Wind Turbine Power Output Calculator

Wind turbine power is calculated using: P = 1/2 × ρ × A × v³ × Cp, where ρ is air density (~1.225 kg/m³ at sea level), A is swept area (π × blade length²), v is wind speed in m/s, and Cp is the Betz limit power coefficient (maximum 0.593, practical 0.35-0.50). The cubic relationship with wind speed is critical: doubling wind speed gives 8× the power output. Doubling blade length gives 4× the swept area and thus 4× the power. A 10m blade at 10 m/s wind with Cp=0.45 produces roughly 1/2 × 1.225 × π × 100 × 1000 × 0.45 = 86.6 kW.

The Betz limit states that no wind turbine can capture more than 59.3% of the kinetic energy in wind. This is because the air must retain some kinetic energy to exit the rotor area. Modern utility turbines achieve Cp values of 0.45-0.50, or 76-84% of the Betz limit. Small residential turbines achieve Cp of 0.25-0.35 due to lower Reynolds numbers and less sophisticated blade design. The Betz limit drives design choices: larger swept areas (longer blades), variable pitch control to maintain optimal tip-speed ratio, and placement in consistently windy areas to maximize energy capture.

Air density at sea level (15°C) is 1.225 kg/m³. At 1,000m elevation, density drops to ~1.11 kg/m³ (9% loss). At 2,000m, ~1.01 kg/m³ (18% loss). Colder temperatures increase density: -10°C air is about 10% denser than 25°C air, increasing power proportionally. Humidity also reduces density slightly (water vapor is lighter than dry air). For accurate power estimation, use local air density: ρ = P / (R × T), where P = air pressure (Pa), R = 287.058 J/kg·K, T = temperature in Kelvin. A 10% density change means 10% power change since power is linearly proportional to density.

Capacity factor is actual annual energy output divided by maximum possible output (running at rated power 24/7/365). Onshore turbines typically achieve 25-40% capacity factors. Offshore turbines achieve 40-55% due to stronger, more consistent winds. A 2 MW turbine with 35% capacity factor produces 2,000 × 0.35 × 8,760 = 6,132 MWh/year. Capacity factor depends on: average wind speed (most critical), turbine availability/maintenance downtime, grid curtailment, and turbine siting. Modern turbines in excellent wind sites (class I, >8.5 m/s average) can exceed 50% capacity factor.