In this article, a systematic fault diagnosability evaluation, including fault detectability and isolability, is established in a quantitative manner for two-dimensional systems. With ingenious data formulation, a parity relation of two-dimensional systems is first established, then the Kullback-Leibler divergence is employed as the key measure for the diagnosability analysis based on the established parity relation. The basic idea is to quantify the distribution differences among each fault scenario-related system dynamic behavior. Explicit necessary and sufficient condition for fault diagnosability is further derived based on the appropriately introduced definitions corresponding to the two directions evolving system properties. Finally, the effectiveness of the proposed method is verified by two examples.