About the Wind Turbine Calculator
This wind turbine calculator estimates how much power a turbine produces and how many kilowatt-hours it generates in a year. Enter the rotor diameter, the average wind speed at hub height, the turbine’s power coefficient and its rated power, and the calculator applies the wind power equation across a realistic spread of wind speeds.
It suits homeowners and farmers weighing a small wind turbine, off-grid cabin builders comparing wind with solar, and students checking the physics. The annual figure is far more useful than the power at the average wind speed, because wind energy rises with the cube of wind speed and gusty hours contribute most of the output.
Wind speeds are modelled with a Rayleigh distribution (the standard assumption when only an average is known), with the turbine producing nothing below its cut-in speed or above its cut-out speed and capped at its rated power. Average wind at your actual hub height is the single most important input — ground-level readings are much lower, so use wind maps or on-site measurements.
With the default inputs, the annual energy production is 10,226 kWh. Change any value above to recalculate instantly.
How to use the wind turbine calculator
- 1Enter the rotor diameter from the turbine specification.
- 2Enter the average wind speed at hub height and choose m/s or mph.
- 3Set the power coefficient and the turbine’s rated power.
- 4Adjust cut-in, cut-out and air density if you know them.
- 5Read the annual kWh and value, and check the power curve.
Formula and method
The power in the wind through the rotor is ½ρAv³, where ρ is air density, A the swept area and v the wind speed. A turbine captures a fraction Cp of it; the theoretical maximum (the Betz limit) is 59.3%, and real small turbines achieve about 25–40% overall including generator losses. Output is zero below cut-in, capped at the rated power, and zero again above cut-out when the turbine shuts down.
Because power depends on the cube of wind speed, annual energy cannot be computed from the average speed alone. The calculator assumes wind speeds follow a Rayleigh distribution f(v) with your average, sums power × probability across speeds to get the average power, and multiplies by 8,760 hours in a year. Capacity factor is average power divided by rated power.
- ρ
- Air density, kg/m³ (1.225 at sea level)
- A
- Rotor swept area, m²
- Cp
- Power coefficient (overall efficiency)
- v
- Wind speed, m/s
- f(v)
- Rayleigh probability of each wind speed given the average
Worked examples
5 kW turbine with a 5 m rotor
A 5 m rotor sweeps 19.6 m². At a steady 5.5 m/s it would make only 0.70 kW, but across a Rayleigh spread of winds averaging 5.5 m/s the average output is about 1.17 kW, giving roughly 10,200 kWh a year — a 23% capacity factor, worth about $1,636 at $0.16/kWh.
10 m rotor, uncapped, 6 m/s average
A 10 m rotor sweeps 78.5 m². With 40% efficiency and no rated-power cap, the power at 6 m/s is 4.16 kW, while the average over the wind distribution is about 7.9 kW, or roughly 69,200 kWh a year.
Small 1.5 kW turbine in 12 mph winds
12 mph is 5.36 m/s. A 3 m rotor at 30% efficiency averages about 0.33 kW, or about 2,880 kWh a year — a 22% capacity factor on its 1.5 kW rating, worth about $577 at $0.20/kWh.
Frequently asked questions
How much electricity does a wind turbine produce?+
It depends mainly on rotor size and wind speed. A small 5 kW turbine with a 5 m rotor in a 5.5 m/s (12 mph) average wind produces roughly 8,000–11,000 kWh a year; a modern 3 MW utility turbine typically produces 6–10 million kWh a year.
Why does wind speed matter so much?+
Wind power rises with the cube of wind speed, so doubling the speed gives eight times the power. A site averaging 6 m/s produces roughly 70% more energy than one averaging 5 m/s, which is why tower height and siting matter more than almost anything else.
What is the Betz limit?+
The Betz limit is the maximum fraction of the wind’s kinetic energy a turbine can capture: 16/27, or 59.3%. Real turbines achieve less — large modern turbines around 45–50% at best, small turbines typically 25–40% including generator losses.
What is a good capacity factor for a wind turbine?+
Capacity factor is average output divided by rated output. Small residential turbines often achieve 10–25%, while large onshore wind farms in the US average about 35% and offshore wind can exceed 40%.
What average wind speed do I need for a home wind turbine?+
Guidance from the U.S. Department of Energy and installers generally puts the minimum at an annual average of roughly 4–4.5 m/s (9–10 mph) at hub height, and output rises steeply above that. Measure at hub height or use wind maps, as ground-level wind is much weaker.