The waveguide bandpass filter with dielectric resonators is usually constructed with a cutoff waveguide including dielectric resonators inside and waveguides which are connected at both ends of the cutoff waveguide. The coupling coefficient between dielectric resonators was obtained by S.B. Cohn. The external Q of a dielectric resonator, however, was not reported in the past, which is necessary for the design of the filter. In this paper, the external Q is obtained by calculating the radiation power by using the displacement current inside the dielectric resonator. The theoretical values of the external Q are obtained corresponding to the distance between input waveguide and a resonator. The results were compared with the experimental results and they were in a good agreement. The external Q is also calculated by using the radiation power from a magnetic dipole source of a resonator. It takes more error than the method by using a displacement current.