The equivalent circuit of a piezoelectric ceramic is established composed of the equivalent circuit parameters derived from the complex materials coefficients. The equivalent circuit parameters are connected to real and imaginary parts of the complex materials coefficients of the piezoelectric ceramics. With respect to the definition of dissipation factors, the dielectric, elastic, and piezoelectric dissipation factors which represent the losses in the materials are thus expressed through the equivalent circuit parameters. In temperature and stress experiments, by measuring the equivalent circuit parameters during the process of the temperature and stress changes, three dissipation factors are computed. Compared with the results of other previous research, a similar increase of the elastic dissipation factor with stress is observed. Moreover, it is also found that the elastic dissipation factor reaches its saturation over a stress level of about 10 MPa. The responses of dissipation factors in lower temperature (-30 degrees C to 20 degrees C) are studied.