Wind Energy Calculator

How it works

1. 1Enter the rotor diameter; the calculator derives the swept area A = π·(d ÷ 2)².
2. 2Supply the air density ρ (1.225 kg/m³ at sea level), the wind speed v, and the power coefficient Cp.
3. 3The formula P = ½·ρ·A·v³·Cp is applied and the result shown in watts, kilowatts, and estimated annual kWh.

Use cases

• Sizing a small or medium wind turbine for a home, farm, or remote site.
• Comparing how tower height (and therefore wind speed) affects energy yield.
• Teaching wind-energy physics and the impact of the Betz limit on turbine design.

Frequently asked questions

What is the formula used?

P = ½·ρ·A·v³·Cp, where ρ is air density (kg/m³), A is the swept area (m²), v is wind speed (m/s), and Cp is the power coefficient. Example: ρ = 1.225, d = 50 m → A ≈ 1963 m², v = 10 m/s, Cp = 0.4 → P ≈ 480 kW.

Why does doubling the wind speed increase power so much?

Wind power scales with v³ (the cube of wind speed). Doubling from 5 to 10 m/s multiplies the power by 2³ = 8, which is why turbines are sited where average wind speed is highest.

What is the Betz limit and why is Cp capped at 0.59?

Albert Betz proved no turbine can extract more than 16/27 ≈ 59.3% of the wind’s kinetic energy — the Betz limit. Real large turbines reach Cp ≈ 0.45–0.50; the input is capped at 0.59 to prevent physically impossible values.