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Wind Power

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Theoretically power in moving air - or wind - can be calculated

P = ρ A v3 / 2

= ρ π d2v3 / 8                                           (1)


P = power (W)

ρ = density of air (kg/m3 )

A = wind mill area perpendicular to the wind (m2)

v = wind speed (m/s)

π = 3.14....

d = wind mill diameter (m)

Be aware that the density of air decreases with temperature and altitude and that the major factor in wind power generation is wind speed .

  • 20% increase in wind velocity will increase the power generation with 73%

The theoretical and rated wind power generation from a typical windmill is indicated in the "wind speed-power curve" below. Cut-in wind speed, rated wind speed, shut-down wind speed and rated power for windmills with 20% and 40% efficiency.


Actual Available Power

Actual available wind power can be calculated

P a = ξ ρ A v3 / 2

ξ ρ π d2v3 / 8 (2)


ξ = efficiency of the windmill (in general less than 0.4 - or 40%)

Example - Wind Power

The actual available power from a wind mill with diameter 1 m , efficiency 0.2 (20%) - with wind velocity 10 m/s - can be calculated as

P a = (0.2) (1.2 kg/m3 ) π (1 m)2(10 m/s)3 / 8

= 94.2 W

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Online Wind Power Calculator

The calculator below can be used to calculate the available power from a windmill:


Generated Wind Energy

The energy generated over time depends on the wind mill potential power generation (as indicated above) - and how often, or how many hours the wind blows - or more scientifically - the "wind speed frequency distribution" at the actual location.

The total energy generated over a year can be calculated by summarizing the power generation for all velocities (ranging from the actual windmill cut-in speed to the shut-down speed) multiplied with the no. of hours the wind blows at the actual speeds.

A typical wind speed frequency distribution diagram with energy produced at the different velocities is indicated below.

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Related Topics


Climate, meteorology, solar, wind, emissions and environmental related engineering resources.

Fluid Mechanics

The study of fluids - liquids and gases. Involving velocity, pressure, density and temperature as functions of space and time.

Related Documents

Air - Density and Specific Volume vs. Altitude

Density and specific volume of air varies with elevation above sea level.

Air - Density vs. Pressure and Temperature

Air density at pressure ranging 1 to 10 000 bara (14.5 - 145000 psi) and constant selected temperatures.

Air - Density, Specific Weight and Thermal Expansion Coefficient vs. Temperature and Pressure

Online calculator, figures and tables showing density, specific weight and thermal expansion coefficients of air at temperatures ranging -100 to 1600 °C (-140 to 2900 °F) at atmospheric and higher pressure - Imperial and SI Units.

Air - Thermophysical Properties

Thermal properties of air at different temperatures - density, viscosity, critical temperature and pressure, triple point, enthalpi and entropi, thermal conductivity and diffusivity and more.


Efficiency is the ratio useful energy output to energy input.


Power is the rate at which work is done or energy converted.

Wind Energy

Available wind energy.

Wind Load vs. Wind Speed

Wind load on surface - Wind load calculator.

Wind Shear

Wind slowed down at surface by trees and obstructions.

Wind Turbine Power Calculator

Online wind turbine calculator.

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