---
title: "Gaussian Beam Propagation calculator — AperiOptic"
description: "Beam radius w(z), ROC R(z) at distance z from waist, and far-field divergence. Free online optics calculator, with the formula and code snippets."
url: "https://aperioptic.com/calculators/gaussian-beam-propagation"
---

# Gaussian Beam Propagation calculator

Beam radius w(z), ROC R(z) at distance z from waist, and far-field divergence.

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

Formula: `w(z) = w₀·√(1+(z/zR)²) · θ = λ/(π·w₀)`

## Inputs

| Input | Parameter | Unit | Default |
| --- | --- | --- | --- |
| Waist w₀ | `w0` | µm | 100 |
| λ | `lam` | nm | 1064 |
| Distance z | `z` | mm | 100 |

## Result with the default inputs

- w(z): 353.1364 µm
- Rayleigh zR: 29.5262 mm
- ROC R(z): 108.718 mm
- Half-angle div.: 3.3868 mrad

Open it with your own values: put each input in the address as a parameter, for example [`/calculators/gaussian-beam-propagation?w0=100`](https://aperioptic.com/calculators/gaussian-beam-propagation?w0=100). A unit other than the listed one goes in `<parameter>_unit`.

Read more: [Wikipedia: Gaussian beam](https://en.wikipedia.org/wiki/Gaussian_beam)

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

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