# Laser Beam Expander Calculator

URL: https://speedycalculator.com/calculators/physics/laser-beam-expander/
Last updated: 2026-10-30

> The laser beam expander calculator finds the magnification, output diameter, output divergence and beam size at a distance for a Keplerian or Galilean beam expander.

## Inputs

- Design
- Input (image) lens focal length |f_I| (mm, cm, m, in, µm)
- Output (objective) lens focal length f_O (mm, cm, m, in, µm)
- Input beam diameter (mm, cm, m, in, µm)
- Input divergence (mrad)
- Distance from the expander (m, cm, mm, km, in, ft, yd, mi)

## Results

- Magnification
- Output diameter
- Output divergence
- Diameter at distance L
- Lens separation

## Formula

```
M = |f_O / f_I|,  D_O = M·D_I,  Θ_O = Θ_I / M,  D_L = D_O + L·Θ_O
```

## Explanation

A beam expander is a small telescope used backwards: it widens a laser beam and, in exchange, reduces its divergence. Expanded beams can be focused to smaller spots and travel farther without spreading.

### How to use the Laser Beam Expander Calculator

- **Design**
- **Input (image) lens focal length |f_I|**
- **Output (objective) lens focal length f_O**
- **Input beam diameter**
- **Input divergence (mrad)**
- **Distance from the expander**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Choose the design. Keplerian expanders use two positive lenses (with an internal focus); Galilean ones use a negative input lens and are shorter. Enter the input beam and the distance to evaluate.

### Inputs explained

FieldWhat to enterDesignChoose one: Keplerian, GalileanInput (image) lens focal length |f_I|Units: mm, cm, m, in, µmOutput (objective) lens focal length f_OUnits: mm, cm, m, in, µmInput beam diameterUnits: mm, cm, m, in, µmInput divergence (mrad)A numberDistance from the expanderUnits: m, cm, mm, km, in, ft …

### What each result means

- **Magnification** = [Output (objective) lens focal length f_O]÷[Input (image) lens focal length |f_I|]
- **Output diameter** = [Magnification]×[Input beam diameter]
- **Output divergence** = [Input divergence (mrad)]÷[Magnification]
- **Diameter at distance L** = [Magnification]×[Input beam diameter] + [Distance from the expander]×[Input divergence (mrad)]÷[Magnification]÷1000

### Example values

How the main result changes when **Input** changes and everything else stays at the example values above:

Input (image) lens focal length |f_I| (mm)Magnification (×)12.5818.755.333325431.253.237.52.6667502

## Worked example

Inputs — Design: Keplerian; Input (image) lens focal length |f_I|: 25 mm; Output (objective) lens focal length f_O: 100 mm; Input beam diameter: 1 mm; Input divergence (mrad): 1; Distance from the expander: 10 m.

Results — **Magnification = 4 ×**; Output diameter = 4 mm; Output divergence = 0.25 mrad; Diameter at distance L = 6.5 mm; Lens separation = 125 mm.

## Key terms

- **Beam expander**: An afocal telescope that enlarges a beam.

## FAQ

**Why expand a laser beam?**
To reduce divergence and allow a smaller focused spot.

**Keplerian or Galilean?**
Galilean is shorter and has no internal focus (better for high power).

**Does the expander change the laser power?**
No, apart from small lens losses.

**What is the lens spacing?**
The sum (Keplerian) or difference (Galilean) of the focal lengths.


## Sources

- [OpenStax – University Physics Volume 3](https://openstax.org/details/books/university-physics-volume-3)
- [HyperPhysics (Georgia State University)](http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)