The solid electrolyte interface (SEI) is a hierarchical structure formed in the transition zone between the electrode and the electrolyte. The properties of lithium-ion (Li-ion) battery such as cycle life irreversible capacity loss self-discharge rate electrode corrosion and safety are usually ascribed to the quality of the SEI which are highly dependent on the thickness. Thus understanding the formation mechanism and the SEI thickness is of prime interest. First we apply dimensional analysis to obtain an explicit relation between the thickness and the number density in this study. Then the SEI thickness in the initial charge-discharge cycle is analyzed and estimated for the first time using the Cahn-Hilliard phase-field model. In addition the SEI thickness by molecular dynamics simulation validates the theoretical results. It has been shown that the established model and the simulation in this paper estimate the SEI thickness concisely within order-of-magnitude of nanometers. Our results may help in evaluating the performance of SEI and assist the future design of Li-ion battery.