A generic reaction under Curtin–Hammett can be described by the following parameters:
In order for rapid equilibration to be a good assumption, the rate of conversion from the less stable of A or B to the product C or D must be at least 10 times slower than the rate of equilibration between A and B.
The rate of formation for compound C from A is given as
and that of D from B as
with the second approximate equality following from the assumption of rapid equilibration.  Under this assumption, the ratio of the products is then
In other words, because equilibration is fast compared to product formation,  throughout the reaction. As a result,  also remains roughly constant throughout the reaction.  In turn, integration with respect to time implies that  likewise takes on an approximately constant value through the course of the reaction, namely . 
In terms of the ground state and transition state energies, the product ratio can therefore be written as:
Importantly, inspection of the energy diagram above allows us to identify 
with the energy difference of the transition states, giving us a simplified equation that captures the essence of the Curtin-Hammett principle: 
Thus, although the product ratio depends on the equilibrium constant between A and B and the difference in energy between the barriers from A to C and from B to D, both of these factors are automatically taken into account by the energy difference of the transition states leading to the products, ΔΔG.