About the Wind Turbine Power Calculator
This calculator estimates the electrical power a wind turbine can generate from the physical properties of the wind and the rotor. It implements the standard wind power equation used throughout wind-energy engineering:
P = 0.5 × ρ × A × v³ × Cp
- P — electrical power output, in watts (W).
- ρ (rho) — air density, in kg/m³. At sea level and 15°C, standard air density is about 1.225 kg/m³. Air density falls with altitude and rises in cold weather, so mountain or high-elevation sites generate less power for the same wind speed.
- A — the rotor's swept area, in m², calculated as A = π × r², where r is the blade (rotor) radius. A utility-scale turbine with 40 m blades sweeps roughly 5,027 m² — about ten American football fields.
- v — wind speed, in m/s, measured at hub height. Power depends on the cube of wind speed: doubling wind speed increases available power eightfold, which is why turbine siting is so sensitive to local wind resource.
- Cp — the power coefficient, a dimensionless efficiency factor describing how much of the available wind energy the turbine actually converts to electricity. Real-world turbines typically achieve Cp between 0.35 and 0.45.
The Betz limit
No turbine can capture 100% of the wind's kinetic energy — extracting all of it would mean stopping the air completely, which would block the flow behind the rotor. German physicist Albert Betz showed in 1919 that the theoretical maximum fraction of wind power any turbine can extract is 16/27 ≈ 0.593, known as the Betz limit. Any Cp value entered above 0.593 is not physically achievable and this calculator will flag it.
Why the cube of wind speed matters
The kinetic energy of a parcel of air is proportional to v², and the mass flow rate of air passing through the rotor is itself proportional to v (more air moves through per second at higher speed). Multiplying these together gives a v³ relationship for available power. This is the single most important fact in wind-energy siting: a site with average wind speeds of 7 m/s has roughly 59% more energy potential than one at 6 m/s (7³/6³ ≈ 1.59), not just 17% more.
Typical reference values
- Air density (ρ): 1.225 kg/m³ at sea level, 15°C, standard atmospheric pressure (1013.25 hPa). Roughly 1.1–1.2 kg/m³ is typical at higher elevations or warmer temperatures.
- Small residential turbines: rotor radius of 1–3 m, rated output often 1–10 kW.
- Utility-scale turbines: rotor radius of 40–80+ m, rated output commonly 2–6 MW at rated wind speed (typically 11–15 m/s).
- Cut-in speed: most turbines start generating around 3–4 m/s and reach rated power around 12–15 m/s, after which pitch control holds output roughly constant up to a cut-out speed near 25 m/s for safety.
From instantaneous power to annual energy
The power figure from the formula is an instantaneous value at one specific wind speed. Real wind speed varies constantly, so estimating annual energy production properly requires integrating power over a full wind speed distribution (commonly modeled with a Weibull distribution) rather than assuming one constant speed all year. The "estimated annual energy" figure on this page is a simplified projection that assumes the entered wind speed holds constant for 8,760 hours — useful for understanding scale, but production estimates for an actual project should use site wind-resource data and a power curve from the turbine manufacturer.