---
title: "Johnson–Nyquist Noise calculator — AperiOptic"
description: "Thermal noise voltage / current of a resistor at temperature T. Free online optics calculator, with the formula and code snippets."
url: "https://aperioptic.com/calculators/johnson-nyquist-noise"
---

# Johnson–Nyquist Noise calculator

Thermal noise voltage / current of a resistor at temperature T.

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

Formula: `Vn = √(4kT·R·Δf)`

## Inputs

| Input | Parameter | Unit | Default |
| --- | --- | --- | --- |
| Resistance | `R` | Ω | 1000000 |
| Temperature | `T` | K | 295 |
| Bandwidth | `BW` | Hz | 1000 |

## Result with the default inputs

- Voltage noise: 4036.2926 nV
- Current noise: 4036.2926 fA

Open it with your own values: put each input in the address as a parameter, for example [`/calculators/johnson-nyquist-noise?R=1000000`](https://aperioptic.com/calculators/johnson-nyquist-noise?R=1000000). A unit other than the listed one goes in `<parameter>_unit`.

Read more: [Wikipedia: Johnson–Nyquist noise](https://en.wikipedia.org/wiki/Johnson%E2%80%93Nyquist_noise)

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

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