For a binary mixture the following functions are used:
with
Here,  and  are the dimensionless interaction parameters, which are related to the interaction energy parameters  and  by:
Here R is the gas constant and T the absolute temperature, and U is the energy between molecular surface i and j.  U is the energy of evaporation. Here U has to be equal to U, but  is not necessary equal to .
The parameters  and  are the so-called non-randomness parameter, for which usually  is set equal to . For a liquid, in which the local distribution is random around the center molecule,  the parameter . In that case the equations reduce to the one-parameter Margules activity model:
In practice,  is set to 0.2, 0.3 or 0.48. The latter value is frequently used for aqueous systems. The high value reflects the ordered structure caused by hydrogen bonds. However, in the description of liquid-liquid equilibria the non-randomness parameter is set to 0.2 to avoid wrong liquid-liquid description. In some cases a better phase equilibria description is obtained by setting  . However this mathematical solution is impossible from a physical point of view, since no system can be more random than random ( =0). In general  NRTL offers more flexibility in the description of phase equilibria than other activity models due to the extra non-randomness parameters. However, in practice this flexibility is reduced in order to avoid wrong equilibrium description outside the range of regressed data.
The limiting activity coefficients, also known as the activity coefficients at infinite dilution, are calculated by:
The expressions show that at  the limiting activity coefficients are equal. This situation that occurs for molecules of equal size, but of different polarities.<br /> It also shows, since three parameters are available, that multiple sets of solutions are possible.