Wind Turbine Power Calculator
A wind turbine extracts power from moving air according to the wind power equation: power equals one half times the air density, times the rotor swept area, times the cube of the wind speed, times the power coefficient. The swept area is the circle traced by the blades, pi times the rotor radius squared. Because wind speed appears cubed, the available power rises steeply with wind speed, which is why turbine siting prioritises consistently windy locations. This calculator takes your rotor diameter, wind speed, air density, and power coefficient and returns the swept area, the total power in the wind, and the captured power for your coefficient. The Betz limit caps any turbine's coefficient at about 0.593.
Wind power formula
Swept area A = pi * (diameter / 2)^2
Power in wind = 0.5 * rho * A * v^3
Captured power = power in wind * Cp
Captured kW = captured power / 1,000
rho is air density in kilograms per cubic metre, v is wind speed in metres per second, and Cp is the dimensionless power coefficient. The Betz limit gives the theoretical maximum Cp of 16/27, about 0.593.
Wind power context
- The swept area scales with the square of the rotor diameter, so larger rotors capture far more power.
- Power scales with the cube of wind speed: a 26 percent increase in wind speed roughly doubles the available power.
- Standard sea-level air density is about 1.225 kg/m^3; it falls with altitude and rises in cold air.
- No turbine can exceed the Betz limit of about 0.593; real machines typically reach 0.35 to 0.45.
- Captured power is mechanical power at the rotor; generator and drivetrain losses reduce delivered electricity.
Wind turbine power: frequently asked questions
What is the wind turbine power equation?
Power equals one half times air density times swept area times wind speed cubed times the power coefficient: P = 0.5 * rho * A * v^3 * Cp. The swept area A is pi times the rotor radius squared. Because wind speed is cubed, doubling the wind speed gives eight times the available power.
What is the power coefficient Cp?
The power coefficient is the fraction of the wind's kinetic energy a turbine actually converts to mechanical power. The Betz limit sets the theoretical maximum at 16/27, about 0.593. Real utility-scale turbines typically reach roughly 0.35 to 0.45 at their best operating point. Enter your own coefficient as an input.
What air density should I use?
Standard sea-level air density is about 1.225 kilograms per cubic metre at 15 degrees Celsius. Air density falls with altitude and rises in cold weather, so the value is a user-editable input. Higher density means more power for the same wind speed.
Why is wind speed cubed in the formula?
Kinetic energy is proportional to the square of speed, and the rate at which air mass passes through the rotor is proportional to speed, so power scales with speed cubed. This strong dependence is why turbines are sited where average wind speeds are high.
Is this the electrical output of the turbine?
It is the mechanical power captured at the rotor for the coefficient you enter. Generator and drivetrain losses reduce the electrical output further. For net electricity, multiply by the combined drivetrain and generator efficiency or use a lower effective coefficient.
Official sources
- U.S. Department of Energy: How Do Wind Turbines Work.
- U.S. Energy Information Administration: Wind Explained.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.