---
title: "Time–Bandwidth Product calculator — AperiOptic"
description: "Minimum pulse duration for transform-limited Gaussian / sech² pulses. Free online optics calculator, with the formula and code snippets."
url: "https://aperioptic.com/calculators/time-bandwidth-product"
---

# Time–Bandwidth Product calculator

Minimum pulse duration for transform-limited Gaussian / sech² pulses.

Category: [Laser & Ultrafast](https://aperioptic.com/calculators)

Formula: `Δν·Δτ = 2·ln2/π = 0.4413 (Gauss), 4·ln²(1+√2)/π² = 0.3148 (sech²) · Δν = c·Δλ/λ²`

## Inputs

| Input | Parameter | Unit | Default |
| --- | --- | --- | --- |
| Center λ | `lam` | nm | 800 |
| Δλ (FWHM) | `dlam` | nm | 30 |

## Result with the default inputs

- Δν: 14.0528 THz
- Δτ Gauss: 31.401 fs
- Δτ sech²: 22.4036 fs

Open it with your own values: put each input in the address as a parameter, for example [`/calculators/time-bandwidth-product?lam=800`](https://aperioptic.com/calculators/time-bandwidth-product?lam=800). A unit other than the listed one goes in `<parameter>_unit`.

Read more: [Wikipedia: Bandwidth-limited pulse](https://en.wikipedia.org/wiki/Bandwidth-limited_pulse)

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

---

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