---
title: "Pockels Cell Half-Wave Voltage calculator — AperiOptic"
description: "Vπ for a longitudinal/transverse EO modulator from r-coefficient and geometry. Free online optics calculator, with the formula and code snippets."
url: "https://aperioptic.com/calculators/pockels-cell-half-wave-voltage"
---

# Pockels Cell Half-Wave Voltage calculator

Vπ for a longitudinal/transverse EO modulator from r-coefficient and geometry.

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

Formula: `Vπ = λ·d/(n³·r·L) (transverse phase modulator)`

## Inputs

| Input | Parameter | Unit | Default |
| --- | --- | --- | --- |
| Wavelength | `lam` | nm | 1064 |
| Refractive index n | `n` |  | 2.2 |
| EO coeff r (pm/V) | `r` |  | 30.9 |
| L/d ratio | `LD` |  | 1 |

## Result with the default inputs

- Vπ: 3233.8145 V

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

Read more: [Wikipedia: Pockels effect](https://en.wikipedia.org/wiki/Pockels_effect)

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

---

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