We analyzed the noise characteristics of two-dimensional (2-D) and three-dimensional (3-D) images obtained from the GE Advance positron emission tomography (PET) scanner. Three phantoms were used: a uniform 20-cm phantom, a 3-D Hoffman brain phantom, and a chest phantom with heart and lung inserts. Using gated acquisition, we acquired 20 statistically equivalent scans of each phantom in 2-D and 3-D modes at several activity levels. From these data, we calculated pixel normalized standard deviations (NSD's), scaled to phantom mean, across the replicate scans, which allowed us to characterize the radial and axial distributions of pixel noise. We also performed sequential measurements of the phantoms in 2-D and 3-D modes to measure noise (from interpixel standard deviations) as a function of activity. To compensate for the difference in axial slice width between 2-D and 3-D images (due to the septa and reconstruction effects), we developed a smoothing kernel to apply to the 2-D data. After matching the resolution, the ratio of image-derived NSD values (NSD2D/NSD3D)2 averaged throughout the uniform phantom was in good agreement with the noise equivalent count (NEC) ratio (NEC3D/NEC2D). By comparing different phantoms, we showed that the attenuation and emission distributions influence the spatial noise distribution. The estimates of pixel noise for 2-D and 3-D images produced here can be applied in the weighting of PET kinetic data and may be useful in the design of optimal dose and scanning requirements for PET studies. The accuracy of these phantom-based noise formulas should be validated for any given imaging situation, particularly in 3-D, if there is significant activity outside the scanner field of view.