 Mathematical models can predict the performances of batteries, such as their state of charge and state of health. Among physicochemical governing equations, Fick’s first and second laws describe ionic intercalation and solid-state diffusion in electrode particles, respectively. Conventionally, molar concentration and current density are the main descriptors for ionic intercalation and solid-state diffusion in the electrochemical models. However, more relevant and typical descriptors for rechargeable batteries are intercalation quantity (i.e., x in LixC6) and C-rate. Herein, we translate the governing equations of Fick’s laws based on intercalation quantity and C-rate, instead of the molar concentration and current density. The new governing equations enabled faster computation of the electrochemical models, benefited by the intrinsically dimensionless properties of the descriptors. Moreover, the newly derived equations provide a practical insight to design the morphology of particles for the improved rate capability. Implementing the newly derived governing equations to a single-particle model demonstrated faster, efficient, and reliable simulation to investigate the effects of particle size, diffusivity, and C-rate on lithium-ion batteries performances. These new governing equations can be implemented in various models for batteries in general, enabling an efficient computation and facilitated communication among researchers investigating energy storage.