Wind Turbine Power Calculator
Estimate the power output of a wind turbine.
Default 1.225
Default 0.4; Betz limit 0.593
Results update as you type.
How it works
This calculator estimates the electrical power a wind turbine can produce from its blade size and the wind speed. You enter the blade radius, the wind speed, and optionally the air density and a power coefficient, and it returns the power output in kilowatts and watts. The physics is captured by the wind power equation: power rises with the area the blades sweep, which grows with the square of the blade radius, and, most dramatically, with the cube of the wind speed. This cubic relationship is why wind speed matters so much; doubling the wind speed produces eight times the power, which is why turbines are sited in consistently windy locations. The power coefficient, or Cp, accounts for the fact that a turbine cannot capture all the wind's energy; the theoretical maximum, called the Betz limit, is about 0.593, and real turbines achieve roughly 0.35 to 0.45. Air density also matters, falling at higher altitudes and warmer temperatures, which reduces output. This is an idealized estimate of instantaneous power at a given wind speed; actual energy over time depends on the wind speed distribution at the site and the turbine's cut-in and cut-out speeds. Use it to understand turbine scaling and compare designs. Enter the blade radius and wind speed to estimate wind turbine power.
P = ½ · ρ · A · v³ · Cp
A wind turbine's power equals one half times the air density, times the swept area of the blades, times the cube of the wind speed, times a power coefficient. The swept area is pi times the blade radius squared. Because power depends on wind speed cubed, small increases in wind speed produce large jumps in output. The Betz limit caps Cp at 0.593.
Source:Wind energy physics
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter blade radius and wind speed.
- 2
Adjust the options
Adjust air density and power coefficient (cp) if they apply — sensible defaults are already set.
- 3
Read your result
Power output updates instantly as you type — no button to press.
Frequently asked questions
How is wind turbine power calculated?
Use the wind power equation: one half times air density, times the blades' swept area, times wind speed cubed, times the power coefficient. The swept area is pi times the blade radius squared. Enter these values and the calculator returns the instantaneous power output in kilowatts and watts for the given wind speed.
Why does wind speed have such a big effect?
Power depends on the cube of the wind speed, so small changes have large effects. Doubling the wind speed multiplies the power by eight, and a 10 percent increase raises output by about a third. This cubic relationship is why turbine siting in consistently windy locations matters far more than almost any other factor.
What is the Betz limit?
The Betz limit is the theoretical maximum fraction of wind energy a turbine can extract, about 0.593 or 59.3 percent. No turbine can exceed it, because slowing the air too much would block the flow behind the blades. Real turbines achieve power coefficients of roughly 0.35 to 0.45, well below this ideal ceiling.
What power coefficient should I use?
Modern large turbines reach power coefficients around 0.40 to 0.45 near their optimal wind speed, while smaller or older designs are lower. The default of 0.40 is reasonable for a good turbine. The value cannot exceed the Betz limit of 0.593, and it varies with wind speed and blade design, so use a figure appropriate to your turbine.
Is this the actual energy a turbine produces?
No, it is the instantaneous power at a single wind speed under ideal conditions. Real energy output over time depends on how often each wind speed occurs at the site, the turbine's cut-in and cut-out speeds, and mechanical and electrical losses. Use this for understanding and comparison, and consult performance curves for actual annual energy estimates.