Cortical thickness varies throughout the cortex in a systematic way. However, it is challenging to investigate the patterns of cortical thickness due to the intricate geometry of the cortex. The cortex has a folded nature both in radial and tangential directions which forms not only gyri and sulci but also tangential folds and intersections. In this article, cortical curvature and depth are used to characterize the spatial distribution of the cortical thickness with much higher resolution than conventional regional atlases. To do this, a computational pipeline was developed that is capable of calculating a variety of quantitative measures such as surface area, cortical thickness, curvature (mean curvature, Gaussian curvature, shape index, intrinsic curvature index, and folding index), and sulcal depth. By analyzing 501 neurotypical adult human subjects from the ABIDE-I dataset, we show that cortex has a very organized structure and cortical thickness is strongly correlated with local shape. Our results indicate that cortical thickness consistently increases along the gyral–sulcal spectrum from concave to convex shape, encompassing the saddle shape along the way. Additionally, tangential folds influence cortical thickness in a similar way as gyral and sulcal folds; outer folds are consistently thicker than inner.