The size of a Peer-to-Peer (P2P) network is an important parameter for performance tuning of P2P routing algorithms. This paper introduces and evaluates a new efficient method for participants in an unstructured P2P network to establish the size of the overall network. The presented method is highly efficient, propagating information about the current size of the network to all participants using O(|E|) operations where |E| is the number of edges in the network. Afterwards, all nodes have the same network size estimate, which can be made arbitrarily accurate by averaging results from multiple rounds of the protocol. Security measures are included which make it prohibitively expensive for a typical active participating adversary to significantly manipulate the estimates. This paper includes experimental results that demonstrate the viability, efficiency and accuracy of the protocol.