Thrust measurements of rotating detonation engine of (1) ethylene / gas-oxygen and (2) methane / gas-oxygen with various throat geometries in a vacuum chamber to simulate different back-pressure conditions ranging from 1.1-104 kPa were conducted. For throatless rotating detonation engine, we defined equivalent throat area as the detonation channel area, and then tested four nozzle contraction ratios of 1, 1.5, 2.5, and 8. Engines could be successfully ignited by electric ignitors when initial pressure was high enough to have, at least, one detonation cell in RDE channel. We measured the combustor pressure and reveled that it was almost proportional to the throat mass flux regardless of contraction ratios and the propellant combinations. The specific impulse of methane / gas-oxygen case could achieve 84 ± 1% of ideal specific impulse at the optimum expansion for each back pressure.