Wind Energy Calculator

The Wind Energy Calculator estimates wind turbine power output using the equation P = ½ρAv³Cp. It adjusts wind speed for hub height using the log wind profile, generates power curves with cut-in/cut-out speeds, calculates annual energy production (AEP), and shows the Betz limit — with interactive charts AI cannot replicate. Free, no signup.

Turbine Presets

Terrain Type

z₀ = 0.03 m

Rotor Diameter (m) (m)

Wind Speed (m/s) (m/s)

Air Density (kg/m³) (kg/m³)

Power Coefficient (Cp) (Cp)

Generator Efficiency (%) (%)

Availability (%) (%)

Hub Height (m) (m)

Measurement Height (m) (m)

Terrain Roughness (m) (m)

Results

Swept Area

6,361.73 m²

Theoretical Power

5530.55 kW

Betz Limit Power

3277.36 kW

Actual Power Output

2140.49 kW

Annual Energy (AEP)

18750.67 MWh/year

Capacity Factor

38.70%

Wind Speed at Hub Height

11.24 m/s

CO₂ Saved/Year

7500.27 tonnes CO₂/year

Tip Speed Ratio: 7Betz limit: 59.3% — maximum theoretical extraction

Power Curve

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What is a Wind Energy Calculator?

A Wind Energy Calculator estimates the electrical power output of a wind turbine using the fundamental wind power equation: P = ½ × ρ × A × v³ × Cp × η, where ρ is air density (1.225 kg/m³ at sea level), A is the swept area (π × r²), v is wind speed, Cp is the power coefficient, and η is generator efficiency. The Betz limit (59.3% or 16/27) represents the theoretical maximum energy extraction from wind. Real turbines achieve Cp = 0.35-0.48. The calculator adjusts wind speed from measurement height to hub height using the logarithmic wind profile, accounting for terrain roughness.

How to Use This Calculator

Enter the turbine rotor diameter or select a preset (from micro to offshore turbines)
Input the average wind speed at your measurement height
Select terrain type for roughness correction (affects hub height wind speed)
Adjust power coefficient Cp (typical 0.35-0.45) and generator efficiency
View power output, annual energy production (AEP), power curve, and CO₂ savings

Frequently Asked Questions

What is the Betz limit and why is it 59.3%?

The Betz limit (16/27 ≈ 59.3%) is the theoretical maximum fraction of kinetic energy a wind turbine can extract from the wind. Derived by Albert Betz in 1919, it occurs because the wind must continue moving past the turbine — if all energy were extracted, wind would stop and block incoming flow. Modern turbines achieve power coefficients (Cp) of 0.35-0.48, with the best offshore turbines approaching 0.50 in optimal conditions.

Why does wind power increase with the cube of wind speed?

Wind power follows P = ½ρAv³ because kinetic energy depends on velocity squared (½mv²) and the mass of air passing through the rotor per second increases linearly with speed. Combining these gives a cubic relationship: doubling wind speed from 5 to 10 m/s increases power by 8× (2³ = 8). This is why site selection is critical — a location with 8 m/s average wind produces 3.4× more energy than one with 5.5 m/s.

How does hub height affect energy production?

Wind speed increases with altitude due to reduced surface friction (boundary layer effect). The logarithmic wind profile shows that raising hub height from 30m to 80m typically increases wind speed by 20-35% depending on terrain roughness. Since power scales with v³, this translates to 70-150% more energy production. Rough terrain (forests, cities) shows the largest improvement from height increase because surface friction effects diminish more dramatically at altitude.

What is a good capacity factor for a wind turbine?

Capacity factor is the ratio of actual energy produced to the theoretical maximum. Onshore wind farms typically achieve 25-40% capacity factor, while offshore installations reach 40-55% due to stronger, more consistent winds. A well-sited onshore turbine at a 7+ m/s average wind speed site can achieve 35%+. Factors reducing capacity factor include low wind speeds, turbine downtime for maintenance, grid curtailment, and wake effects from neighboring turbines.