Directional antennas can be useful in significantly increasing the capacity of wireless ad hoc networks. With directional antennas, independent communications between nodes can occur in parallel, even if the nodes are within range of each other. However, mutual interference by simultaneous transmissions limits the maximum number of such concurrent communications. Furthermore, it poses bounds on the amount of capacity gain one can achieve by using directional antennas instead of omni-directional ones. These bounds depend on the specific antenna type and its parameters, as well as higher layer protocol requirements. In this paper, we calculate interference based capacity bounds for a generic antenna model as well as a real-world antenna model and analyze how these bounds are affected by important antenna parameters like gain and beamwidth.