Debye Length Calculator — Electrostatic Screening
Enter solution temperature, relative permittivity, electrolyte concentration and ion valence to compute the Debye length — the characteristic distance over which a charge is screened by surrounding ions in an electrolyte or plasma.
K
mol/L
Electrostatic screening length in nanometres
- 1
Ion number density n₀
0.1 × 1000 × Nₐ = 60,221,407,600,000,000,000,000,000Converts mol/L to ions per m³. - 2
Ratio under the √
(ε₀ × εr × k_B × T) ÷ (2 × n₀ × z² × e²) = 0 - 3
λ_D (m)
√(0) = 0 - 4
λ_D (nm)
0 × 10⁹ = 0.9620
How does this calculator work?
λ_D = √(ε₀ εr k_B T / (2 n₀ z² e²)). In water at 25 °C: λ_D ≈ 0.304/√c nm (c in mol/L, z = 1). At 1 mM → ~9.6 nm; 0.1 M → ~0.96 nm; 1 M → ~0.30 nm. Higher εr or T lengthens λ_D; higher concentration or valence shortens it. Governs colloidal stability, double-layer capacitance, and plasma sheaths.
Formula
How this is calculated
The Debye length (λ_D) is the electrostatic screening length of an electrolyte or plasma: the potential around a point charge decays as e^(−r/λ_D)/r, so beyond a few Debye lengths the charge is effectively invisible to other particles. It emerges from Debye–Hückel theory by linearising the Poisson–Boltzmann equation around a reference ion.
The formula λ_D = √(ε₀ εr k_B T / (2 n₀ z² e²)) shows that screening lengthens in a more polarisable medium (higher εr) or at higher temperature (more thermal agitation opposes ordering), and shortens when ion density n₀ or valence z increases. For aqueous NaCl at 25 °C, the convenient approximation is λ_D ≈ 0.304/√c nm (c in mol/L): at 1 mM → ~9.6 nm; 0.1 M → ~0.96 nm; 1 M → ~0.30 nm. Divalent salts screen four times more strongly at the same molar concentration because z² = 4.
The Debye length governs colloidal stability (DLVO theory), the capacitance of electric double layers (supercapacitors, biosensors, electrodes), the Debye–Hückel correction to activity coefficients, and sheath thickness in plasmas. This calculator assumes a symmetric z:z electrolyte; for mixed or asymmetric electrolytes, replace 2n₀z² with the full sum Σ n_i z_i² over all ion species.
Frequently asked questions
It is the e-folding distance for electrostatic screening: the electric potential around an ion decays by a factor of 1/e ≈ 37% over each Debye length. Within about 3 λ_D the charge is almost completely shielded; beyond that, the electrolyte looks electrically neutral.
More ions in solution provide more screening charge, compressing the diffuse double layer. The Debye length falls as 1/√c: doubling the salt concentration shrinks λ_D by a factor of √2 ≈ 1.41. This is why colloids that are stable at low ionic strength aggregate (coagulate) when salt is added.
This calculator assumes a z:z symmetric electrolyte. For CaCl₂ (Ca²⁺ + 2 Cl⁻), compute the ionic strength I = ½ Σ cᵢzᵢ² = ½(c×4 + 2c×1) = 3c. Then enter that ionic strength as concentration with z = 1 to obtain the correct Debye length.
Also known as
TG we-Calculate Editorial Team. (2026). Debye Length Calculator — Electrostatic Screening [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/debye-length-calculator
TG we-Calculate Editorial Team. "Debye Length Calculator — Electrostatic Screening." TG we-Calculate. 2026. https://we-calculate.com/calculator/debye-length-calculator.
TG we-Calculate Editorial Team, "Debye Length Calculator — Electrostatic Screening," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/debye-length-calculator
@misc{wecalculate_debye_length_calculator, title = {Debye Length Calculator — Electrostatic Screening}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/debye-length-calculator}}, year = {2026}, note = {TG we-Calculate} }
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