What this calculator does
Find out how much electricity a wind turbine can make, right now and over a year. Wind is moving air, and moving air carries energy of motion (kinetic energy). The power flowing through a turbine's rotor depends on three things. They are how much area the blades sweep, how dense the air is, and above all, how fast the wind blows. Power rises with the cube of wind speed (speed × speed × speed). So doubling the speed gives eight times the power.
No turbine can catch all of that power, because the air has to keep moving to get out of the way. The calculator works out the power in the wind. It finds the most any rotor could catch, called the Betz limit. And it finds your turbine's output from its power coefficient (Cp), the share of the wind's power it turns into electricity. Then it turns that output into a yearly energy estimate using a capacity factor.
Where it's used
Why this math matters outside the classroom:
- Cube law. Wind farm planners know power grows with the cube of wind speed, so doubling the speed gives 8 times the power.
- Site surveys. Developers measure wind speed at a site for months before deciding whether a turbine is worthwhile.
- Small rotors. A rotor 10 m across in 8 m/s wind at 1.225 kg/m³ meets ½ × 1.225 × 78.5 × 512 ≈ 24.6 kW of wind power.
- Betz limit. Students learn that no turbine can capture more than 16/27, about 59%, of the wind's power.
- Annual energy. A 2 kW turbine at a 25% capacity factor makes about 2 × 8,760 × 0.25 = 4,380 kWh a year.
How to use it
- Choose whether you know the rotor diameter or the swept area, and enter it in meters or feet.
- Enter the wind speed at hub height in m/s, km/h, mph or knots.
- Keep the typical air density and Cp, or replace them with values for your site and turbine. Cp can't go above the Betz limit of 16/27.
- Enter a capacity factor to see the yearly energy. Then read the power and the step-by-step working.
What the inputs mean
- Rotor diameter
- Tip-to-tip diameter, twice the blade length plus the hub.
- Wind speed at hub height
- Wind speed rises with height above the ground. So a reading taken at ground level understates what the rotor feels.
- Air density (typical sea-level value: 1.225)
- 1.225 kg/m³ is the standard value for dry air at sea level and 15 °C. Air is thinner up high and in hot weather. Air at 1,500 m is roughly 14% less dense than at sea level. Local weather data or an air density calculator can give a better figure.
- Power coefficient Cp (typical: 0.35)
- Cp is the share of the wind's power that ends up as electricity. 0.35 is a typical round value for a working turbine. Large modern machines can reach the mid-0.4s at their best wind speed, and small turbines often manage less. A maker's power curve (a chart of output at each wind speed) lets you work out Cp at each speed.
- Capacity factor (example: 25%)
- The capacity factor is the turbine's average output over a year, divided by what it would give running flat out the whole time. It depends on how often and how hard the wind blows at the site. The 25% default is only an example. Wind studies for your site, or records from similar turbines nearby, give a realistic figure.
Formula and method
A = π × (d ÷ 2)² P_wind = ½ × ρ × A × v³ P_max = (16 ÷ 27) × P_wind (Betz limit) P = Cp × P_wind annual energy (kWh) = P (kW) × 8,760 h × capacity factor
In the formulas, d is the rotor diameter and A is the swept area, the circle the blades cover. ρ (rho) is the air density, v is the wind speed, and π is pi, the number used for circles. P stands for power.
The air flowing through the rotor each second has a mass of ρ × A × v. Each kilogram carries energy of motion of ½v². Multiply the two to get the power in the wind, ½ρAv³. It comes out in watts when you use metric (SI) units.
Albert Betz showed in 1919 that a perfect open rotor can take out at most 16/27 of that power, about 59.3%. The calculator won't accept a Cp above that limit.
For the yearly figure, the power is treated as the turbine's typical output. It's multiplied by the 8,760 hours in a 365-day year, and by the capacity factor.
Worked example
A small turbine has a 10 m rotor in a 7 m/s wind, with sea-level air (1.225 kg/m³), a typical Cp of 0.35, and an example capacity factor of 25%.
- Swept area: π × (10 ÷ 2)² = 78.54 m².
- Power in the wind: 0.5 × 1.225 × 78.54 × 7³ = 16,500.23 W.
- Betz limit: 16/27 × 16,500.23 = 9,777.92 W at most.
- Turbine output: 0.35 × 16,500.23 = 5,775.08 W, which is 5.775 kW.
- Annual energy: 5.775 kW × 8,760 h × 25% = 12,647.43 kWh.
Result: The turbine delivers about 5.78 kW in a steady 7 m/s wind. That's roughly 12,647 kWh a year at a 25% capacity factor.
Understanding the result
The power figure is for one steady wind speed. Real wind changes all the time. So a turbine's average output is far below its output in a strong gust.
Because power grows with the cube of speed, a small error in wind speed causes a large error in power. Guess the speed 10% too high, and the power comes out about 33% too high.
Comparing the result with the Betz maximum shows how much room the design leaves. A Cp near 0.45 is excellent; 0.25 or lower is common for small rooftop machines.
Assumptions and limitations
- Wind blows steadily and straight into the rotor, at the same speed across the whole swept area.
- Air density is constant at the value entered.
- Real turbines only start turning at a minimum speed, and they cap their output above a rated speed. Neither is modeled. So the formula keeps rising with v³ where a real machine would level off.
- It doesn't replace a maker's power curve or a measured study of the wind at your site.
- Using the power at the average wind speed underestimates average power. That's because the cube of an average is smaller than the average of the cubes. Use the capacity factor for yearly energy instead.
- Gusty, swirling air (turbulence), the wind shadow of nearby obstacles, and electrical losses after the generator aren't included.
Frequently asked questions
What is the Betz limit?
It's the largest share of the wind's power that any open rotor could ever catch: 16/27, or about 59.3%. If a turbine stopped the air completely, no new air could flow through. So the air leaving the rotor must keep some speed. Real turbines reach roughly 70% to 80% of the Betz limit at best.
Why does wind speed matter so much more than rotor size?
Power grows with the square of the rotor diameter, through the swept area. But it grows with the cube of wind speed. Doubling the diameter gives four times the power; doubling the wind speed gives eight times. That's why placing a turbine where the wind is strongest matters so much.
How do I get a capacity factor for my site?
Look for a wind study for your area or published output records from turbines nearby. A maker's estimate based on an average wind speed also works. Small turbines in built-up areas often reach only low single-digit to low double-digit percentages. Large turbines in good spots do much better.
Can I use this for a turbine on my house?
You can, but keep your expectations modest. Roofs sit in swirling air, where buildings and trees slow and disturb the wind. So measured output from rooftop turbines is often far below what a steady-wind formula suggests.
How this calculator is checked
Method: Kinetic power of an air stream, P = ½ρAv³; Betz (1919) limit Cp ≤ 16/27; annual energy via capacity factor × 8,760 h. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.
Embed this calculator
Put this Wind Turbine Calculator on your own website or blog for free. Paste this code where you want it to appear: