Summary: The coagulation-fragmentation process models the stochastic evolution of a population of \(N\) particles distributed into groups of different sizes that coagulate and fragment at given rates. The process arises in a variety of contexts and has been intensively studied for a long time. As a result, different approximations to the model were suggested. Our paper deals with the exact model which is viewed as a time-homogeneous interacting particle system on the state space \(\Omega_N\), the set of all partitions of \(N\). We obtain the stationary distribution (invariant measure) on \(\Omega_N\) for the whole class of reversible coagulation-fragmentation processes, and derive explicit expressions for important functionals of this measure, in particular, the expected numbers of groups of all sizes at the steady state. We also establish a characterization of the transition rates that guarantee the reversibility of the process. Finally, we make a comparative study of our exact solution and the approximation given by the steady-state solution of the coagulation-fragmentation integral equation which is known in the literature. We show that in some cases the latter approximation can considerably deviate from the exact solution.