---
title: "Angle-Dependent Fresnel (s & p) calculator — AperiOptic"
description: "s- and p-polarized reflectance/transmittance at any incidence angle. Free online optics calculator, with the formula and code snippets."
url: "https://aperioptic.com/calculators/angle-dependent-fresnel-s-p"
---

# Angle-Dependent Fresnel (s & p) calculator

s- and p-polarized reflectance/transmittance at any incidence angle.

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

Formula: `rs, rp from cosθi, cosθt · R = |r|²`

## Inputs

| Input | Parameter | Unit | Default |
| --- | --- | --- | --- |
| n1 | `n1` |  | 1 |
| n2 | `n2` |  | 1.5 |
| Angle θi | `th` | deg | 45 |

## Result with the default inputs

- Rs: 9.201 %
- Rp: 0.847 %
- Ravg: 5.024 %

Open it with your own values: put each input in the address as a parameter, for example [`/calculators/angle-dependent-fresnel-s-p?n1=1`](https://aperioptic.com/calculators/angle-dependent-fresnel-s-p?n1=1). A unit other than the listed one goes in `<parameter>_unit`.

Read more: [Wikipedia: Fresnel equations](https://en.wikipedia.org/wiki/Fresnel_equations)

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

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