Betz Limit Power Calculator

Work out betz limit power instantly with clear inputs, formula shown and shareable results.

About Betz Limit Power Calculator

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.

Formulas

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

Worked example

With the default values below, Betz Limit Power Calculator returns Turbine Power Output of 4.5514. Change any input above and every figure here is recalculated in your browser.

Inputs used

Rotor Diameterminimum 0.01 m: 145 m
Wind Speedminimum 0 m/s: 10 m/s
Air Densityminimum 0.01 kg/m3: 1.225 kg/m3
Power Coefficient Cpaccepts 0.01–0.593: 0.45

Results

Turbine Power Output: 4.5514
Betz Limit Power: 5.9937
Total Wind Power Through Rotor: 10.1142
Achievement Of Betz Limit: 75.94%

Step by step

1Values used
2Wind power
3Extracted power
4Turbine Power Output= 4.5514
5Betz Limit Power= 5.9937
6Total Wind Power Through Rotor= 10.1142
7Achievement Of Betz Limit= 75.94

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why can't a turbine extract all the wind energy?

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.

Why does the cube law matter so much?

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.