The computed tomography (CT) radiation dose to pediatric patients has received considerable attention recently. Moreover, it is important to be able to determine CT radiation doses for various patient sizes ranging from infants to large adults. The current AAPM protocol only measures CT radiation dose using a 16 cm acrylic phantom to represent an adult head and a 32 cm acrylic phantom to represent an adult body. The goal of this paper is to study the dependence of the computed tomography dose index (CTDI) upon the size of the phantom, the kVp selected and the scan mode employed. Our measurements were done on phantom sizes ranging from 6 cm to 32 cm. The x-ray tube potential ranged from 80 to 140 kVp. The scan modes utilized for the measurements included: consecutive axial scans, single-slice helical scans with variable pitch and multislice helical scans with variable pitch. The results were consolidated into simplified equations which related the phantom diameter and kVp to the measured CTDI. Some generalizations were made about the relationship between the scan modes of the various CT units to the measured radiation doses. The CTDI appears to be an exponential function of phantom diameter. For the same kVp and mAs, the radiation doses for smaller phantoms are much greater than for larger sizes. The derived relationship can be used to estimate the radiation doses for a variety of scan conditions and modes from measurements with the two standard reference phantoms. A method was also given for converting axial CT dose measurements to appropriate MSAD values for helical CT scans.