Wind Turbine Power Output Calculator

Wind turbine power output is governed by a formula from fluid dynamics that relates power to the cube of wind speed, a relationship that makes wind resource quality critically important.

Wind power formula:

P = 0.5 × ρ × A × v³ × Cp

Variable definitions:

• P = Power output (watts)
• ρ (rho) = Air density — typically 1.225 kg/m³ at sea level, 15°C
• A = Rotor swept area = π × r² (where r = blade length in meters)
• v = Wind speed in m/s. This is the most critical variable.
• Cp = Power coefficient (turbine efficiency)

The Betz limit: In 1919, physicist Albert Betz proved theoretically that no wind turbine can extract more than 59.3% of the wind’s kinetic energy (the “Betz limit”). Real turbines achieve 35–45% efficiency (Cp = 0.35–0.45) — about 75% of the theoretical maximum.

Why wind speed is everything: Power scales with v³, meaning wind speed is exponentially important.

• Wind at 8 m/s produces 8× more power than wind at 4 m/s
• Wind at 10 m/s produces 3.9× more power than wind at 7 m/s
• A 10% increase in wind speed yields a 33% increase in power output

Turbine size reference:

Wind speed classes (Beaufort scale relevant range):

Most turbines reach their rated power at around 12–13 m/s and shut down above 25 m/s to prevent structural damage.

Worked example: A residential turbine with 5 m blade radius at 8 m/s wind speed:

• A = π × 5² = 78.5 m²
• P = 0.5 × 1.225 × 78.5 × 8³ × 0.40 = 9,797 W ≈ 9.8 kW

Site factors that change real output:

• Air density and altitude. Air density drops with altitude. At 1,500 m (5,000 ft) elevation, density falls to about 1.06 kg/m³, cutting power output by roughly 13% compared to sea level. Cold air is denser than warm air at the same altitude, so a winter site delivers slightly more power than a summer site at the same wind speed.
• Turbulence from obstacles. Trees, buildings, and uneven terrain create turbulent flow that reduces the effective wind speed feeding the rotor. The standard guideline is to mount the rotor at least 9 m (30 ft) above the highest obstacle within 150 m (500 ft).
• Annual energy production, not peak power. A turbine’s rated power is what it produces in ideal conditions, not what it averages. Sites with strong, steady wind (coastal, plains, ridge tops) realize 30 to 45% of rated capacity as annual production; sheltered or variable sites produce 15 to 25%. The wind speed distribution at the site matters more than the average.
• Ideal sites. Average wind speeds above 6 m/s (13 mph or 22 km/h) generally make a small turbine economic. Below 5 m/s, the math rarely works for grid-tied installations.