Knowledge of the interaction between carbon nanotubes (CNTs) and planar surfaces is essential to optimizing CNT applications as well as reducing their environmental impact. In this work, the surface element integration (SEI) technique was coupled with the DLVO theory to determine the orientation-dependent interaction energy between a single-walled carbon nanotube (SWNT) and an infinite isotropic planar surface. For the first time, an analytical formula was developed to describe accurately the interaction between not only pristine but also surface-charged CNTs and planar surfaces with arbitrary rotational angles. Compared to other methods, the new analytical formulas were either more convenient or more accurate in describing the interaction between CNTs and planar surfaces, especially with respect to arbitrary angles. The results revealed the complex dependences of both force and torque between SWNTs and planar surfaces on the separation distances and rotational angles. With minor modifications, the analytical formulas derived for SWNTs can also be applied to multiwalled carbon nanotubes (MWNTs). The new analytical expressions presented in this work can be used as a robust tool to describe the DLVO interaction between CNTs and planar surfaces under various conditions and thus to assist in the design and application of CNT-based products.