Two-dimensional (2D) materials are categorized into van der Waals (vdW) and non-vdW types. However, no relevant descriptors have been proposed for identifying the latter. Here, we identify the non-vdW 2D materials by calculating the thickness-dependence of total energy of thin films truncated from surfaces. The non-vdW 2D materials exhibit a deviation from the law of exfoliation energy inverse to the number of layers in the monolayer limit. This framework is applied to explore single- and multi-component systems, which predicts the synthesizability of several non-vdW 2D materials including silicene and goldene that are overlooked in the dimensional analysis of the parent crystals and also predicts that a Janus structure exists in nature but is hidden in 3D crystals.