This study presents a novel closed-form analytical formulation for defining the biaxial curvature and ductility domains of reinforced concrete (RC) rectangular cross-sections. Developed with a data-driven calibration approach leveraging extensive numerical simulations, this formulation accurately captures the sectional response from the elastic range up to ultimate conditions, under combined axial load and biaxial bending. The formulation precisely delineates both elastic and ultimate curvature limits, which are governed by the yielding of reinforcement and the crushing of concrete, respectively. Unlike traditional numerical fiber-based analyses that can be computationally intensive, this proposed analytical approach offers a direct and efficient method for comprehensively assessing sectional behavior under complex loading scenarios. The validity and robustness of this closed-form solution are rigorously demonstrated through extensive comparisons with a parametric dataset. This dataset was generated from numerical simulations, encompassing a wide range of geometrical configurations, reinforcement ratios, and material properties. This research provides a functional and user-oriented tool for structural engineers, enabling the rapid and accurate evaluation of the biaxial curvature and ductility of RC sections, thereby significantly advancing current design practices and contributing to more resilient structural systems.