The wear of cutting blades during the preparation of building stones is an inevitable issue that occurs due to the contact of the blade with rock components. The present study aims to investigate the feasibility of proposing experimental relations of strength parameters and mineralogical hardness with Cerchar and LCPC tests. For this purpose, 18 samples of granite building stones were selected and Equivalent Quartz Content (EQC), compressive and Brazilian tensile strength (UCS and BTS), Cerchar, and LCPC abrasivity indices (CAI and LAC) were determined. The results showed the lack of any significant relationship between strength and abrasion properties. However, when evaluating the simultaneous impact of EQC and UCS using the rock abrasion index (), significant valid empirical relationships between RAI-CAI and RAI-LAC were derived. To investigate the simultaneous effect of UCS, BTS, and EQC, a dimensionless parameter, i.e. modified rock abrasion index () was introduced. Moreover, it was found that the empirical relationship between MRAI-CAI was more significant and valid than the previous relations. Verification of the proposed relationship with the values of other researchers and 6 new samples for estimating CAI and LAC based on UCS, BTS, and EQC was found to be highly accurate for granite building stones.