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It is still a great challenge to design and synthesize high-efficiency and low-cost single-atom catalysts (SACs) as promising bifunctional electrocatalysts for the oxygen reduction reaction (ORR) and the oxygen evolution reaction (OER). Herein, theoretical insights into Sn-N4 embedded carbon nanotubes, graphene quantum dots, and graphene nanosheets (denoted as Sn-N4-CNTs, Sn-N4-GQDs, and Sn-N4-Gra, respectively) for the ORR/OER are systematically provided. These results show that the protruding Sn atom creates a Sn-N4 pyramid and induces varied strain transfer between Sn-N4 and different carbon substrates prior to adsorption of O intermediates, resulting in the opposite response of the adsorption strengths of O intermediates to the substrate curvature of Sn-N4-CNTs and Sn-N4-GQDs. The torsional strain induced by OH* and OOH* on the Sn atom of Sn-N4-CNTs breaks the scaling relations between the adsorption strengths of O intermediates. Consequently, Sn-N4-CNTs with suitable curvature achieve outstanding ORR performance with very low overpotentials (0.28 V). Furthermore, the increase of curvature boosts the OER activity of Sn-N4-CNTs. For Sn-N4-GQDs, high curvature contributes to promoted OER activity but reduced ORR activity. The electronic interactions reveal the electron transfer from the s/p-bands of Sn to the half-filled β states of the frontier orbitals of O intermediates.