---
title: "Gaussian Beam Waist calculator — AperiOptic"
description: "Waist radius and Rayleigh range of a focused Gaussian beam. Free online optics calculator, with the formula and code snippets."
url: "https://aperioptic.com/calculators/gaussian-beam-waist"
---

# Gaussian Beam Waist calculator

Waist radius and Rayleigh range of a focused Gaussian beam.

Category: [Diffraction](https://aperioptic.com/calculators)

Formula: `w₀ = (λ·f/(π·w))/√(1 + (λ·f/(π·w²))²) · zR = π·w₀²/λ`

## Inputs

| Input | Parameter | Unit | Default |
| --- | --- | --- | --- |
| λ | `lam` | nm | 1064 |
| Focal length | `f` | mm | 100 |
| Input waist | `w` | mm | 2 |

## Result with the default inputs

- Waist w₀: 16.9335 µm
- Rayleigh zR: 0.8466 mm
- Divergence: 20.0007 mrad

Open it with your own values: put each input in the address as a parameter, for example [`/calculators/gaussian-beam-waist?lam=1064`](https://aperioptic.com/calculators/gaussian-beam-waist?lam=1064). A unit other than the listed one goes in `<parameter>_unit`.

[All optics calculators](https://aperioptic.com/calculators)

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The interactive page: https://aperioptic.com/calculators/gaussian-beam-waist (AperiOptic runs in the browser; free, no account). Every page of the site as Markdown: https://aperioptic.com/llms.txt