Vertebral morphological measurements are important across various disciplines, including spinal biomechanics and clinical applications, pre- and post-operatively. These measurements also play a crucial role in anthropological longitudinal studies, where spinal metrics are repeatedly documented over extended periods. Traditionally, such measurements have been manually conducted, a process that is time-consuming. In this study, we introduce a novel, fully automated method for measuring vertebral morphology using 3D meshes of lumbar and thoracic spine models.Our experimental results demonstrate the method's capability to accurately measure low-resolution patient-specific vertebral meshes with mean absolute error (MAE) of 1.09 mm and those derived from artificially created lumbar spines, where the average MAE value was 0.7 mm. Our qualitative analysis indicates that measurements obtained using our method on 3D spine models can be accurately reprojected back onto the original medical images if these images are available.