Wind turbine energy calculator

A wind turbine converts kinetic energy in moving air into mechanical shaft work and then electricity. Site scouts, students, and small-project designers often need a transparent wattage and annual-energy figure from four numbers they already have: rotor diameter, mean wind speed, air density, and the rotor power coefficient. This wind turbine energy output calculator applies the actuator-disk kinetic-flux formula: power in watts is one-half times air density times swept area times wind speed cubed times the efficiency coefficient Cp, with swept area equal to pi times diameter squared over four. Annual energy in kilowatt-hours is that power times 8760 hours divided by 1000, treating the stated wind speed as a constant for the year.

What wind-turbine power means and how P = ½ ρ A v³ Cp is applied

Instantaneous wind-turbine power in this capability is the kinetic energy flux through the rotor disk times a power coefficient, not a manufacturer power curve and not a Weibull site assessment. The actuator-disk model starts from the mass of air that would pass through the swept area A in one second, density times area times speed, and from the kinetic energy per unit mass, one-half speed squared.

Their product is one-half times density times area times speed cubed: the available wind power in watts when density is in kilograms per cubic metre, area in square metres, and speed in metres per second. The rotor cannot extract all of that flux. Betz's limit says the theoretical maximum power coefficient Cp is sixteen twenty-sevenths, about zero point five nine three.

Real horizontal-axis machines typically operate between about zero point three and zero point four five on the rising part of the curve, below rated speed. This calculator multiplies the available flux by the efficiency coefficient you supply, so power equals one-half times air density times swept area times wind speed cubed times Cp. Swept area is the disk pi D squared over four, where D is the rotor diameter in metres, not the tower height and not the blade chord.

Annual energy in kilowatt-hours is that instantaneous power times eight thousand seven hundred sixty hours in a non-leap year, divided by one thousand watt-hours per kilowatt-hour. That annualization treats the stated wind speed as constant for the whole year: it is a first-order bound from a mean speed, not a capacity-factor or Weibull integral. The tool does not apply cut-in, rated, or cut-out speeds, does not fetch weather, and does not convert kilowatt-hours to money or carbon.

It answers the watts-and-annual-energy question from diameter, wind speed, density, and Cp so you can pair the result with your own tariff, emissions factor, or measured capacity factor.

What to enter, and why wind speed cannot be negative

A negative wind speed is rejected because kinetic energy flux is undefined for a reversed speed in this first-order model: there is no negative v that still cubes into a meaningful wattage, so the task fails rather than returning a signed power that a buggy client might treat as generation. Zero wind speed is valid and yields power of zero and annual energy of zero. Diameter and density must be strictly positive; a zero-area disk or a vacuum is not a turbine.

Efficiency must lie in the closed interval from zero through one; values above one would claim more than the kinetic flux. Numeric fields are rounded to twelve decimal places for stable goldens across runtimes. Example: an eighty-metre rotor, ten metres per second, density 1.225, and Cp 0.4 yields about 1.23 megawatts and about 10.8 million kilowatt-hours if that speed holds all year.