A topological index is a numerical number associated with a graph that describes its topology. History traces a long path on the study of topological indices. A circulant graph is one of the most comprehensive families, as its specializations give some important families like complete graphs, crown graphs, rook graphs, complete bipartite graphs, cocktail party graphs, empty graphs, etc. The aim of this report is to compute the first and second K Banhatti indices of circulant graph. We also compute the first and second K hyper Banhatti indices of this family of graph. Moreover, we plot our results to see the dependences of the first and second K Banhatti indices and the first and second K hyper Banhatti indices on the involved parameters.