About Wind Turbine Power Calculator
The wind turbine power calculator returns the kinetic power available in the wind passing through a rotor and the realistic electrical power a horizontal-axis turbine can extract from it. Because the wind power scales with the cube of wind speed, doubling the wind speed produces eight times the available power, so accurate speed data dominates the result. The tool reports the rotor swept area, the available power, the actual electrical output after the rotor power coefficient (Cp) and drivetrain/generator efficiency, and how close the chosen Cp sits to the theoretical Betz limit.
Enter the rotor diameter, hub-height wind speed, air density (about 1.225 kg/m^3 at sea level), a power coefficient Cp, and the combined drivetrain efficiency. Optionally add a nameplate rated power and an annual capacity factor to estimate the annual energy production (AEP). The calculator flags any Cp above the Betz limit of 16/27 = 0.593 as physically impossible and plots the cubic power curve so you can see cut-in and rated behaviour.
How It Works
- Enter rotor diameter (m), wind speed (m/s), air density (kg/m^3), the power coefficient Cp, and the drivetrain/generator efficiency (0-1).
- The calculator computes the swept area A = (pi/4) D^2 and the available kinetic power P_avail = 0.5 rho A v^3.
- Actual electrical power = P_avail x Cp x efficiency; the tool also reports Cp as a percentage of the Betz limit (16/27 = 0.593) and flags any Cp above it.
- Optionally supply a rated power and capacity factor to estimate annual energy production: AEP = rated power x capacity factor x 8760 hours.
Worked Example
A utility turbine has a 100 m rotor in 12 m/s wind at sea-level air density 1.225 kg/m^3. The swept area is (pi/4) x 100^2 = 7854 m^2. The available kinetic power is 0.5 x 1.225 x 7854 x 12^3 = 0.5 x 1.225 x 7854 x 1728 = 8.31 MW. With a power coefficient Cp = 0.4 and a 100% drivetrain (eta = 1) the electrical power is 8.31 x 0.4 = 3.32 MW, which is 0.4 / 0.593 = 67.5% of the Betz limit. For a 3 MW machine at a 35% capacity factor the annual energy is 3000 x 0.35 x 8760 = 9.20 million kWh (9198 MWh).
Formulas
- Rotor swept area
A = (pi / 4) * D^2- Available kinetic wind power
P_avail = 0.5 * rho * A * v^3- Actual electrical power
P = P_avail * Cp * eta- Betz limit
Cp_max = 16 / 27 = 0.5926- Annual energy production
AEP = P_rated * CF * 8760
Standards & References
- Betz law (Albert Betz, 1919) — maximum extractable fraction 16/27 = 0.593
- IEC 61400-1 (wind turbine design requirements)
- IEC 61400-12-1 (power performance measurements)
- Wind energy fundamentals (kinetic flux P = 0.5 rho A v^3)
Frequently Asked Questions
Why does wind power depend on the cube of wind speed?
The kinetic energy flux through the rotor is proportional to the mass flow (rho A v) times the kinetic energy per unit mass (0.5 v^2), giving 0.5 rho A v^3. Doubling the wind speed therefore multiplies the available power by eight, which is why good site wind data matters most.
What is the Betz limit and can a turbine beat it?
The Betz limit, 16/27 = 0.593, is the maximum fraction of the wind kinetic power any open rotor can extract, because the air must keep some velocity to leave the rotor. No real turbine exceeds it; the calculator flags any Cp above 0.593 as physically impossible.
What power coefficient and efficiency are realistic?
Modern large turbines reach a peak Cp of about 0.45-0.50 (roughly 75-85% of the Betz limit) near their optimum tip-speed ratio, with drivetrain and generator efficiency around 0.92-0.96. Below cut-in or above rated speed the effective Cp is much lower.
How is annual energy production estimated?
AEP = rated power x capacity factor x 8760 hours. The capacity factor (typically 0.25-0.45 onshore, higher offshore) folds the wind-speed distribution and downtime into a single figure, avoiding the error of using the instantaneous power continuously for a year.