Experiments are performed to investigate the combustion characterization and operating diagram under the lean fuel condition in a laboratory-scale H-2/air rotating detonation combustor (RDC). Pressure signals are obtained at different circumferential and axial positions on the RDC. Equivalence ratios ranging from 0.6 to 1.0 and air mass flow rates ranging from 25 to 225 g/s are used in the experiments. The operating diagram includes fast deflagration (FD), unstable detonation (UD), quasi-stable detonation, and stable detonation sub-regions characterized by the combustion mode. The results indicate that the occurrence of fast deflagration is mainly determined by the fuel-injection conditions and the acoustic properties of the annular combustor. The alternating occurrence of FD and detonation is typically observed in the UD region; therefore, the speed fluctuation of the wave propagation is very high, usually changed from 65% to 75% of its mean speed. In the quasi-stable detonation region, the FD completely disappears, but single/double-detonation wave inversion occurs. The statistical probability of the inversion of the single detonation wave is approximately 10% of the 100 test runs conducted in the quasi-stable detonation region. In the stable-detonation region, a stable-detonation wave is formed and propagates stably without wave inversion or splitting. The speed and pressure fluctuations of the stable detonation wave are less than 15% of the mean ones. The present results serve as a guide for the design and practical application of rotating detonation engines. (C) 2018 Elsevier Ltd. All rights reserved.