Abstract: In the mathematical analyses of ad hoc network theories,the node space distribution of a mobility model is an important foundation for the theoretic research of many relevant characteristic of ad hoc network,e.g.,network connectivity,MST,average path length,network capacity etc.,and is a key factor to the simulation results. Random direction mobility model is a commonly used mobility model in the field of ad hoc network. In this paper,the space probabilistic distribution of this mobility model is investigated. Through the analyses of the probability and average length of the events that contribute to the node space distribution,the exact formula of the node space probabilistic distribution are derived in both 1D and 2D regions. The results of this paper provide precise theoretic foundations for derivations,proofs,simulations and applications of ad hoc network based on random direction mobility model.