The precession factor of hemispherical resonator gyroscopes (HRG) operating in the whole angle (WA) mode is only related to the spherical shell resonator. However, the detection errors such as the gap mismatch, the non-orthogonal coupling of the readout electrode and gain error of the detection circuit etc., will cause the circumferential consistency degradation of the precession factor. Thus the precession factor of ideal HRG is theoretically deduced firstly, then the influence of the detection errors on the precession factor is analyzed, and a correction method of the detection errors is proposed in the specific WA control circuit and algorithms. Finally, the effectiveness of the correction method is verified by experiments. The experimental results show that the circumferential consistency of the precession factor has been improved by two orders of magnitude.