Betz Limit Calculator

Calculator Inputs

Use the responsive form below. It displays in three columns on large screens, two on medium screens, and one on mobile devices.

Air Density (kg/m³)

Wind Speed (m/s)

Rotor Input Mode

Rotor Diameter (m)

Rotor Radius (m)

Swept Area (m²)

Turbine Count

Overall System Efficiency (%)

Operating Hours Per Day

Actual Turbine Output (kW) (optional)

Formula Used

1) Swept Area
Using diameter: A = π × D² / 4
Using radius: A = π × r²

2) Power Available in Wind
P_wind = 0.5 × ρ × A × v³ × N
where ρ is air density, A is swept area, v is wind speed, and N is turbine count.

3) Betz Maximum Extractable Power
C_p,max = 16 / 27 ≈ 0.59259
P_Betz = P_wind × (16 / 27)

4) Net Practical Maximum
P_net = P_Betz × η
where η is the overall system efficiency factor.

5) Actual Performance Check
C_p,actual = P_actual / P_wind
Betz Utilization = (P_actual / P_Betz) × 100

The Betz limit states that no wind turbine can capture more than 59.259% of the kinetic power passing through its rotor area.

How to Use This Calculator

Enter the air density for your site or use a standard atmospheric value.
Provide wind speed in meters per second.
Choose whether you want to enter rotor diameter, radius, or swept area.
Enter turbine count for a single machine or a small wind farm estimate.
Add overall system efficiency to include mechanical and electrical losses.
Optionally enter actual turbine output to compare measured performance against the Betz maximum.
Enter daily operating hours to estimate daily and yearly maximum energy.
Click the calculate button to display the result section under the page header and above the input form.

Example Data Table

Case	Air Density (kg/m³)	Wind Speed (m/s)	Rotor Diameter (m)	Turbines	Efficiency (%)	Betz Max (kW)	Net Practical Max (kW)
Site A	1.225	10.00	40.00	1	90.00	455.97	410.38
Site B	1.200	8.50	32.00	2	88.00	213.68	188.04
Site C	1.150	12.00	50.00	1	92.00	1,157.17	1,064.60

FAQs

1) What does the Betz limit represent?

It is the theoretical maximum fraction of wind power a turbine can extract from moving air. That maximum power coefficient equals 16/27, or about 59.259%.

2) Why can a turbine not capture all wind energy?

Air must keep moving through the rotor plane. If all kinetic energy were removed, airflow would stop and no more wind could pass through the turbine.

3) Why does wind speed affect output so strongly?

Wind power scales with the cube of wind speed. A modest increase in speed can produce a much larger increase in theoretical and practical turbine power.

4) What is swept area in this calculator?

Swept area is the circular area covered by the rotating blades. Larger swept areas intercept more airflow and therefore increase the available wind power.

5) Why include overall system efficiency?

Real turbines lose energy in blades, shafts, gearboxes, generators, converters, and cables. Efficiency lets you estimate a more practical upper output after those losses.

6) Can actual output exceed the Betz limit?

No. If your entered actual output exceeds the Betz maximum, one or more assumptions are likely wrong, such as wind speed, air density, rotor size, or measured output.

7) Does air density matter much?

Yes. Denser air contains more mass flow through the rotor, which raises power. Temperature, altitude, and pressure all influence site air density.

8) Is this calculator useful for wind farms?

Yes. You can enter a turbine count to estimate combined theoretical output. It is still a simplified model and does not include wake losses between turbines.