Free · Physics models
Ideal Electrostatic Screening Length
Estimate plasma or electrolyte Debye length from temperature and number density or ionic strength.
- Formula & worked example
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Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
Debye length = 0.0011953. This worked example uses the displayed units and declared assumptions.
Debye_length = one_way(sqrt(permittivity_0 * boltzmann_cte * temperature/(electron_density * electron_charge^2))); Debye_length_ev = one_way(sqrt(permittivity_0 * temperature_ev/(electron_density * electron_charge))); Dl_electrolyte = one_way(sqrt(permittivity_r * permittivity_0 * boltzmann_cte * temperature_electro/(2 * ionic_strength * electron_charge^2 * mol_n)))
Worked example
Enter these known values and leave the other values blank.
- Medium to compute the Debye length
- 0
- Choose the units for temperature
- 0
- Temperature
- 300 K
- Electron density
- 1000000000000000000 electrons / m³
- Debye length
- 0.0011953 mm
Assumptions and limitations
- Linearized weak-coupling, equilibrium Debye screening is assumed. Plasma uses electron density per cubic meter; electrolyte ionic strength is mol/L. The retained vacuum permittivity and 6.02e26 per-m³ molarity conversion are rounded references.
- Clear an unknown to solve a supported inverse; keep known values fixed with locks. Singular or underdetermined inverses may remain incomplete.
Common questions
What assumptions apply?
Linearized weak-coupling, equilibrium Debye screening is assumed. Plasma uses electron density per cubic meter; electrolyte ionic strength is mol/L. The retained vacuum permittivity and 6.02e26 per-m³ molarity conversion are rounded references.
Which unknowns can I solve?
Editable controls preserve the supported captured inverse branches. Clear the desired unknown and provide enough independent known quantities; singular or underdetermined inverses may remain incomplete.
References
Linearized weak-coupling, equilibrium Debye screening is assumed. Plasma uses electron density per cubic meter; electrolyte ionic strength is mol/L. The retained vacuum permittivity and 6.02e26 per-m³ molarity conversion are rounded references. Clear an unknown to solve a supported inverse; keep known values fixed with locks. Singular or underdetermined inverses may remain incomplete.