Wind turbines convert the kinetic energy in moving air into electricity, and the physics behind that conversion follows one deceptively simple-looking formula: P = ½ρAv³Cp. Understanding each term — and especially why wind speed is cubed — explains why turbine siting, rotor size, and realistic efficiency expectations matter so much more than most people assume.
Why Wind Speed Matters More Than Anything Else
Because power scales with the cube of wind speed, small differences in average wind speed translate into large differences in energy output. A site averaging 8 m/s has roughly double the power potential of a 6.3 m/s site — not 27% more, but close to double, because (8/6.3)³ ≈ 2.05. This is the single biggest reason wind energy projects spend so much time and money on wind resource assessment before committing to a site: getting the location right matters more than almost any equipment choice.
Rotor Diameter and Swept Area
Swept area — the disc traced by the spinning blades — scales with the square of rotor diameter (A = π(D/2)²). Doubling the rotor diameter quadruples the swept area and, all else equal, roughly quadruples power output. This is why utility-scale turbines have grown from 40-50 m rotor diameters in the 1990s to 150-220 m today: bigger rotors capture proportionally far more energy per turbine, spreading fixed costs (foundation, tower, grid connection) over much more generation.
The Betz Limit: Why 100% Efficiency Is Impossible
In 1919, German physicist Albert Betz proved that no wind turbine — regardless of design — can extract more than 59.3% of the kinetic energy in wind passing through its rotor disc. The reasoning: if a turbine extracted 100% of the wind's energy, the air would have to come to a complete stop right at the rotor, which would block incoming wind entirely. Some energy must remain in the air so it can flow away and make room for more wind behind it. Real turbines fall further below this limit due to mechanical friction, generator losses, and blade aerodynamics — modern utility turbines typically achieve Cp values of 0.4-0.5, meaning they capture 70-85% of the theoretical Betz-limit maximum.
From Instantaneous Power to Annual Energy
This calculator's headline number is instantaneous power at the wind speed you enter — useful for understanding the physics, but real turbines see constantly varying wind. Annual energy production depends on the full distribution of wind speeds a site experiences over a year, typically modeled with a Weibull distribution, and is usually expressed via a capacity factor (actual average output divided by rated output). This calculator's annual estimate applies a simplified 35% capacity factor assumption for a rough sense of scale — a full site energy assessment would use actual measured wind speed data across the year.