Wind Turbine Power Output Calculator

The power available in moving air through a turbine's swept area is P = ½ × air density × swept area × wind speed³ — the kinetic energy flowing through that area per second — and a real turbine only captures a fraction Cp (the power coefficient) of it, so extracted power = Cp × P. Swept area comes from the blade radius as π × radius². Verified via web search against MIT's wind-energy course materials and Electrical4U's turbine-theory reference rather than relied on from memory.

Because power depends on wind speed cubed, doubling the wind speed multiplies output by 8× — the single biggest factor in turbine siting. Betz's law caps Cp at 16/27 (about 59.3%) for any horizontal-axis turbine, a physical limit derived from momentum conservation in the airflow rather than an engineering shortfall, so this calculator rejects a Cp above it the same way it would reject a negative resistance. Real turbines run well under that ceiling, with 0.30-0.45 the commonly cited practical range — the gauge below shows how close an entered Cp sits to the theoretical maximum.

Blade radius and wind speed are converted to meters and meters/second (the units these formulas are published in) before the formula runs, the same convert-to-canonical-then-back pattern this site's Flywheel Kinetic Energy and Body Fat Navy calculators use for their own unit-toggled fields. Air density and the power coefficient are left as plain, un-toggled inputs since kg/m³ and a dimensionless 0-1 fraction are already the standard units used worldwide in wind-energy engineering.