Wind Turbine Power Output Calculator
Estimate how many kilowatts a wind turbine generates given its rotor size, wind speed, and efficiency. Use this when siting a turbine or comparing turbine models for a renewable energy project.
About this calculator
A spinning wind turbine extracts kinetic energy from moving air. The theoretical power available in the wind is P = 0.5 × ρ × A × v³, where ρ is air density (kg/m³), A is the rotor swept area (m²), and v is wind speed (m/s). The swept area is π × (D/2)², where D is rotor diameter. Because no turbine can capture 100% of that energy (the Betz limit caps theoretical efficiency at ~59.3%), a real efficiency percentage is applied. The full formula used here is: P (kW) = 0.5 × 1.225 × π × (rotorDiameter/2)² × windSpeed³ × (efficiency/100) / 1000. Power scales with the cube of wind speed, so doubling wind speed increases power eightfold—making site selection critical.
How to use
Suppose a turbine has a rotor diameter of 40 m, faces a wind speed of 8 m/s, and operates at 35% efficiency. Step 1 — Swept area: π × (40/2)² = π × 400 ≈ 1,256.6 m². Step 2 — Raw power: 0.5 × 1.225 × 1,256.6 × 8³ = 0.5 × 1.225 × 1,256.6 × 512 ≈ 394,617 W. Step 3 — Apply efficiency and convert: 394,617 × 0.35 / 1,000 ≈ 138.1 kW. Enter those three values into the calculator to confirm the result instantly.
Frequently asked questions
Why does wind speed have such a large effect on turbine power output?
Power is proportional to the cube of wind speed (v³), meaning even small increases in wind speed dramatically raise output. For example, wind at 10 m/s carries eight times more power than wind at 5 m/s. This cubic relationship is why wind resource assessment is the most important step before installing a turbine. A site with consistently high average wind speeds will vastly outperform a site with the same rated turbine in calmer conditions.
What is a realistic efficiency percentage to use for a modern wind turbine?
Most commercial horizontal-axis wind turbines achieve efficiencies between 35% and 45% under optimal conditions. The hard physical ceiling is the Betz limit of approximately 59.3%, which represents the maximum fraction of wind energy any turbine can theoretically extract. Real-world losses from blade aerodynamics, mechanical friction, and electrical conversion push efficiency lower. For preliminary planning, 38–42% is a common and conservative estimate for modern utility-scale machines.
How does air density affect wind turbine power and when should I change the default value?
This calculator uses the standard sea-level air density of 1.225 kg/m³. Air density decreases with altitude and increases with cold temperatures, directly scaling the power output. At 2,000 m elevation, air density drops to roughly 1.006 kg/m³, cutting available power by about 18% compared to sea level. If your turbine sits at high elevation or in a region with extreme temperatures, you should adjust the formula's density value accordingly for accurate estimates.