# Brewster’s Angle Calculator

URL: https://speedycalculator.com/calculators/physics/brewster-angle/
Last updated: 2026-10-30

> The Brewster's angle calculator finds the angle of incidence at which reflected light is completely polarised, from the refractive indices of the two media.

## Inputs

- First medium
- Refractive index n₁
- Second medium
- Refractive index n₂

## Results

- Brewster angle θ_B
- Refraction angle at θ_B

## Formula

```
θ_B = arctan(n₂ / n₁)
```

## Explanation

At Brewster's angle, light polarised in the plane of incidence passes into the second medium without any reflection. Polarised sunglasses cut glare from water and roads for this reason, and laser windows are tilted at Brewster's angle to avoid losses.

### How to use the Brewster's Angle Calculator

- **First medium**
- **Refractive index n₁**
- **Second medium**
- **Refractive index n₂**

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

### How it works

Choose or enter the refractive index of the medium the light comes from (n₁) and the one it enters (n₂).

### Inputs explained

FieldWhat to enterFirst mediumChoose one: Vacuum, Air, Water at 20 °C, Ethanol …Refractive index n₁A numberSecond mediumChoose one: Vacuum, Air, Water at 20 °C, Ethanol …Refractive index n₂A number

### What each result means

- **Brewster angle θ_B** = deg(atan([n2]÷[n1]))
- **Refraction angle at θ_B** = 90 - [Brewster angle θ_B]

### Example values

How the main result changes when **Refractive index n₁** changes and everything else stays at the example values above:

Refractive index n₁Brewster angle θ_B (°)156.65161.2556.65161.556.6516256.6516

## Worked example

Inputs — First medium: Air; Second medium: Window glass.

Results — **Brewster angle θ_B = 56.6516 °**; Refraction angle at θ_B = 33.3484 °.

## Key terms

- **Polarisation**: The orientation of a light wave's electric field.

## FAQ

**What is Brewster's angle for air to glass?**
About 56.7°.

**Why are reflections at Brewster's angle polarised?**
The p-polarised component has zero reflectance there.

**How do polarised sunglasses use this?**
They block the horizontally polarised glare from flat surfaces.

**Do the reflected and refracted rays make a special angle?**
Yes – they are perpendicular at Brewster's angle.


## 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)