Wind Turbine Power Calculator

What this tool does

The power carried by the wind grows with the cube of its speed, so a site with 25 % more wind has nearly twice the energy. No rotor can capture more than 16/27 of it — about 59 %, the Betz limit — because the air has to keep moving to get out of the way; good modern blades reach roughly 45–50 % at their best point. Above the rated wind speed the blades pitch to spill power, which is why a real power curve flattens into a plateau and stops altogether in a storm. The output here uses one Cp for every wind speed, so the curve's knee is sharper than a real one.

Formula

P = ½ ρ A v³ C_p (C_p ≤ 16/27 ≈ 0.593, Betz limit) · limited to the rated power between cut-in and cut-out

Variables

Symbol	Meaning	Unit
`dr`	Rotor diameter	m
`v`	Wind speed	m/s
`ro`	Air density	kg/m³
`cp`	Power coefficient Cp	—
`pr`	Rated power	kW
`vi`	Cut-in wind speed	m/s
`vo`	Cut-out wind speed	m/s
`P`	Electrical output	kW
`PW`	Power carried by the wind	kW
`PB`	Most any rotor could take (Betz limit)	kW
`SA`	Swept area	m²
`VR`	Wind speed at which rated power is reached	m/s
`SR`	Running at, as a share of rated power	%

Worked example

Rotor diameter90 m
Wind speed8 m/s
Air density1.225 kg/m³
Power coefficient Cp0.42
Rated power2000 kW
Cut-in wind speed3.5 m/s
Cut-out wind speed25 m/s

Electrical output837.9 kW
Power carried by the wind1995.0 kW
Most any rotor could take (Betz limit)1182.2 kW
Swept area6362 m²
Wind speed at which rated power is reached10.69 m/s
Running at, as a share of rated power41.9 %

Limitations

The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
Coverage and consumption figures vary between products. Take the values from the manufacturer's datasheet for the product you are actually using.