Enter the permittivity of free space, boltzmann constant, electron temperature, the density of electrons, and the charge of electrons into the calculator to determine the debye length.

Debye Length Formula

The following formula is used to calculate a debye length.

λD = SQRT ( ε0 * kB *Te / ( ne *qe^2) )


  • λD is the Debye length,
  • ε0 is the permittivity of free space,
  • kB is the Boltzmann constant,
  • qe is the charge of an electron,
  • Te is the electron temperature
  • ne is the density of electrons

What is a debye length?


A debye length is a measure of a charge carrier’s net electrostatic effect in a solution and how far that effect persists. This is an important metric in plasma physics.

How to calculate debye length?

Example Problem:

The following example outlines how to calculate a debye length.

First, determine the permittivity of free space. In this example, this is .00000000008854187.

Next, determine the Boltzmann constant. This is known to be 1.380649×10−23 J⋅K−1.

Next, determine the charge of the electrons. This is found to be .000024.

Next, determine the electron temperature. This is measured to be 500K.

Next, determine the density of the electrons. This is calculated to be 5000.

Finally, calculate the debye length using the formula above:

λD = SQRT ( ε0 * kB *Te / ( ne *qe^2) )

λD = 4.606857137614981e-13