It is known that the transport capacity of a dense wireless ad hoc network with n nodes scales like √n. We show that the transport capacity divided by √n approaches a nonrandom limit with probability 1 when the nodes are uniformly distributed on the unit square. To show the existence of the limit, we prove that the transport capacity under the protocol model is a subadditive Euclidean functional and use the machinery of subadditive functions in the spirit of Steele.