Wind power calculator
Power in the wind and the power a rotor can extract, against the Betz limit.
Fill in the fields and the result will appear here automatically.
Find instantaneous mechanical power of an idealised rotor from diameter, wind speed, density and Cp. The 24-hour row assumes unchanged wind and Cp; it is not a forecast of daily or yearly electricity generation.
How it works
Formula and logic
A=πD²/4, Pflow=ρAv³/2, Protor=Cp·Pflow. Betz power uses the exact fraction 16/27, not rounded 0.593. This form requires positive Cp≤16/27; v=0 is allowed and gives zero power.
Example
D=3 m,v=7 m/s,ρ=1.225 kg/m³,Cp=0.4 give≈0.594 kW rotor power,≈1.485 kW flow and≈0.8800 kW Betz limit.24 unchanged hours give≈14.256 kWh mechanical energy.
Fields and units
- Rotor diameter — m
- Wind speed — m/s
- Power coefficient — 1
- Air density — kg/m³
How to use
- — Enter wind at the rotor and appropriate density; tower height itself is not an input.
- — Do not treat mean wind speed as an energy forecast under changing wind.
- — Capacity factor=actual energy/(rated power×time); this form does not determine it.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- DOE: exact 16/27 bound and Cp meaning
- Limitation
- Ideal aerodynamic model of an isolated rotor. Cp does not automatically include generator losses, power limiting, shutdowns or control curves. Energy needs the time distribution of wind speeds and a power curve: mean v³ is not the cube of mean v.
FAQ
Why is the Betz limit exactly 16/27?
It follows from mass and momentum conservation: extracting energy means slowing the flow, but air brought fully to rest has nowhere to leave from behind the rotor. The optimum slows it to a third of the original speed and yields 59.3 per cent.
Why does speed matter more than diameter?
Diameter enters squared, speed cubed. Twice the wind gives eight times the power; matching that with a bigger rotor would take almost three times the diameter.
Why is real output below the calculation?
Ideal aerodynamic model of an isolated rotor. Cp does not automatically include generator losses, power limiting, shutdowns or control curves. Energy needs the time distribution of wind speeds and a power curve: mean v³ is not the cube of mean v. Capacity factor=actual energy/(rated power×time); this form does not determine it.
Is tower height included?
Enter wind at the rotor and appropriate density; tower height itself is not an input.