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This paper introduces a novel approach to evaluate the performance of ad hoc networks based on their spatial capacity, defined as the maximum spatial spectral efficiency supported by the network while a zero outage probability is guaranteed for all communication links. Specifically, the spatial capacity together with upper and lower bounds is derived in closed-form for networks where transmitters follow a Poisson point process and their respective receivers are located at a fixed distance. In this scenario, the spatial capacity is achieved using a rate adaptation technique that adjusts the link spectral efficiency in accordance with the distance between the receivers and their closest interferers. Besides, the spatial capacity is analytically proved to be always greater than or equal to the maximum spatial spectral efficiency achieved when a fixed spectral efficiency and an unbounded outage probability are considered. Numerical results show that the spatial-capacity-achieving setting leads to a spatial spectral efficiency about 125% higher than the one reached with the fixed spectral efficiency strategy.