---
title: "Thick Lens Equation calculator — AperiOptic"
description: "Effective focal length & principal planes for a thick lens. Free online optics calculator, with the formula and code snippets."
url: "https://aperioptic.com/calculators/thick-lens-equation"
---

# Thick Lens Equation calculator

Effective focal length & principal planes for a thick lens.

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

Formula: `1/f = (n-1)[1/R₁ - 1/R₂ + (n-1)d/(n·R₁·R₂)]`

## Inputs

| Input | Parameter | Unit | Default |
| --- | --- | --- | --- |
| Index n | `n` |  | 1.5 |
| R₁ | `R1` | mm | 100 |
| R₂ | `R2` | mm | -100 |
| Thickness d | `d` | mm | 5 |

## Result with the default inputs

- EFL f: 100.8403 mm
- H₁ (from V₁): 1.6807 mm
- H₂ (from V₂): -1.6807 mm

Open it with your own values: put each input in the address as a parameter, for example [`/calculators/thick-lens-equation?n=1.5`](https://aperioptic.com/calculators/thick-lens-equation?n=1.5). A unit other than the listed one goes in `<parameter>_unit`.

Read more: [Wikipedia: Thick lens](https://en.wikipedia.org/wiki/Thick_lens)

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

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