What is the Betz limit?

The Betz limit (Cp ≈ 0.593) is the theoretical maximum fraction of wind energy a turbine can extract. No turbine can exceed this value; modern high-performance turbines achieve Cp values of 0.45–0.50.

Why does power scale with the cube of wind speed?

Kinetic energy is proportional to v², and the mass flow rate through the rotor is also proportional to v, giving a combined v³ dependence. Doubling wind speed increases power eight-fold.

How do I find air density at my site?

Standard sea-level air density is 1.225 kg/m³. At higher elevations or warmer temperatures, density decreases. Use the formula rho = P / (R_specific × T) with local pressure and temperature, or consult a meteorological table.

What is a typical power coefficient for real turbines?

Most commercial wind turbines operate between Cp = 0.35 and Cp = 0.45 at their rated wind speed. Small turbines may be lower (0.25–0.35), while highly optimized large rotors can reach 0.48–0.50.

Does this include gearbox and generator losses?

No. The formula gives aerodynamic power extracted from the wind. Multiply by drivetrain efficiency (typically 0.90–0.95) and generator efficiency (0.92–0.97) to estimate net electrical output.

Wind Turbine Power Calculator

Calculate theoretical wind turbine power output using rotor diameter, wind speed, air density, and power coefficient.

Turbine Parameters

Quick Presets

Rotor Diameter (m)

Tip-to-tip blade diameter. Swept area = π × (D/2)².

Wind Speed (m/s)

Hub-height wind speed. Typical sites: 6–15 m/s.

Air Density (kg/m³)

Sea level standard: 1.225 kg/m³. Lower at altitude.

Power Coefficient Cp (0.01 – 0.593)

Betz limit = 0.593. Typical turbines: 0.35–0.50.

Power Output

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Watts (W)

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Kilowatts (kW)

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Megawatts (MW)

Calculation Breakdown

Swept Area (A = π × r²) —

Wind Energy Flux (0.5 × rho × v³) —

Available Wind Power (× A) —

Extracted Power (× Cp) —

P = 0.5 × rho × A × Cp × v³

Wind Speed Sensitivity

Power output at Cp and density above, varying wind speed:

Run calculation to see sensitivity table.

Summary

This calculator applies the wind power equation P = 0.5 × rho × A × Cp × v³ to estimate the theoretical electrical output of a wind turbine. Enter your rotor diameter, wind speed, air density, and power coefficient (Cp) to instantly see power in watts, kilowatts, and megawatts. Useful for wind energy project planning, academic study, and turbine performance benchmarking.

How it works

Enter the rotor diameter in meters to define the swept area (A = π × r²).
Input the wind speed in meters per second at hub height.
Set the air density in kg/m³ (standard sea-level value is 1.225 kg/m³).
Adjust the power coefficient Cp (Betz limit is 0.593; typical turbines range 0.35–0.45).
The calculator computes P = 0.5 × rho × A × Cp × v³ and displays results in W, kW, and MW.
Use the presets to quickly load common turbine profiles for comparison.

Use cases

Estimating energy yield for a small or utility-scale wind turbine installation.
Comparing turbine designs at different rotor diameters and power coefficients.
Teaching the wind power equation in engineering or physics courses.
Evaluating how wind speed changes affect turbine output (cubic relationship).
Quick feasibility checks before detailed site assessment.
Understanding the impact of air density at altitude vs sea level.

Frequently Asked Questions

Last updated: 2026-06-04 · Reviewed by Nham Vu