Equivalent conicity (EC) in-service has been required in TSI INF and TSI LOC & PAS for several years. However, due to implementation difficulties, only a few infrastructure managers and railway undertakings currently include EC requirements in their maintenance programmes. A novel method called the Gradient Index Profile (GIP), which combines gradient index for wheel (GIPw) and gradient index for rail (GIPr), has been developed to complement and support EC. In this study, based on a large number of on-track measured rail profiles, we investigate the distribution functions of GIPr on tangent tracks. We also examine the correlations of GIPr with track EC with the nominal S1002 wheel profile (EC S1002) and in-service EC with a reference worn wheel profile (EC ref. worn), respectively. Finally, we propose maintenance limit values for GIPr, which should be useful for rail surface management related to vehicle running stability.