---
title: "M² ↔ Divergence calculator — AperiOptic"
description: "Beam parameter product, M² and far-field divergence relations. Free online optics calculator, with the formula and code snippets."
url: "https://aperioptic.com/calculators/m2-divergence"
---

# M² ↔ Divergence calculator

Beam parameter product, M² and far-field divergence relations.

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

Formula: `θ = M² · λ/(π·w0) · BPP = w0·θ`

## Inputs

| Input | Parameter | Unit | Default |
| --- | --- | --- | --- |
| Wavelength | `lam` | nm | 1064 |
| Waist w0 | `w0` | µm | 100 |
| M² | `M2` |  | 1.1 |

## Result with the default inputs

- Half-angle div.: 3.7255 mrad
- Full-angle div.: 7.451 mrad
- BPP: 0.3725 mm·mrad

Open it with your own values: put each input in the address as a parameter, for example [`/calculators/m2-divergence?lam=1064`](https://aperioptic.com/calculators/m2-divergence?lam=1064). A unit other than the listed one goes in `<parameter>_unit`.

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

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

---

The interactive page: https://aperioptic.com/calculators/m2-divergence (AperiOptic runs in the browser; free, no account). Every page of the site as Markdown: https://aperioptic.com/llms.txt