Wind Turbine Calculator
The power a wind turbine makes from its blade length, the wind speed, the air density and its power coefficient, the Betz limit for that wind, and the energy in a year.
Result…
How it's calculated
A = π r² (r = blade length) P(wind) = ½ ρ A v³ P(turbine) = Cp × ½ ρ A v³, with Cp ≤ 16/27 ≈ 0.593 (Betz limit) Energy a year = P × capacity factor × 8,760 h, or average power × 8,760 h
The wind carries kinetic energy, and the power passing through the circle the blades sweep is ½ × air density × area × wind speed cubed. The area is π times the blade length squared, so doubling the blades gives four times the power, and doubling the wind speed gives eight times. A turbine can only take part of that: the power coefficient Cp. Betz's law shows no turbine can capture more than 16/27, about 59.3%, of the wind's power, because the air must keep moving to leave the rotor. Standard sea-level air at 15 °C has a density of 1.225 kg/m³; it falls with altitude and heat. For a year's energy, multiply the power by a capacity factor (the average output as a share of it) and by 8,760 hours, or enter an average power you already know.
Your numbers, step by step
About the Wind Turbine calculator
This wind turbine calculator estimates the power a rotor makes from the wind and the energy it could give in a year. Enter the blade length in metres or feet, the wind speed at hub height in m/s, km/h or mph, the air density and the turbine's power coefficient Cp from its maker. It works out the swept area, the power carried by the wind through that circle, the share the turbine turns into electricity, and the Betz limit: the most any turbine could take from that wind. For the year, enter a capacity factor or an average power you already know. Anyone weighing a small turbine for a home, farm or boat, or studying how wind power scales, can see each step with their own numbers and the cube law at work in the chart.
How to use it
- Choose “Blade length in” metres or feet and enter the “Blade length (rotor radius)”, half the rotor diameter.
- Enter the “Wind speed” at hub height and pick its unit.
- Keep the standard “Air density” or enter one for your altitude and temperature.
- Enter the “Power coefficient Cp” from the maker's power curve at that wind speed.
- Under “Yearly energy from”, enter a “Capacity factor” or an “Average power over the year” to get the energy in kWh.
Worked example
A small turbine has 1.5 m blades in an 8 m/s wind at sea level (1.225 kg/m³). The swept area is π × 1.5² = 7.07 m². The wind carries 0.5 × 1.225 × 7.07 × 8³ = 2,217 W through it. With Cp = 0.35 the turbine makes 0.35 × 2,217 = 776 W, or 0.776 kW; the Betz limit for that wind is 1.314 kW. At a 25% capacity factor that is 0.776 × 25% × 8,760 h = 1,699 kWh a year.
Updated
Questions people ask
How do I calculate the power of a wind turbine?
Multiply ½ × air density × swept area × wind speed cubed to get the power in the wind, then multiply by the power coefficient Cp. The swept area is π times the blade length squared.
What is the Betz limit?
It is the most power any turbine can take from the wind: 16/27, about 59.3%, as set out in Betz's law. The air has to keep flowing past the rotor, so it can never be stopped completely. Real turbines reach less than this.
What air density should I use?
The International Standard Atmosphere gives 1.225 kg/m³ (0.07647 lb/ft³) at sea level and 15 °C, as listed under density of air. Air is thinner at higher altitude and in warmer weather, which lowers the power.
Why does wind speed matter so much?
Power rises with the cube of the wind speed. Twice the wind gives eight times the power, so a site with slightly stronger wind, or a taller tower, can make a large difference.
Is it a mistake to use the average wind speed?
Often, yes. Because of the cube law, the power at the average wind speed is not the average power. Real turbines also only start above a cut-in speed and stop rising at their rated power, so the maker's power curve with wind data for your site gives a better yearly figure.
What is the energy worth?
Take the yearly kWh to the electricity cost calculator with your own price per kWh. Planning rules, grid connection and export payments differ by country, so check them locally before buying.