Circular distance between vertices of a graph has a significant role, which is defined as summation of detour distance and geodesic distance. Attention is paid, this is metric on the set of all vertices of graph and it plays an important role in graph theory. Some bounds have been carried out for circular distance in terms of pendent vertices of graph. Some results and properties have been found for circular distance for some classes of graphs and applied this distance to Cartesian product of graphs $P_2 \times C_n$. Including $P_2 \times C_n$, some graphs acted as a circular self-centered. Using this circular distance there exists some relations between various radii and diameters in path graphs. The possible applications were briefly discussed.