# Wind Turbine Power Calculator

URL: https://speedycalculator.com/calculators/ecology/wind-turbine/
Last updated: 2026-10-25

> The wind turbine calculator estimates the power and yearly energy from a wind turbine using its rotor diameter, wind speed, air density and efficiency (power coefficient).

## Inputs

- Rotor diameter (m, cm, mm, km, in, ft, yd, mi)
- Wind speed (m/s, km/h, mph, ft/s, knots)
- Air density (kg/m³)
- Power coefficient (Cp)
- Capacity factor (%)

## Results

- Power output
- Energy per year (with capacity factor)

## Formula

```
P = ½ ρ A v³ Cp
```

## Explanation

Power rises with the cube of wind speed, so doubling the wind gives eight times the power. The Betz limit caps efficiency at 59.3%.

### How to use the Wind Turbine Power Calculator

- **Rotor diameter**
- **Wind speed**
- **Air density**
- **Power coefficient (Cp)**
- **Capacity factor**

Results update as you type, and every field accepts the units shown in its menu.

### How it works

The swept area of the rotor and the cube of wind speed give the wind’s power; the power coefficient gives the share captured.

### Inputs explained

FieldWhat to enterRotor diameterUnits: m, cm, mm, km, in, ft …Wind speedUnits: m/s, km/h, mph, ft/s, knotsAir densityIn kg/m³Power coefficient (Cp)A numberCapacity factorIn %

### What each result means

- **Power output** = 0.5×[Air density]×pi×([Rotor diameter]÷2)^2×[Wind speed]^3×[Power coefficient (Cp)]
- **Energy per year (with capacity factor)** = [Power output]×8760×[Capacity factor]÷100÷1000

### Example values

How the main result changes when **Rotor diameter** changes and everything else stays at the example values above:

Rotor diameter (m)Power output (kW)51.447.53.25105.7812.59.021512.992023.1

## Worked example

Inputs — Rotor diameter: 10 m; Wind speed: 7 m/s; Air density: 1.225 kg/m³; Power coefficient (Cp): 0.35; Capacity factor: 30 %.

Results — **Power output = 5.78 kW**; Energy per year (with capacity factor) = 15,177 kWh.

## FAQ

**What is the Betz limit?**
No turbine can capture more than 16/27 (59.3%) of the wind’s kinetic energy.

**What is capacity factor?**
Actual yearly output as a share of the maximum possible; typically 25–45% for wind.

**What formula does the Wind Turbine Power Calculator use?**
P = ½ ρ A v³ Cp.