Enter the beam waist (mm) and the wavelength (mm) into the Calculator. The calculator will evaluate the Rayleigh Length. 

Rayleigh Length Formula

Zr = pi * w^2 / l


  • Zr is the Rayleigh Length (mm)
  • w is the beam waist (mm)
  • l is the wavelength (mm)

To calculate Rayleigh Length, multiply pi times the beam waist squared, then divide by the wavelength.

How to Calculate Rayleigh Length?

The following steps outline how to calculate the Rayleigh Length.

  • First, determine the beam waist (mm). 
  • Next, determine the wavelength (mm). 
  • Next, gather the formula from above = Zr = pi * w^2 / l.
  • Finally, calculate the Rayleigh Length.
  • After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

beam waist (mm) = 80

wavelength (mm) = 90

Frequently Asked Questions

What is Rayleigh Length in laser physics?

Rayleigh Length is a measure of the distance over which a laser beam’s cross-sectional area doubles in size. It is a key parameter in understanding the propagation and focusing of laser beams, especially Gaussian beams.

Why is the beam waist size important in laser applications?

The beam waist size determines the focusability of the laser beam. A smaller beam waist allows for a more concentrated focus, which is crucial in applications requiring high precision, such as laser cutting, engraving, and medical surgeries.

How does wavelength affect the Rayleigh Length?

The wavelength of a laser beam inversely affects the Rayleigh Length. A shorter wavelength results in a shorter Rayleigh Length, allowing the beam to focus more tightly over a shorter distance, which is beneficial for high-resolution applications.

Can the Rayleigh Length be adjusted in a practical setting?

Yes, the Rayleigh Length can be adjusted by changing the beam waist size or the wavelength of the laser. This can be achieved through optical components such as lenses and mirrors, allowing for customization of the beam’s focus for different applications.