To calculate the pressure drop in a given reactor, the following equation may be deduced
This arrangement of the Ergun equation makes clear its close relationship to the simpler Kozeny-Carman equation which describes laminar flow of fluids across packed beds via the first term on the right hand side. On the continuum level, the second order velocity term demonstrates that the Ergun equation also includes the pressure drop due to inertia, as described by the Darcy–Forchheimer equation. Specifically, the Ergun equation gives the following permeability  and inertial permeability  from the Darcy-Forchheimer law:
and 
The extension of the Ergun equation to fluidized beds, where the solid particles flow with the fluid, is discussed by Akgiray and Saatçı (2001).