Wind Turbine Power Calculator

Estimate a turbine's output from its rotor size and the wind speed.

How the Math Works

The Wind Turbine Power Calculator uses the formula P = ½ ρ A v³ Cp to estimate power output. Here, P represents power in watts, ρ (rho) is air density (fixed at 1.225 kg/m³ for standard conditions), A is the swept area of the turbine blades in square meters, v is wind speed in meters per second, and Cp is the power coefficient (efficiency factor, typically between 0 and 1). The swept area A is calculated as π × (blade length)², meaning larger blades capture more wind energy. The cubic relationship between wind speed and power means even small increases in wind speed dramatically boost output, while Cp reflects how effectively the turbine converts wind kinetic energy into electricity, limited by the Betz limit (~59.3%).

Practical Applications

To use this calculator, input the wind speed at hub height, the turbine's blade length (to determine A), and the manufacturer-provided Cp value. For example, a 50-meter blade turbine has A = π × 50² ≈ 7,854 m². Multiply this by ½ × 1.225 × v³ × Cp to find power. If wind speed is 10 m/s and Cp is 0.4, power = 0.5 × 1.225 × 7,854 × 1,000 × 0.4 ≈ 1,944,000 watts (1.94 MW). This helps compare turbines for specific sites, optimize placement, and estimate energy generation for project planning.

Day-to-Day Use

This calculation empowers individuals and communities to evaluate wind energy feasibility for homes, businesses, or municipalities. Homeowners can assess whether installing a small turbine on their property yields meaningful savings on electricity bills. Urban planners use it to integrate renewable energy into city grids, reducing reliance on fossil fuels. Students and educators gain insights into sustainable energy systems, fostering informed decisions about green investments. By quantifying wind power potential, users can advocate for cleaner energy policies, understand local climate resilience, and participate in the transition to a low-carbon future.

Worked example

20 m rotor, 8 m/s, Cp 0.4 → ~39 kW.

FAQ