Electrical output of a small wind turbine from the wind power equation, and why a 25% rise in wind speed nearly doubles the power.
| Rotor diameter | 30 m |
| Wind speed | 8 m/s (and 10 m/s for comparison) |
| Air density | 1.225 kg/m³ (sea level, 15 °C) |
| Power coefficient Cp | 0.42 (Betz limit 0.593) |
| Generator and drive efficiency | 94% |
Above rated wind speed the turbine limits its output by pitch or stall control, so the equation only applies up to the rated point. Real Cp also varies with wind speed; the manufacturer's power curve should be used for yield estimates.
| Check | Requirement | Actual | Status |
|---|---|---|---|
| Cp within Betz limit | ≤ 0.593 | 0.42 | ✓ PASS |
| Output at 8 m/s | Calculated | 87.5 kW | ✓ PASS |
| Output at 10 m/s | Calculated | 170.9 kW | ✓ PASS |
Key insight: Power rises with the cube of wind speed: (10/8)³ = 1.95. A small error in the site's wind speed becomes a large error in energy, which is why site wind measurement matters more than any other input.
Every input in this example is editable in the live calculator — no signup needed.
Open Wind Turbine Power Output calculator →Air density falls with altitude and temperature, and power falls in direct proportion. At 1000 m density is roughly 10% lower than at sea level.
The Betz limit shows that no turbine can extract more than 16/27 of the kinetic energy in the wind, because the air must keep moving to leave the rotor.