---
title: "Beam Width: FWHM ↔ 1/e² ↔ σ calculator — AperiOptic"
description: "Convert between Gaussian beam width conventions. Free online optics calculator, with the formula and code snippets."
url: "https://aperioptic.com/calculators/beam-width-fwhm-1-e2-sigma"
---

# Beam Width: FWHM ↔ 1/e² ↔ σ calculator

Convert between Gaussian beam width conventions.

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

Formula: `σ = FWHM/(2√(2 ln2)) · 1/e² diam = 4σ ≈ 1.6986·FWHM`

## Inputs

| Input | Parameter | Unit | Default |
| --- | --- | --- | --- |
| FWHM | `fwhm` | µm | 100 |

## Result with the default inputs

- FWHM: 100 µm
- σ: 42.4661 µm
- 1/e radius: 60.0561 µm
- 1/e² radius: 84.9322 µm
- 1/e² diameter: 169.8644 µm

Open it with your own values: put each input in the address as a parameter, for example [`/calculators/beam-width-fwhm-1-e2-sigma?fwhm=100`](https://aperioptic.com/calculators/beam-width-fwhm-1-e2-sigma?fwhm=100). A unit other than the listed one goes in `<parameter>_unit`.

Read more: [Wikipedia: Beam diameter](https://en.wikipedia.org/wiki/Beam_diameter)

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

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The interactive page: https://aperioptic.com/calculators/beam-width-fwhm-1-e2-sigma (AperiOptic runs in the browser; free, no account). Every page of the site as Markdown: https://aperioptic.com/llms.txt