Free · Thermodynamics and heat calculators 🌡️

Classical Mobility, Diffusion and Carrier Charge

Relate diffusion coefficient, electrical mobility, absolute temperature and positive carrier-charge magnitude using the classical Einstein relation and exact SI Boltzmann constant.

  • Formula & worked example
  • Private in your browser
  • No signup
Go to tool

Calculator inputs

Loading calculator…

How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. 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

For electrical mobility 1,000 mm²/(V·s), temperature 26.85°C (300 K) and charge magnitude one elementary charge, the classical diffusion coefficient is about 25.852 mm²/s.

D = μk_B T/|q|; k_B = 1.380649 × 10⁻²³ J/K.

Worked example

Enter these known values and leave the other values blank.

Electrical mobility μ
1000 mm²/(V·s)
Absolute temperature T
26.85 °C
Carrier charge magnitude |q|
1 e
Diffusion coefficient D
25.85 mm²/s

Assumptions and limitations

  • This is the classical, thermal-equilibrium Einstein relation for positive electrical-mobility and charge magnitudes. It assumes nondegenerate carriers with the applicable equilibrium fluctuation-dissipation behavior; it is not a general high-field, quantum-degenerate or active-medium transport model.
  • Mobility is entered in the retained fixed mm²/(V·s) units and diffusion in mm²/s. Their common area scale cancels in D/μ. In SI, multiply either numeric value by 10⁻⁶ to express its square-meter unit.
  • T is absolute temperature in the equation. Select Celsius, Fahrenheit or kelvins without changing the physical temperature; only T>0 K is allowed. This is not a temperature difference.
  • Charge is a positive carrier-charge magnitude. One elementary charge is exactly 1.602176634×10⁻¹⁹ C; signed electron-direction information is outside this magnitude relation.
  • The retained model requires μ,D,T and |q| to be positive. Clear the intended unknown before using an inverse. The relation does not independently measure a material’s mobility or diffusion coefficient.

Common questions

Can I use Celsius directly in the formula?

The formula requires kelvins. The Celsius and Fahrenheit selectors convert an absolute temperature to kelvins before calculation.

Why are mobility and diffusion shown in square millimeters?

Both retained controls use the same area scale, so it cancels in their ratio. Divide each numeric value by one million to express square-meter units.

Does the relation apply to every material?

No. It is a classical equilibrium model. Degenerate carriers, high fields and nonequilibrium media can require a different transport relation.

References

The classical Einstein relation uses exact SI k_B=1.380649e-23 J/K rather than the captured pre-redefinition value 1.3806503e-23. Replace all four variants together and guard positive inverse denominators. Absolute temperature is in kelvins in the equation; the source affine Celsius/Fahrenheit/Kelvin selectors remain. Both bare mobility and diffusion controls use square millimeters, so their shared area scale cancels.

Explore thermodynamics and heat calculators 🌡️ or browse all physics calculators.