Sodium-ion batteries (NIBs) and potassium-ion batteries (KIBs) are gaining extensive attention as promising alternatives to lithium-ion batteries owing to their superior energy density and cost-effectiveness. However, the larger ionic radius of Na+ and K+ ions in comparison to Li+ ions poses a challenge in designing anode materials characterized by enduring structures and elevated voltage to facilitate the efficacy of high-performance NIBs and KIBs. Carbon nanomaterials, particularly carbon nanotubes (CNTs), have emerged as a potential candidate in anode materials. Herein, we used density functional theory calculations to study the cell voltage of CNTs in relation to Na-ion and K-ion storage as a function of CNT size. The adsorption energy profiles of both Na+@CNT and K+@CNT systems exhibit a descending trend concomitant with the increase in the CNT diameter, where Na+/K+ ion primarily prefers to adsorb in the interior wall of CNT. Conversely, the cell voltage for the Na and K system gradually increases with the increasing diameter of CNT, which can be attributed to the stronger electrostatic interaction validated by energy decomposition calculation. The voltage of Na-ion adsorbed on the inter wall of (10,10) CNT attains 1.29 V, close to the previously theoretical voltage of Li-ion on the same CNT (1.35 V), while the much lower voltage pertaining to K-ion adsorption on the inter wall of (10,10) CNT just stands at 0.59 V, suggesting the viability of CNT-based electrode for NIBs but not for KIBs. These findings lay a solid foundation for delineating the interrelationship between the voltage properties of CNT as prospective anode material and their structural characteristics, thereby expanding the application of CNT-based optoelectronic devices.