Wind Turbine Output Calculator
Wind Power Doesn't Scale in a Straight Line
Double the wind speed and turbine output doesn't double — it roughly increases eightfold, because power output depends on the cube of wind speed. That cubic relationship is why turbine site selection is so sensitive to even small differences in average wind speed, and why a modest-looking wind speed increase can be the difference between a marginal site and a strong one.
The Formula
A = π × r² (swept area)
ρ is air density, A is the swept area of the rotor blades, v is wind speed, and Cp is the power coefficient — the fraction of the wind's kinetic energy the turbine actually captures. Cp is capped at the Betz limit of 59.3%, the theoretical maximum for any wind turbine; real turbines typically run lower, often in the 35–45% range.
Where This Is Useful
- Site evaluation — compare expected output between candidate sites using measured average wind speeds.
- Turbine selection — a larger blade radius increases swept area (and therefore output) with the square of the radius, useful for comparing turbine models.
- Energy yield estimates — multiply instantaneous power by expected operating hours to project energy output over a day, month, or year.
Output Scales With the Cube of Wind Speed
| Wind speed | Power output |
|---|---|
| 4 m/s | 0.20 kW |
| 6 m/s | 0.67 kW |
| 8 m/s | 1.58 kW |
| 10 m/s | 3.08 kW |
| 12 m/s | 5.32 kW |
Going from 4 to 8 m/s (double the wind speed) increases output roughly eightfold, illustrating the v³ relationship directly.
How to Use This Calculator
- Enter the Blade Radius in meters.
- Enter the Wind Speed in meters per second.
- Optionally enter Air Density — defaults to 1.225 kg/m³ (sea level, 15°C) if left blank.
- Optionally enter the Power Coefficient (Cp) as a percentage — defaults to 40% if left blank.
- Optionally enter Hours to also get total energy output over that period.
- Select Calculate to get power output in kilowatts, and energy in kWh if hours were provided.
Related Calculations
Compare this against water-based generation with the Hydropower Output Calculator, or size a battery to store the output with the Battery Backup Calculator.