P = ½ × ρ × A × v³ × Cp
Wind power is proportional to the cube of wind speed (P ∝ v³), meaning doubling wind speed increases power 8×. This cubic relationship makes site selection critical: a location with 8 m/s average wind produces nearly 3× more power than one with 6 m/s. The theoretical maximum fraction of wind energy that can be extracted is 59.3%, known as the Betz limit (derived by Albert Betz in 1919). Modern turbines achieve 35-45% of available wind energy (Cp = 0.35-0.45). The swept area A = πr² determines the "capture zone" — a turbine with a 126m rotor diameter (like the GE Haliade-X) sweeps 12,469 m². Larger turbines are more efficient because they reach higher altitudes where wind is stronger and more consistent. The world's largest turbine (Vestas V236-15.0 MW) has a rotor diameter of 236m and can power 20,000 homes. Global wind capacity reached 906 GW in 2023, generating 7.8% of world electricity, with costs falling 70% since 2009.