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Enter the rotor diameter in metres and the wind speed in metres per second at hub height. This wind turbine power calculator first finds the swept area, pi times diameter squared divided by 4, then applies the wind power formula with standard air density 1.225 kg per cubic metre and a power coefficient Cp of 0.35, a typical value for a small turbine. For example, a 5 metre rotor at 8 metres per second sweeps 19.63 square metres and gives about 2,155 watts, or 2.16 kW. A 2 metre rotor at 6 metres per second sweeps 3.14 square metres and gives about 145 watts. This is a screening estimate, not a manufacturer certified output.
The wind turbine power formula has four steps. To calculate the output, work in watt units first, then convert to kW. First, find the swept area, the circle the blades sweep: pi times diameter squared divided by 4. Second, find the raw wind power passing through that area: 0.5 times air density times swept area times wind speed cubed. Third, apply the power coefficient Cp, the share of wind power the rotor actually captures. Fourth, in a full model, apply generator efficiency. This calculator uses standard air density 1.225 kg per cubic metre and Cp 0.35, and reports power in watts and kW, so you can check every step by hand.
Doubling rotor diameter quadruples swept area, because area grows with diameter squared. A 2 metre rotor sweeps 3.14 square metres, a 5 metre rotor sweeps 19.63 square metres, and a 10 metre rotor sweeps 78.54 square metres. That is why a rotor swept area calculator matters more than the nameplate rating alone: a slightly larger rotor in the same wind captures far more energy. Competitor tables show the same effect, for example a 5 metre blade radius at 8 metres per second giving about 10 kW, while a 2 metre blade radius at 5 metres per second gives under 0.2 kW.
Wind power doubling wind speed 8 times is the single most important rule in wind energy, because power grows with wind speed cubed. Going from 8 metres per second to 10 metres per second raises power by about 95 percent. Going from 6 to 8 metres per second raises it by about 2.37 times before efficiency limits. This is why site choice beats turbine choice: a site with a little more wind is worth far more than a slightly bigger turbine in poor wind. Always enter hub height wind speed, not a 10 metre weather station reading, and adjust 10 metre data with a wind shear model first.
The Betz limit 0.593 is the physical ceiling on Cp: no turbine can capture more than 59.3 percent of the wind power passing through its rotor, because the air must keep moving to leave the rotor. Modern turbines reach a Cp of about 0.35 to 0.50, and this calculator uses 0.35, a conservative small turbine value. A Cp above 0.593 is impossible, so any calculator that lets you enter one is wrong. If you know your turbine rated Cp, use that value in a full model, but never above the Betz limit.
Air density wind turbine output is directly proportional to density, so a 10 percent density drop gives a 10 percent power drop. Standard density is 1.225 kg per cubic metre at sea level. Air density altitude wind turbine power correction uses about 1.225 times exp(-0.000118 times elevation in metres), so high altitude and warm air both lower output. This is why output drops at high altitude even at the same wind speed. For a screening estimate at sea level, standard density is fine; for a mountain site, apply the altitude correction before trusting the result.
This wind turbine power at different wind speeds table uses a 5 metre rotor at Cp 0.35 to show the cube law in action. At 4 metres per second, about 269 watts. At 6 metres per second, about 908 watts. At 8 metres per second, about 2,155 watts. At 10 metres per second, about 4,208 watts. At 12 metres per second, about 7,270 watts. Compare this with competitor examples: a 50 metre rotor at 10 metres per second and Cp 0.40 gives about 480 kW, and a 100 metre rotor at 12 metres per second and Cp 0.45 gives about 2.97 MW. Small turbines follow the same physics at a smaller scale.
Wind turbine power calculator for home use starts from household demand, not from the biggest turbine you can buy. A typical American household uses about 10,000 kWh per year, about 27.4 kWh per day. At 5 metres per second average wind and a 25 percent capacity factor, a 5 kW turbine might suffice in that worked example, because 1.14 kW average need divided by 0.25 gives 4.56 kW. How much power does a 500W wind turbine produce at half its rated wind speed? Only about 62.5 watts, because power falls with the cube: 500 times (6 divided by 12) cubed. A 500W turbine rated at 12 metres per second gives about 657 kWh per year at 5 metres per second average and 15 percent capacity factor.
Wind turbine cut-in rated cut-out speed behaviour caps real output in ways a simple formula does not. Cut-in is often 3 to 4 metres per second, below which the turbine does not generate. Rated speed is about 11 to 13 metres per second, where output reaches its nameplate limit and stays there. Cut-out is commonly 20 to 25 metres per second, where the turbine stops for safety. Wind turbine rated power vs actual output therefore differs at high wind: this calculator gives instantaneous power with no rated cap, so treat very high results, above 50,000 watts, as a check against realistic rating limits, exactly as competitor result bands advise.
Annual energy production wind turbine estimates need more than instantaneous power. Annual kWh from a small wind turbine rotor diameter can be estimated as power in kW times 8,760 hours times capacity factor. Onshore capacity factors are often 25 to 45 percent, small wind about 9 to 22 percent. A back of envelope rule for small wind in imperial units is annual kWh equals 0.01328 times diameter in feet squared times wind speed in mph cubed, at hub height. For a wind turbine power calculator mph feet imperial units version, convert mph to metres per second by multiplying by 0.447, and feet to metres by multiplying by 0.3048, before applying the formula. A generator efficiency wind turbine factor of about 0.85 to 0.93, a tip speed ratio calculator check, and the manufacturer wind turbine power curve are needed for a bankable result.
The Betz limit is 0.593, the maximum share of wind power any turbine can capture. Air must keep moving past the rotor, so 100 percent extraction is impossible.
Modern turbines reach about 0.35 to 0.50. This calculator uses 0.35, a conservative small turbine value. Never enter a Cp above 0.593.
Power is directly proportional to air density. A 10 percent density drop gives a 10 percent power drop, and density falls with altitude and warmer temperature.
Enter hub height wind speed. Adjust 10 metre weather data with a wind shear model first, or the result will understate output.
Yes, when the nameplate is known, because rated power caps unrealistic high wind results. This screening calculator has no cap, so check very high results against the rating.
No, it gives instantaneous power only. Estimate annual energy as power in kW times 8,760 hours times capacity factor, typically 25 to 45 percent onshore.
Changing wind, turbulence, yaw error, control limits, rated power limits, generator losses, icing and curtailment all lower real output below the screening formula.
No. Also consider site suitability, structure, the manufacturer power curve, control limits, electrical integration, and engineering review.
It depends on wind and demand. A household using 10,000 kWh per year might need about a 5 kW turbine at 5 metres per second average wind and 25 percent capacity factor.
About 62.5 watts, because power falls with the cube of wind speed: 500 times (6 divided by 12) cubed.