This paper presents an approach for substantially reducing the time needed to calculate the shortest paths between all concepts in a wordnet. The algorithm exploits the unique "star-like" topology of wordnets to cut down on time-expensive calculations performed by algorithms to solve the all-pairs shortest path problem in general graphs. The algorithm was applied to two wordnets of two different languages: Princeton WordNet (Fellbaum, 1998) for English, and GermaNet (Kunze and Lemnitzer, 2002), the German language wordnet. For both wordnets, the time needed for finding all shortest paths was brought down from several days to a matter of minutes.