Ecology

Wind Turbine Power Calculator

Estimate the power output of a wind turbine.

Rotor diameter

Wind speed

Efficiency (Cp)

Calculated Output

Power output (kW) 39.408

Formula: P = ½ ρ A v³ Cp, ρ = 1.225

Step-by-Step Breakdown

1. Values used:

2. Rotor diameter = 20

3. Wind speed = 8

4. Efficiency (Cp) = 0.4

6. Power output = 39.408kW

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The math behind it

P = ½ × air density (1.225) × swept area × wind speed³ × Cp. Power scales with the cube of wind speed.

20 m rotor, 8 m/s, Cp 0.4 → ~39 kW.

Betz limit?

No turbine can exceed Cp ≈ 0.593 — the theoretical maximum efficiency.