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The capacity of IEEE 802.11-based ad hoc networks is a critical issue because multi-hop communication requires additional capacity which is not available for transmitting application data. Furthermore, the distributed coordination function (DCF) of IEEE 802.11 causes various channel access problems which can lead to bad utilization of the channel capacity and to unfair capacity assignment for the connections in a network. In this paper we present an approach for calculating an upper bound capacity for a given fairness constraint. Our calculations can be used for networks with any node distribution, routing and traffic pattern. We also discuss the performance of the DCF in regard to the calculated upper bound capacity by simulating example scenarios. Our results show that a DCF is able to provide about 55% of the upper bound capacity.