Wind Turbine Calculator
Enter your turbine dimensions, wind speed, and loss factors to get instantaneous power, RPM, torque, annual energy yield, and estimated revenue. Works for both horizontal-axis (HAWT) and vertical-axis (VAWT) turbines.
Formula
Worked example
A HAWT with a 40 m blade radius at 12 m/s, Cp = 0.4, site at sea level 15 °C: A = pi x 40^2 = 5,027 m^2; wind power = 0.5 x 1.225 x 5,027 x 1,728 = 5,320 kW; after Cp: 2,128 kW; after 5% wake + 3% mechanical + 2% electrical + 1% grid + 3% downtime losses (keepFrac = 0.868): net = 1,847 kW. At TSR = 7: omega = 7 x 12 / 40 = 2.1 rad/s = 20.1 RPM; torque = 1,847,000 / 2.1 = 879 kN·m.
How wind turbine power is calculated
The power available in the wind passing through a turbine rotor is P = 0.5 x rho x A x v^3 x Cp. Here rho is the air density in kg/m^3, A is the swept area of the rotor, v is the wind speed in m/s, and Cp is the power coefficient, which is the fraction of kinetic energy the rotor actually captures. For a horizontal-axis turbine (HAWT), the swept area is the circle traced by the blades: A = pi x r^2. For a vertical-axis turbine (VAWT), the swept area is the rectangle of rotor diameter times blade height: A = D x H. This calculator also corrects air density for altitude and temperature using the International Standard Atmosphere model, so sites at elevation or in hot climates give more accurate estimates.
System losses and real efficiency
The raw Cp figure is only part of the story. A real turbine loses energy at every stage of the conversion chain. Wake losses arise when upstream turbines in a wind farm strip energy from the incoming flow, reducing output for downstream machines by 5-15%. Mechanical losses in the blades, shaft, and gearbox typically consume another 2-5%. Electrical losses in the generator and power electronics inside the nacelle add 1-4%, and further losses occur in the transmission cable and transformer between the turbine and the grid. Finally, maintenance shutdowns and faults mean the turbine is not generating for some fraction of the year, often 2-5%. This calculator applies all five loss categories multiplicatively to give the net power after all deductions, and reports the combined figure as the real efficiency.
RPM, torque, and the tip speed ratio
The tip speed ratio (TSR) is the ratio of the blade-tip speed to the free wind speed. It determines how fast the rotor spins. Most utility-scale HAWTs operate at a TSR of 6-9 for peak aerodynamic efficiency; VAWTs are typically 1-3. From the TSR and the wind speed, the rotor angular velocity (omega = TSR x v / r) and RPM can be computed directly. Torque follows from the net power: T = P / omega. High-TSR machines spin fast with low torque and suit direct-drive generators; low-TSR designs spin slowly with high torque. Knowing the RPM and torque is important for gearbox selection and structural loading.
Annual energy yield and revenue
The instantaneous net power at one wind speed is not the same as what the turbine earns over a year, because wind speed varies constantly. Annual energy is estimated here using a capacity factor, which is the average fraction of the rated power delivered over the year, accounting for wind variability. Onshore sites typically achieve 25-45%, offshore 35-55%. Multiply the net power in kW by 8,760 hours and by the capacity factor to get annual energy in kWh. Multiply that by the electricity tariff to get annual revenue. These are planning figures: a full energy yield assessment requires the actual wind speed distribution (usually a Weibull distribution) at hub height.
The Betz limit and real Cp values
No turbine can capture all the energy in the wind: the air must keep moving downstream to make room for the next parcel of air. Albert Betz showed in 1919 that the theoretical maximum power coefficient is 16/27, or about 0.593. Modern utility HAWTs reach a Cp of 0.35-0.45 near their optimal wind speed; small residential turbines and VAWTs typically fall in the range 0.25-0.40. The Betz limit holds for any turbine type, including VAWTs. Values above 0.55 in practice are extremely rare and would require near-perfect aerodynamic design with negligible blade drag.
Typical wind turbine scales and characteristics
| Class | Rotor size | Rated power | Typical TSR | Capacity factor | Typical use |
|---|---|---|---|---|---|
| Micro / pico | 1-3 m dia. | 0.1-1 kW | 3-6 | n/a | Boats, cabins, IoT sensors |
| Small residential | 3-10 m dia. | 1-25 kW | 5-7 | 20-30% | Homes, farms |
| Mid-size commercial | 10-40 m dia. | 25-500 kW | 6-8 | 25-40% | Communities, small wind farms |
| Utility (onshore) | 80-130 m dia. | 2-4 MW | 7-9 | 30-45% | Onshore wind farms |
| Utility (offshore) | 150-220 m dia. | 8-15 MW | 7-9 | 40-55% | Offshore arrays |
Approximate figures; exact values depend on turbine design, site wind class, and hub height.
Frequently asked questions
What is a good power coefficient (Cp) to use?
Modern utility-scale HAWTs achieve a Cp of about 0.35 to 0.45 near their optimal wind speed, so 0.4 is a reasonable default. VAWTs are typically 0.25-0.40. The theoretical maximum is the Betz limit of 0.593, so values above about 0.5 are unrealistic in practice.
What is the tip speed ratio and why does it matter?
The tip speed ratio (TSR) is the speed of the blade tip divided by the wind speed. It controls both efficiency and rotor RPM. Utility HAWTs run at TSR 6-9 to stay near their Cp peak. Too low a TSR wastes potential energy; too high creates excessive drag. The TSR also sets the rotational speed: at TSR 7, a 40 m radius turbine in 12 m/s wind spins at about 20 RPM.
Why does the output change so much when I adjust wind speed?
Power is proportional to the cube of wind speed (v^3). A 25% increase in wind speed nearly doubles the power, and doubling the wind multiplies the output by eight. This is why turbine siting, hub height, and local wind resource dominate the economics of a wind project.
What is a realistic capacity factor for a wind turbine?
Onshore turbines in good locations typically achieve a capacity factor of 30-40%, meaning they produce about one-third of what they would if running at full rated power all year. Offshore sites with stronger, steadier winds can reach 45-55%. Small or poorly sited turbines may fall below 20%.
How does altitude affect wind turbine output?
Air density decreases with altitude following the barometric formula. At 1,000 m above sea level, air density is roughly 10-12% lower than at sea level, so power output falls by the same fraction for the same wind speed. This calculator uses the standard atmosphere model to correct for both altitude and temperature.
What is the difference between a HAWT and a VAWT?
A horizontal-axis wind turbine (HAWT) has blades that rotate around a horizontal axis and must face into the wind. A vertical-axis turbine (VAWT) rotates around a vertical axis and can capture wind from any direction, but generally has a lower peak Cp. The swept area formula differs: HAWTs use a circle (pi x r^2) while VAWTs use a rectangle (diameter x height).
Is this the annual energy production?
No. The main result is instantaneous power at steady wind. Real wind varies constantly, so annual energy requires combining the power curve with the site wind distribution. The revenue estimate section provides a quick approximation using a capacity factor, but a formal energy yield assessment uses hourly wind data and the full turbine power curve.