Wind Turbine Calculator

Power goes as the cube of wind speed, so 20 percent more wind is 73 percent more energy.

Power at this wind speed3.3251 MW3,325.1 kW

Swept area7,854 m²

At double the wind speed26.6 MWeight times, because the speed is cubed

With 20 % more wind5.7457 MW72.8% more power — which is why siting dominates

With double the rotor diameter13.3 MWfour times, because area goes as the square

Betz limit0.59259exactly 16/27 — a hard ceiling on every design

At the Betz limit this rotor would give4.926 MW

Annual output10,195 MWhat a 35% capacity factor

Annual revenue611,678at 60 per MWh

Betz proved in 1919 that no turbine can take more than 16/27 of the wind, and the reason is simple: extracting all the energy would stop the air dead behind the rotor, and stationary air cannot get out of the way of what is coming.

The formula

P = 0.5 * rho * A * v^3 * Cp, and Cp cannot exceed 16/27

The cube is everything

Power goes as the CUBE of wind speed, so a site with 20 % more wind yields 73 % more energy and one with double the wind yields eight times. Nothing else in the equation comes close to mattering as much, which is why site selection dominates turbine economics and why turbines keep getting taller: wind speed rises with height above the ground.

The Betz limit is a hard ceiling

No turbine of any design can extract more than 16/27 — 59.3 % — of the wind's kinetic energy. The reason is simple once seen: taking all the energy would mean the air stops dead behind the rotor, and stationary air cannot get out of the way of the air behind it. Albert Betz proved it in 1919 and it applies to every design ever built. Good modern turbines reach 0.45 to 0.50, which is close to the practical ceiling.

Rotor area, not blade length

Swept area goes as the square of the diameter, so doubling the blade length quadruples the power. That is the other reason turbines have grown: a rotor twice as wide on a tower twice as tall gets four times the area in faster wind, and the economics run away from small machines quickly.

How much to trust a footprint

Life-cycle figures for the same product routinely differ by a factor of two between studies, because deciding what to count — the farm, the packaging, the shop, the drive home, the disposal — is a methodological choice rather than a measurement. The numbers here are central estimates from published meta-analyses. They are reliable for comparing one option against another, which is what people actually use them for, and not reliable to the second significant figure.

The other thing worth keeping in view is scale. Individual choices matter and they are not where the emissions are: the difference between the best and worst quartile of beef producers is larger than most people's entire dietary footprint, and that is a question about agriculture policy rather than about shopping.