Work out betz limit power instantly with clear inputs, formula shown and shareable results.
Power in the wind crossing a rotor is 0.5 x air density x swept area x velocity cubed. No turbine can extract more than 16/27, or 59.26%, of that — the Betz limit — because the air must retain enough velocity to leave the rotor. Modern turbines achieve a power coefficient of 0.45-0.50, about 76-84% of Betz.
Wind power
P_available = 0.5 x rho x A x v^3, with A = pi D^2 / 4
Extracted power
P = 0.5 x rho x A x v^3 x Cp; Betz limit Cp = 16/27 = 0.5926
Extracting all kinetic energy would bring the air to a standstill behind the rotor, which would block further flow. The optimum slows the wind to one third of its upstream speed, giving the 16/27 limit.
Doubling wind speed gives eight times the power. It is why site selection dominates wind project economics, and why gusty sites need robust structural design.