text: Using the dielectric formalism, the IMFP  can be calculated by solving the following integral:
  with the minimum (maximum) energy loss  (), the dielectric function , the energy loss function (ELF)  and the smallest and largest momentum transfer . In general, solving this integral is quite challenging and only applies for energies above 100 eV. Thus, (semi)empirical formulas were introduced to determine the IMFP.
  A first approach is to calculate the IMFP by an approximate form of the relativistic Bethe equation for inelastic scattering of electrons in matter. Equation  holds for energies between 50 eV and 200 keV:
  with
  and
  and the electron energy  in eV above the Fermi level (conductors) or above the bottom of the conduction band (non-conductors).  is the electron mass,  the vacuum velocity of light,  is the number of valence electrons per atom or molecule,  describes the density (in ),  is the atomic or molecular weight and , ,  and  are parameters determined in the following. Equation  calculates the IMFP and its dependence on the electron energy in condensed matter.
  Equation  was further developed to find the relations for the parameters , ,  and  for energies between 50 eV and 2 keV:
  Here, the bandgap energy  is given in eV. Equation  an  are also known as the TTP-2M equations and are in general applicable for energies between 50 eV and 200 keV. Neglecting a few materials (diamond, graphite, Cs, cubic-BN and hexagonal BN) that are not following these equations (due to deviations in ), the TTP-2M equations show precise agreement with the measurements.
  Another approach based on Equation  to determine the IMFP is the S1 formula. This formula can be applied for energies between 100 eV and 10 keV:
  with the atomic number  (average atomic number for a compound),  or  ( is the heat of formation of a compound in eV per atom) and the average atomic spacing :
  with the Avogadro constant  and the stoichiometric coefficients  and  describing binary compounds . In this case, the atomic number becomes 
  with the atomic numbers  and  of the two constituents. This S1 formula shows higher agreement with measurements compared to Equation .
  Calculating the IMFP with either the TTP-2M formula or the S1 formula requires different knowledge of some parameters. Applying the TTP-2M formula one needs to know ,  and  for conducting materials (and also  for non-conductors). Employing S1 formula, knowledge of the atomic number  (average atomic number for compounds),  and  is required for conductors. If non-conducting materials are considered, one also needs to know either  or .
  An analytical formula for calculating the IMFP down to 50 eV was proposed in 2021. Therefore, an exponential term was added to an analytical formula already derived from  that was applicible for energies down to 500 eV:
  For relativistic electrons it holds:
  with the electron velocity ,  and .  denotes the velocity of light.  and  are given in nanometers. The constants in  and  are defined as following: