What is the Debye length?

The Debye length λ_D is the distance over which mobile charge carriers screen an external electric field. Beyond roughly 3λ_D, the potential from a point charge falls to less than 5% of its unscreened value. Shorter Debye length = stronger screening.

What formula does this calculator use?

λ_D = √(ε₀ ε_r k_B T / (n q²)), where ε₀ = 8.854 × 10⁻¹² F/m, ε_r is the relative permittivity, k_B = 1.381 × 10⁻²³ J/K, T is temperature in kelvin, n is carrier number density in m⁻³, and q is carrier charge in coulombs. This is the single-species form; for a 1:1 electrolyte with both anions and cations, divide n by 2 or use the ionic-strength form.

What is a typical Debye length in water?

For a 0.1 M NaCl solution at 25 °C, λ_D ≈ 0.96 nm. For 1 mM NaCl, λ_D ≈ 9.6 nm. Pure water (very low ion concentration) can have λ_D on the order of micrometers, though in practice surface charges limit this.

How does temperature affect λ_D?

λ_D scales as √T. Higher temperature increases thermal motion, which partially overcomes screening, so the effective screening length grows. Doubling T increases λ_D by about 41%.

What value should I use for carrier density in an electrolyte?

For a monovalent electrolyte of concentration c (mol/L), the ion number density is n = c × 1000 × N_A (in m⁻³), where N_A = 6.022 × 10²³. For example, 0.1 M = 6.022 × 10²⁵ m⁻³. Enter this value in the density field.

Debye Length Calculator

Name: Debye Length Calculator
Availability: InStock
Author: Nham Vu

Calculate the Debye screening length in electrolytes or plasmas from temperature, permittivity, and carrier concentration.

Parameters

Presets

Temperature T (K)

Relative permittivity ε_r (dimensionless)

Carrier number density n (m⁻³)

Carrier charge z (multiples of e)

Select a preset or enter parameters and click Calculate

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Summary

Calculate the Debye screening length in electrolytes or plasmas from temperature, permittivity, and carrier concentration.

How it works

Select a preset (water, silicon, plasma) or enter custom parameters.
Enter the temperature T in kelvin, relative permittivity ε_r, carrier number density n in m⁻³, and carrier charge q in units of elementary charge.
The Debye length is computed as λ_D = √(ε₀ ε_r k_B T / (n q²)).
Results appear in meters with a scientific-notation breakdown and a context bar showing scale.
For aqueous 1:1 electrolytes at room temperature, λ_D ≈ 0.304 / √(I) nm, where I is the molar ionic strength.

Use cases

Estimate the double-layer thickness in an electrochemical cell or electrode interface.
Determine Debye screening length in a semiconductor depletion region.
Calculate plasma screening distance for fusion or astrophysics problems.
Explore how temperature and ionic concentration affect charge screening.
Verify hand calculations for electrostatics coursework or research.
Compare screening lengths across aqueous, organic, and semiconductor media.

Frequently Asked Questions

Last updated: 2026-07-01 · Reviewed by Nham Vu