In this paper, we study capacity estimation for mobile ad hoc networks (MANETs) using directional antennas. A matrix-based fast calculation algorithm is proposed to calculate the network capacity in a network scenario in which there is no channel sharing among multiple sessions and there is an end-to-end delay constraint between each source and destination pair. The algorithm calculates the network capacity in terms of the maximum number of k-hop paths based on the k-hop adjacency matrix of the network. Through numerical and simulation results, we show that our proposed algorithm can estimate network capacity much faster than the Brute-Force Search Algorithm with the same accuracy. In addition, our proposed algorithm can also be adapted to a transmission environment using omni-directional antennas.