Wind Power Calculator (P = ½ρAv³)
Wind power depends heavily on wind speed because the energy scales with the cube of velocity. Doubling wind speed means 8 times more power. This calculator takes wind speed, blade length, air density, and turbine efficiency to estimate real-world power output, from a backyard turbine to a utility-scale wind farm.
The Wind Power Equation
P = 1/2 x rho x A x v cubed
Where rho is air density (1.225 kg/m cubed at sea level), A is the swept area of the rotor (pi x r squared), and v is wind speed in m/s.
The Cubic Relationship
This is the single most important thing about wind power: energy scales with the cube of wind speed.
| Wind Speed | Relative Power |
|---|---|
| 5 m/s | 1x (baseline) |
| 10 m/s | 8x |
| 15 m/s | 27x |
| 20 m/s | 64x |
A site with average 8 m/s winds produces more than twice the energy of a site with 6 m/s winds.
The Betz Limit
German physicist Albert Betz proved in 1919 that no wind turbine can extract more than 59.3% of the wind's kinetic energy. If it captured 100%, the air would stop and pile up behind the rotor. Modern utility turbines achieve 35-45% overall efficiency (including generator and gearbox losses), which is impressively close to the theoretical maximum.
Turbine Size Comparison
| Type | Blade Length | Rated Power |
|---|---|---|
| Small residential | 1-3 m | 0.4-10 kW |
| Community | 10-25 m | 50-500 kW |
| Utility onshore | 50-70 m | 2-5 MW |
| Offshore | 80-115 m | 8-15 MW |
Air Density Effects
Air density decreases with altitude and temperature. At 1,500 m elevation on a hot day, density might be 1.05 kg/m cubed instead of 1.225, reducing output by about 14%. Wind farms in highlands account for this in their projections.