# Laser Linewidth and Bandwidth Calculator

URL: https://speedycalculator.com/calculators/physics/laser-linewidth/
Last updated: 2026-10-30

> The laser linewidth calculator estimates the fundamental (Schawlow–Townes) linewidth of a laser from its frequency, cavity linewidth and output power, and converts between wavelength and frequency bandwidth.

## Inputs

- Calculate
- Laser frequency ν (THz, GHz, Hz)
- Cavity linewidth Δν_c (MHz, kHz, GHz, Hz)
- Power P (mW, W)
- Fundamental wavelength λ (nm, µm, mm, m, pm, Å)
- Wavelength bandwidth Δλ (nm, µm, mm, m, pm, Å)

## Results

- Linewidth Δν
- Frequency bandwidth Δν

## Formula

```
Δν_ST = π·h·ν·Δν_c² / P · Δν = c·Δλ / λ²
```

## Explanation

Even an ideal laser has a finite spectral width because of spontaneous emission. The Schawlow–Townes formula gives this quantum limit. Bandwidth conversion is used for pulsed lasers, filters and spectroscopy.

### How to use the Laser Linewidth and Bandwidth Calculator

- **Calculate**
- **Laser frequency ν**
- **Cavity linewidth Δν_c**
- **Power P**
- **Fundamental wavelength λ**
- **Wavelength bandwidth Δλ**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Choose the calculation. For bandwidth conversion, enter the central wavelength and the wavelength width.

### Inputs explained

FieldWhat to enterCalculateChoose one: Linewidth (Schawlow–Townes), Bandwidth from wavelength widthLaser frequency νUnits: THz, GHz, HzCavity linewidth Δν_cUnits: MHz, kHz, GHz, HzPower PUnits: mW, WFundamental wavelength λUnits: nm, µm, mm, m, pm, ÅWavelength bandwidth ΔλUnits: nm, µm, mm, m, pm, Å

### What each result means

- **Linewidth Δν** = 6.62607e-34×pi×[Laser frequency ν]×[Cavity linewidth Δν_c]^2÷[Power P]
- **Frequency bandwidth Δν** = 2.99792e+08×[Wavelength bandwidth Δλ]÷[Fundamental wavelength λ]^2

### Example values

How the main result changes when **Laser frequency ν** changes and everything else stays at the example values above:

Laser frequency ν (THz)Linewidth Δν (Hz)2370.0005355.50.00074740.001592.50.00127110.00159480.002

## Worked example

Inputs — Calculate: Linewidth (Schawlow–Townes); Laser frequency ν: 474 THz; Cavity linewidth Δν_c: 1 MHz; Power P: 1 mW.

Results — **Linewidth Δν = 0.000987 Hz**.

## Key terms

- **Linewidth**: Spectral width of a laser's output.

## FAQ

**What limits a laser's linewidth?**
Spontaneous emission noise sets the quantum (Schawlow–Townes) limit.

**Why do real lasers have wider lines?**
Mechanical vibration, temperature drift and pump noise.

**How are Δλ and Δν related?**
Δν = c·Δλ/λ².

**What is a narrow-linewidth laser used for?**
Interferometry, atomic clocks and coherent communications.


## Sources

- [OpenStax – University Physics Volume 3](https://openstax.org/details/books/university-physics-volume-3)
- [HyperPhysics (Georgia State University)](http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)