This study investigated the stress–strain behavior of seamless pipes in the hoop direction using the ring expansion test, which is a non-standardized mechanical testing technique used for evaluating the mechanical properties of round tubes. However, this technique has limitations, such as unidentified specimen geometry, strain measurement, and the estimation of friction coefficients. The study employed experimental, numerical, and analytical methodologies to address these limitations and throughout the study, a novel hoop stress correlation factor (K) was identified to be multiplied by the hoop stress derived equation for reduced section ring specimens. The experimental strain was measured using a newly derived analytical equation, and a mathematical predictive model was developed to estimate the K-factor using the Design of Experiment (DoE) and Design-Expert statistical software. The study concluded that the ring expansion test is a promising technique for evaluating the mechanical properties of seamless pipes similar to the unified axial tensile stress–strain behavior. However, future research is needed to estimate the hoop stress correlation value (K) for all ring geometries. The study's finding of the novel hoop stress correlation factor (K) in the case of a reduced section ring specimen is particularly noteworthy, as it addresses a significant research gap in the field.