cosmocnc evaluates the number count likelihood of galaxy cluster catalogs. Fast Fourier Transform (FFT) convolutions are used to evaluate some of the likelihood integrals. The code supports three types of likelihoods (unbinned, binned, and an extreme value likelihood); it also supports the addition of stacked cluster data (e.g., stacked lensing profiles), which is modeled in a consistent way with the cluster catalog. The package produce mass estimates for each cluster in the sample, which are derived assuming the hierarchical model that is used to model the mass observables, and generates synthetic cluster catalogs for a given observational set-up. cosmocnc interfaces with the Markov chain Monte Carlo (MCMC) code Cobaya (ascl:1910.019), allowing for easy-to-run MCMC parameter estimation.