Calculate steady-wind power output and annual energy production from wind turbines using rotor diameter, wind speed, and efficiency parameters. Efficiency is capped at the Betz limit.
Last updated: March 2026
meters (m)
m/s (meters/sec)
kg/m³ (sea level: 1.225)
% (Betz limit: 59.3%)
% (accounts for downtime, maintenance)
(US avg household: 10,500 kWh/year)
*Betz limit (theoretical maximum efficiency) = 59.3%. Capacity factor = actual output / max theoretical. Annual production is a steady-wind estimate, not a forecast. Real turbines: 35–45%.
Wind power is the kinetic energy in moving air converted into electrical power by turbines. Wind speed has a cubic relationship with power output: doubling wind speed yields 8× more power. This explains why wind farms are located in high-wind areas (coasts, plains, ridgetops). A 2 m/s wind change dramatically affects economics.
The fundamental equation is P = ½ × ρ × A × v³ × η, where the swept rotor area A = π(d/2)². Betz's law states the theoretical maximum efficiency is 59.3%—turbines can't extract all wind energy without stopping the wind entirely. Modern turbines achieve 35–45% efficiency in practice. Air density decreases with altitude and temperature, reducing power output at high elevations or tropical climates.
Wind turbines operate intermittently (capacity factors typically 25–40%), unlike baseload coal plants (90%+). Availability accounts for maintenance, grid downtime, and weather events. Capacity factor = actual annual output ÷ theoretical maximum. A 3 MW turbine in a good wind site might produce 1 MW average power, giving ~33% capacity factor.
Tip: For on-site wind resource assessment, use 12-month wind speed data from local meteorological stations or anemometer measurements. Wind speed varies significantly by location, season, and height.
Scenario: Mid-size utility turbine with 80m rotor (5 MW nameplate capacity) in a good wind site averaging 7 m/s wind speed at hub height, 95% availability.
Calculation: Swept area = π × 40² = 5,027 m²; Wind power available = 0.5 × 1.225 × 5,027 × 7³ = 1,064 kW; Turbine output (35% eff) = 372 kW; Annual energy = 372 kW × 8,322 hours = 3.1 GWh
Result: ~295 US homes powered annually. Capacity factor ≈ 35%, typical for good wind sites. Poor sites (4–5 m/s average) drop to 20–25% capacity factor, making projects marginal.
Q: Why does wind speed matter so much?
A: Power scales with v³ (wind speed cubed). Double the wind speed → 8× more power. A 1 m/s increase at modest speeds dramatically changes output. This is why wind farms are sited in windy locations (coastal plains, mountain passes, offshore).
Q: What is capacity factor?
A: Capacity factor = actual annual output ÷ (rated capacity × 8,760 hours). Excellent sites: 40–50%; Good sites: 30–40%; Marginal sites: 20–30%; Poor sites: <20%. Higher CF improves project economics.
Q: What is the Betz limit?
A: Albert Betz proved that maximum theoretical wind turbine efficiency = 16/27 ≈ 59.3%. You can't exceed this; turbine blades would stop the wind. Real turbines achieve 35–45% due to blade drag, generator losses, and mechanical friction. This 59.3% ceiling is fundamental physics.
Q: How does air density affect output?
A: Power scales linearly with ρ (air density). High altitude (thin air): 10–15% less output. Cold winter: ~3% higher than warm summer. Denver (1 mile up): ρ ≈ 1.0 kg/m³ vs. sea level 1.225 kg/m³. Tropical near-equator: slightly lower due to heat expansion.
Q: What does availability mean?
A: Availability = % of time turbine is operational and grid-connected. Accounts for: scheduled maintenance, unplanned downtime, grid outages, icing, extreme weather curtailment. Modern turbines: 94–98% available. Poor maintenance: 85–90%.
Q: How much area does a turbine "sweep"?
A: Swept area = π(rotor diameter ÷ 2)². An 80m diameter turbine sweeps 5,027 m² (~1.2 acres or 0.5 hectares). Larger rotors capture more wind. 150m rotor sweeps 17,671 m². Doubling diameter → 4× area → 4× power (same wind speed).
Q: How many homes does one turbine power?
A: U.S. average household consumes ~10,500 kWh/year. A typical 2–3 MW onshore turbine powers 400–900 homes, depending on wind resource. Offshore turbines (10–12 MW, 10+ m/s winds) can power 3,000+ homes each.
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