---
title: "V-Number calculator — AperiOptic"
description: "Normalized frequency and mode count of a step-index fiber. Free online optics calculator, with the formula and code snippets."
url: "https://aperioptic.com/calculators/v-number"
---

# V-Number calculator

Normalized frequency and mode count of a step-index fiber.

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

Formula: `V = (2π·a/λ)·NA · single-mode if V < 2.4048 (first zero of J₀)`

## Inputs

| Input | Parameter | Unit | Default |
| --- | --- | --- | --- |
| Core radius | `a` | µm | 4.1 |
| λ | `lam` | nm | 1310 |
| NA | `NA` |  | 0.14 |

## Result with the default inputs

- V: 2.7531
- Modes (≈ V²/2, large V): 3.7898
- SM cutoff λ: 1499.7131 nm

Open it with your own values: put each input in the address as a parameter, for example [`/calculators/v-number?a=4.1`](https://aperioptic.com/calculators/v-number?a=4.1). A unit other than the listed one goes in `<parameter>_unit`.

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

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