Kinetics of ions play a crucial role in the performance of materials for a wide range of applications, including solid electrolytes, fuel cells, and sieving membranes. However, establishing a quantitative correlation between microscopic characteristics of a material and kinetics of conducting species inside remains a major challenge. Combining first-principles and metadynamics methods, we investigate sieving behavior of two-dimensional graphitic carbon nitride (g-CN) for various species (H, Na, K, and Cl). We reveal that mechanism of proton conduction changes with a pore size of carbon-nitrogen ring in g-CN: varying from a pure H transportation when crossing narrow pores into a dual pathways (via both H and hydronium ions HO) when transmitting across wide pores. We introduce a novel local descriptor, nanopore rigidity (C), to quantify the rigidity of a material and relate the dynamics of sieving species to mechanics of the pore. The kinetic barrier of an arbitrary intercalating ion (ΔG) can then be obtained via ΔG=Cδρ+B with B being a residual barrier of the pore and δρ being the local strain of the pore induced by the conducting ion. The descriptor as a microscopic metric can be extended to other porous materials, allowing a screening for electrochemical energy transition materials.