Wind Turbine Calculator
Enter the blade radius, wind speed, and power coefficient to find the swept area and estimated power output.
Assumes standard air density of 1.225 kg/m³ at sea level.
How wind turbine power is calculated
Power output is found from P = 0.5 × air density × swept area × wind speed³ × power coefficient. Swept area (the circular area the blades pass through) is π × radius². Wind speed is cubed because kinetic energy in moving air scales with the cube of its velocity, making wind speed by far the most influential factor.
The power coefficient (Cp) represents how efficiently the turbine converts available wind energy into electricity. The theoretical maximum (the Betz limit) is about 0.593, but real-world turbines typically achieve 0.35-0.45 after accounting for mechanical and electrical losses.
Frequently asked questions
Why does wind speed matter so much more than other factors?
Because power scales with the cube of wind speed, doubling the wind speed increases available power by a factor of 8 (2³). This is why turbine siting in consistently windy locations matters far more than small changes in blade size.
What is the Betz limit and why can't turbines reach it?
The Betz limit (about 59.3%) is the theoretical maximum fraction of wind energy any turbine design can extract, based on fluid dynamics — extracting more would require stopping the wind completely, which isn't physically possible for an open turbine. Real turbines lose additional energy to mechanical friction, generator inefficiency, and blade design imperfections.
Does this account for cut-in and cut-out wind speeds?
No — real turbines have a minimum wind speed to start generating (cut-in speed) and a maximum safe operating speed before they shut down for protection (cut-out speed). This calculator gives the theoretical output at your specified wind speed, not accounting for these operational limits.