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Wind energy is the kinetic energy of air in motion (recall that air has density, hence, mass).
To estimate wind energy, imagine a surface with area A, which is perpendicular to the direction of the wind.
In this case, energy, flowing with the air with density through an imaginary surface with area with the speed during the time is
As you can see, this is formula for kinetic energy with mass of air expanded as multiplication of volume and density of air.
Power is energy per unit time, so the wind power is
Calculator below uses these formulae to calculate wind energy and wind power.
But do not forget that in order to use it, it should be converted into other type of energy, for example, electrical energy. As said in wikipedia, in 1919 the German physicist Albert Betz showed that for a hypothetical ideal wind-energy extraction machine, the fundamental laws of conservation of mass and energy allowed no more than 16/27 (59.3%) of the kinetic energy of the wind to be captured.
To give you the idea about wind energy and power, below are some fun facts for reference.
The heat required to raise the temperature of 1 liter of water from 20°C to 100°C is 335 000 Joules
1 kW·h is 3 600 000 Joules
Energy of explosion of 1 tonn of TNT is 4 184 000 000 Joules
Typical power of electrical kettle ranges from 800 to 2500 Watt
Eurostar train has power of 12 000 000 Watt.