that no wind turbine can capture more than 16/27 (approximately 59.3%) of the kinetic energy in wind. This is a fundamental thermodynamic limit derived from conservation of momentum. Modern commercial turbines typically achieve 35-45% efficiency (power coefficient Cp).
What is the formula for wind turbine power output?
P = 0.5 x rho x A x v^3 x Cp, where P is power in watts, rho is air density (approximately 1.225 kg/m^3 at sea level 15 C per ISO standard atmosphere), A is the rotor swept area in square meters, v is wind speed in m/s, and Cp is the power coefficient (efficiency). This is the standard formula used by IEC 61400-12.
How does wind speed affect power output?
Wind power is proportional to the cube of wind speed. Doubling wind speed increases power output by a factor of 8 (2^3). This cubic relationship means that small increases in average wind speed lead to large increases in annual energy production, which is why turbine siting and hub height optimization are critical.
What is air density and why does it matter?
Air density (rho) is the mass of air per unit volume, approximately 1.225 kg/m^3 at sea level and 15 C (ICAO standard atmosphere). At higher altitudes or temperatures, air density is lower, reducing power output. For example, at 2,000 m elevation, air density is roughly 1.005 kg/m^3, about 18% less than sea level.
What is a realistic power coefficient (Cp) for wind turbines?
The Betz limit sets a theoretical maximum Cp of 0.593. Modern large utility-scale turbines (Vestas V150, GE Haliade) achieve Cp of 0.45-0.50. Small residential turbines typically achieve Cp of 0.25-0.40. For initial site assessment, NREL and DOE recommend using Cp = 0.35-0.40 as a conservative estimate.
Official sources
- NREL: Small Wind Guidebook (NREL/DOE).
- IEC 61400-12-1: Power Performance Measurements of Electricity Producing Wind Turbines (IEC standard, referenced by NREL and DOE).
- U.S. DOE Office of Energy Efficiency: Small Wind Electric Systems (DOE).
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.