We present a new calibration of the Stroemgren metallicity index m1 using red giant (RG) stars in 4 globular clusters (GCs:M92,M13,NGC1851,47Tuc) with metallicity ranging from [Fe/H]=-2.2 to -0.7, marginally affected by reddening (E(B-V)<0.04) and with accurate u,v,b,y photometry.The main difference between the new metallicity-index-color (MIC) relations and similar relations available in the literature is that we adopted the u-y/v-y colors instead of the b-y.These colors present a stronger sensitivity to effective temperature, and the MIC relations show a linear slope. The difference between photometric estimates and spectroscopic measurements for RGs in M71,NGC288,NGC362,NGC6397, and NGC6752 is 0.04+/-0.03dex (sigma=0.11dex). We also apply the MIC relations to 85 field RGs with metallicity raning from [Fe/H]=-2.4 to -0.5 and accurate reddening estimates. We find that the difference between photometric estimates and spectroscopic measurements is-0.14+/-0.01dex (sig=0.17dex). We also provide two sets of MIC relations based on evolutionary models that have been transformed into the observational plane by adopting either semi-empirical or theoretical color-temperature relations. We apply the semi-empirical relations to the 9 GCs and find that the difference between photometric and spectroscopic metallicities is 0.04+/-0.03dex (sig=0.10dex).A similar agreement is found for the sample of field RGs, with a difference of -0.09+/-0.03dex (sig=0.19dex).The difference between metallicity estimates based on theoretical relations and spectroscopic measurements is -0.11+/-0.03dex (sig=0.14dex) for the 9 GGCs and -0.24+/-0.03dex (sig=0.15dex) for the field RGs. Current evidence indicates that new MIC relations provide metallicities with an intrinsic accuracy better than 0.2dex. Comment: 51 pages, 19 figures, accepted for submission to ApJ