This paper evaluates the achievable transmission capacity of the secondary system in cognitive radio networks, defined by the spatial density of successful transmissions while guaranteeing the target outage probabilities of the secondary and the primary systems. By using stochastic geometry, the effects of the spatial densities and the transmission powers on the achievable transmission capacity is presented. Subsequently, the optimal spatial density of the secondary system and the optimal transmission power ratio of the primary system to the secondary system are derived. Furthermore, the maximum achievable transmission capacity is defined using the derived optimal values. From the theoretical results, it is shown that the optimal transmission power ratio is affected by not the density of the primary system, but the system parameters including the target outage probability. In addition, the achievable transmission capacity of the secondary system decreases as the spatial density of the primary system increases at the decreasing rate determined by the system parameters of the primary system.