We present the first algorithm which can estimate the maximum matching size with arbitrary small additive slack in time polynomially sub-linear with respect to the number of edges present in the graph for any input graph. Previous algorithms either required an approximation ratio of 1.499 or for the input graph to have small maximum degree. From this result we simply derive the first algorithm which can maintain a (1+\eps) approximation of the maximum matching size under edge insertions and deletions in update time sub-linear in n.