`z_R = (pi * w_0 ^2)/ lambda `

Enter a value for all fields

The Rayleigh Range calculator computes the distance (z_R) along the propagation direction of a beam from the waist to the place where the area of the cross section is doubled.

INSTRUCTIONS:  Choose units and enter the following:

• (λ)  This is the wavelength
• (w₀) This is the beam waist

Rayleigh Range (z_R): The calculator returns the range in millimeters.  However, this can be automatically converted to other length units via the pull-down menu.

The Math / Science

The Rayleigh Range  equation¹ calculates the Rayleigh range (`z_R`) for a Gaussian Beam.  The Rayleigh range is used as an indicator of how quickly the beam spreads as it travels.  A low Rayleigh Range means the beam is spreading more.  For more information on Rayleigh range and Gaussian Beams in general, please see the Gaussian Beam Calculator.

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Gaussian Beam Calculators

• Rayleigh range 
• Full-angular width (Θ)
• Beam half-width
• Beam Waist

1. ^ Hecht, Eugene. "Modern Optics: Lasers and Other Topics." Optics. Reading, MA: Addison-Wesley, 2002. 618. Print.