Consider the simpler case where there are two binding sites. See the scheme shown below. Each site is assumed to bind either molecule of substrate S or product P. The catalytic reaction is shown by the two reactions at the base of the scheme triangle, that is S to P and P to S. The model assumes the binding steps are always at equilibrium. The reaction rate is given by:
Invoking the rapid-equilibrium assumption we can write the various complexes in terms of equilibrium constants to give:
where . The  and <math>
\pi and  and 
Using the author's own notation, if an enzyme has  sites that can bind ligand, the form, in the general case, can be shown to be: 
The non-cooperative reversible Michaelis-Menten equation can be seen to emerge when we set the Hill coefficient to one. 
If the enzyme is irreversible the equation turns into the simple Michaelis-Menten equation that is irreversible. When setting the equilibrium constant to infinity, the equation can be seen to revert to the simpler case where the product inhibits the reverse step. 
A comparison has been made between the MWC and reversible Hill equation. 
A modification of the reversible Hill equation was published by Westermark et al where modifiers affected the catalytic properties instead.  This variant was shown to provide a much better fit for describing the kinetics of muscle phosphofructokinase.