Our aim was to determine the external radiation dose rates of patients undergoing positron emission tomography/computed tomography (PET/CT) and PET/magnetic resonance imaging (MRI) examinations, and to assess the factors affecting these doses. The external radiation dose rates (ERDR) from (18)F-FDG were measured using the Geiger-Müller tube at a distance of 10, 50, and 100cm from the patients' skin surface from various body regions. Results showed that at 10cm from the body surface for PET/CT examinations, the ERDR immediately after (18)F-FDG i.v. injection at time points 1 and 4 was 522.19±189.59μSvh(-1) and 256.36±74.94μSvh(-1) , respectively. At 10cm from the body surface for PET/MRI examinations, the ERDR at time points 1 and 4 were 258.76±92.09μSvh(-1) and 105.63±27.48μSvh(-1), respectively, always with a precipitous decrease over time. The (18)F-FDG dose was on average 1.93-fold higher and the ERDR was higher approximately 2.01 to 2.42-fold in PET/CT examinations than in PET/MRI examinations. In both PET/CT and PET/MRI patients, the ERDR was significantly higher with lower body weight, shorter stature, and fewer urinations etc. In conclusion, based on our results, the ERDR to patients from PET/CT scans at a distance of 10cm was twice as high than from the PET/MRI. Furthermore, to decrease ERDR to the patients, the dose injected should be adjusted to body weight and height. Factors like post injection fluid intake and urine bladder emptying, decrease ERDR. Other persons should keep a safe distance from the injected patient.