Self-centering buckling-restrained bracing frame (SCBRBF) has both energy dissipating capacity and self-centering capacity, so it has been paid increasing attention. It has a unique trilinear hysteresis, based on which, the equal-strength nonlinear displacement ratio (CR) formula (the CR-R-T relation) was proposed. However, the accuracy of the CR formula in periods around 3 s needs improving. According to this, three improved formulae are proposed in this study. The original data (exact solution) for the regression and the mean CR of another set of ground motion are used for the evaluation of the proposed formulae. The influence of four parameters on the error of CR is analyzed. It is found that the third improved equation is optimal. On the other hand, CR formula based on the bilinear restoring force model has been widely used in self-centering structures before. It is necessary to simplify the trilinear restoring force model of SCBRBF to a bilinear model (the equivalent principle of equal yield force and yield displacement) for the use of that formula. Equivalent principle of equal yield force and yield displacement was used last time, through which it was found that larger error can be introduced by bilinear formula. In order to exclude the influence of different equivalence principles on the error of bilinear model when analyzing SCBRBF, another reasonable bilinear equivalent principle is used in this work. It is found that even with the different equivalence principle, the application of the CR formula from bilinear hysteresis can still cause large error for SCBRBFs.