Seamounts are isolated elevations in the seafloor with circular or elliptical plan, comparatively steep slopes, and relatively small summit area (Menard, 1964). The vertical gravity gradient (VGG), which is the curvature of the ocean surface topography derived from satellite altimeter measurements, has been used to map the global distribution of seamounts (Kim & Wessel, 2011). We used the latest grid of VGG to update and refine the global seamount catalog; we identified 10,796 new seamounts, expanding the catalog by 1/3. 739 well-surveyed seamounts, having heights ranging from 421 m to 2500 m, were then used to estimate the typical radially-symmetric seamount morphology. First, an Empirical Orthogonal Function (EOF) analysis was used to demonstrate that these small seamounts have a basal radius that is linearly related to their height – their shapes are scale invariant. Two methods were then used to compute this characteristic base to height ratio: an average Gaussian fit to the stack of all profiles and an individual Gaussian fit for each seamount in the sample. The first method combined the radial normalized height data from all 739 seamounts to form median and median-absolute deviation. These data were fit by a 3-parameter Gaussian model that explained 99.82% of the variance. The second method used the Gaussian function to individually model each seamount in the sample and further establish the Gaussian model. Using this characteristic Gaussian shape we show that VGG can be used to estimate the height of small seamounts to an accuracy of ~270 m.