The generating function of the sequence counting the number of graph vertices at a given distance from the root is called the spherical growth function of the rooted graph. The vertices farthest from the root form an induced subgraph called the distance-residual graph. These mathematical notions are applied to benzenoid graphs which are used in graph theory to represent benzenoid hydrocarbons. An algorithm for calculating the growth in catacondensed benzenoids is presented, followed by some examples.