An improved biological weighting function (IBWF) is proposed to phenomenologically relatemicrodosimetric lineal energy probability density distributions with the relative biologicaleffectiveness (RBE) for the in vitro clonogenic cell survival (surviving fraction = 10%) of the mostcommonly used mammalian cell line, i.e. the Chinese hamster lung fibroblasts (V79). The IBWF,intended as a simple and robust tool for a fast RBE assessment to compare different exposureconditions in particle therapy beams, was determined through an iterative global-fitting processaimed to minimize the average relative deviation between RBE calculations and literature in vitrodata in case of exposure to various types of ions from 1H to 238U. By using a single particle- andenergy- independent function, it was possible to establish an univocal correlation between linealenergy and clonogenic cell survival for particles spanning over an unrestricted linear energytransfer range of almost five orders of magnitude (0.2 keV μm−1 to 15 000 keV μm−1 in liquidwater). The average deviation between IBWF-derived RBE values and the published in vitro datawas ∼14%. The IBWF results were also compared with corresponding calculations (in vitro RBE10for the V79 cell line) performed using the modified microdosimetric kinetic model (modifiedMKM). Furthermore, RBE values computed with the reference biological weighting function(BWF) for the in vivo early intestine tolerance in mice were included for comparison and to furtherexplore potential correlations between the BWF results and the in vitro RBE as reported in previousstudies. The results suggest that the modified MKM possess limitations in reproducing theexperimental in vitro RBE10 for the V79 cell line in case of ions heavier than 20Ne. Furthermore,due to the different modelled endpoint, marked deviations were found between the RBE valuesassessed using the reference BWF and the IBWF for ions heavier than 2H. Finally, the IBWF wasunchangingly applied to calculate RBE values by processing lineal energy density distributionsexperimentally measured with eight different microdosimeters in 19 1H and 12C beams at tendifferent facilities (eight clinical and two research ones). Despite the differences between thedetectors, irradiation facilities, beam profiles (pristine or spread out Bragg peak), maximum beamenergy, beam delivery (passive or active scanning), energy degradation system (water, PMMA,polyamide or low-density polyethylene), the obtained IBWF-based RBE trends were found to be ingood agreement with the corresponding ones in case of computer-simulated microdosimetricspectra (average relative deviation equal to 0.8% and 5.7% for 1H and 12C ions respectively).