`w_0 = +sqrt( w ^2 - ( lambda * z )/pi)`

Enter a value for all fields

The Gausian Beam Waist calculator computes the beam waist for a Gausian Beam based on the beam half-width, distance on the axis and wavelength.

INSTRUCTIONS: Choose units and enter the following:

• (w) Beam half-width
• (z) Distance along the optical axis from the beam waist
• (`lambda`)  Beam Wavelength

Gausian Beam Waist (w₀): The calculator return the beam waist in nano-meters.  However this can be automatically converted to compatible units via the pull-down menu.

The Math / Science

This Gaussian Beam Waist equation¹ calculates the beam waist for a Gaussian Beam.  The beam half-width (`w`) is used as an indicator of the "size" of a Gaussian Beams.  Gaussian Beams to extend to infinity, but they approach zero as they do so.  It's convenient for us to establish a finite measure of the beam's width. We use the beam half-width, the radial distance (`w`) from the central axis such that `E(w) = E_0/e` (where the electric field is `1/e` of its value at the central axis).  The beam waist is the smallest beam half-width for a given beam (where the beam is "skinniest").  For more information on beam waists and Gaussian Beams in general, please see the Gaussian Beam Calculator.

---

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.