What is the Betz limit?

The Betz limit (16/27 ≈ 59.26%) is the theoretical maximum fraction of kinetic wind energy that any turbine can convert to mechanical power. Derived by Albert Betz in 1919, it follows from momentum conservation: slowing the wind too much prevents new air from entering the rotor.

Why can't a real turbine reach 59.26%?

Blade aerodynamic drag, tip losses, wake rotation, mechanical friction, and generator losses all reduce the power coefficient (Cp) below the Betz limit. Modern large turbines reach Cp ≈ 0.45–0.50; small turbines are often 0.25–0.40.

What air density does this tool assume?

The calculator uses the standard sea-level value of 1.225 kg/m³. At altitude or high temperature, actual density is lower, which reduces available power proportionally.

Why does wind speed matter so much?

Power scales with the cube of wind speed (v³). Doubling the wind speed multiplies available power by 8×. This is why wind class and annual mean speed are the single most important site-selection factors.

Does rotor diameter affect power linearly?

No — power scales with the square of the radius (area = π r²). Doubling the rotor diameter quadruples the swept area and therefore the available power, all else equal.

Betz Limit Calculator

Name: Betz Limit Calculator
Availability: InStock
Author: Nham Vu

Enter rotor diameter and wind speed to see the theoretical maximum power a wind turbine can extract, capped at the Betz limit of 59.26%.

Wind Turbine Inputs

Unit system

Rotor diameter (m)

Tip-to-tip blade span (full diameter, not radius)

Wind speed (m/s)

Real turbine Cp 0.40

0.10 (poor) Betz max ≈ 0.593

Results

Swept Area

— m²

π × (D/2)²

Available Wind Power

— W

½ × ρ × A × v³

Betz Limit Power (max theoretical)

— W

16/27 × P_avail (59.26% of available)

Estimated Real Output

— W

Cp × P_avail — adjust the slider to match your turbine's power coefficient

Betz efficiency 59.26%

0%100% kinetic energy

Real turbine Cp vs Betz limit —%

0%Betz limit100%

Key formulas

A = π × (D/2)²
P_avail = ½ × ρ × A × v³ (ρ = 1.225 kg/m³)
P_betz = (16/27) × P_avail ≈ 0.5926 × P_avail
P_real = Cp × P_avail

Summary

Enter rotor diameter and wind speed to see the theoretical maximum power a wind turbine can extract, capped at the Betz limit of 59.26%.

How it works

Enter the rotor diameter in meters (or feet — toggle the unit).
Enter the wind speed in m/s (or mph).
The tool computes swept area: A = π × (D/2)².
Available wind power is P_avail = ½ × ρ × A × v³ (air density 1.225 kg/m³ at sea level).
Betz-limit power is P_betz = (16/27) × P_avail ≈ 59.26% of available.
A typical real-turbine efficiency slider (20–50%) shows the expected actual output.

Use cases

Estimate the theoretical ceiling before sizing a small wind turbine.
Verify textbook Betz limit examples for coursework.
Compare swept area vs. output across different rotor diameters.
Understand how wind speed cubing affects power more than diameter.
Gauge how far a commercial turbine (Cp ≈ 0.35–0.45) sits below the limit.
Quick sanity check for wind-energy feasibility studies.

Frequently Asked Questions

Last updated: 2026-07-01 · Reviewed by Nham Vu