# Debye Length Calculator

URL: https://speedycalculator.com/calculators/physics/debye-length/
Last updated: 2026-10-30

> The Debye length calculator finds the screening length in a plasma from its electron temperature and density, or in an electrolyte from its temperature, dielectric constant and ionic strength.

## Inputs

- Medium
- Electron temperature (eV, K)
- Electron density (m⁻³, cm⁻³)
- Temperature (K, °C)
- Relative permittivity of the solvent
- Ionic strength (mol/L)

## Results

- Debye length λ_D

## Formula

```
Plasma: λ_D = √(ε₀·k·T_e / (n_e·e²)) · Electrolyte: λ_D = √(ε₀·ε_r·k·T / (2·N_A·e²·I))
```

## Explanation

Mobile charges rearrange to cancel out electric fields beyond a short distance – the Debye length. It defines when an ionised gas behaves as a plasma, and in salty water it sets how far electrostatic forces between colloids and biomolecules reach.

### How to use the Debye Length Calculator

- **Medium**
- **Electron temperature**
- **Electron density**
- **Temperature**
- **Relative permittivity of the solvent**
- **Ionic strength (mol/L)**

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

### How it works

Choose plasma or electrolyte and enter the parameters. For an electrolyte, ionic strength is in mol/L (0.15 for physiological saline).

### Inputs explained

FieldWhat to enterMediumChoose one: Plasma, ElectrolyteElectron temperatureUnits: eV, KElectron densityUnits: m⁻³, cm⁻³TemperatureUnits: K, °CRelative permittivity of the solventA numberIonic strength (mol/L)A number

### Example values

How the main result changes when **Electron temperature** changes and everything else stays at the example values above:

Electron temperature (eV)Debye length λ_D (nm)50.78557.50.7855100.785512.50.7855150.7855200.7855

## Worked example

Inputs — Medium: Electrolyte; Temperature: 298.15 K; Relative permittivity of the solvent: 78.5; Ionic strength (mol/L): 0.15.

Results — **Debye length λ_D = 0.78546 nm**.

## Key terms

- **Ionic strength**: ½·Σcᵢzᵢ², a measure of ion concentration.

## FAQ

**What is the Debye length of seawater?**
Under 1 nm (ionic strength ≈ 0.7 mol/L).

**Why does it define a plasma?**
A plasma must be much larger than its Debye length so collective effects dominate.

**How does salt affect it?**
More ions shorten the screening length (λ ∝ 1/√I).

**What is it in physiological saline?**
About 0.8 nm.


## Sources

- [OpenStax – University Physics Volume 2](https://openstax.org/details/books/university-physics-volume-2)
- [HyperPhysics (Georgia State University)](http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)
- [OpenStax – Chemistry 2e](https://openstax.org/details/books/chemistry-2e)