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Based on photometric data of the central parts of eight globular clusters andone open cluster presented by An and his collaborators, we select redhorizontal branch (RHB) stars in the (g-r)0-g0 diagram and make a statisticalstudy of the distributions of their colors and absolute magnitudes in the SDSSugriz system. Meanwhile, absolute magnitudes in the Johnson VRI system arecalculated through the translation formulae between gri and VRI in theliterature. The calibrations of absolute magnitude as functions of metallicityand age are established by linear regressions of the data.  It is found that metallicity coefficients in these calibrations decrease,while age coefficients increase, from the blue $u$ filter to the red $z$filter. The calibration of Mi= 0.06[Fe/H]+0.040t+0.03 has the smallest scatterof 0.04 mag, and thus i is the best filter in the $ugriz$ system when RHB starsare used for distance indicators. The comparison of the MI calibration from ourdata with that from red clump stars indicates that the previous suggestion thatthe $I$ filter is better than the V filter in distance determination may not betrue because of its significant dependence on age.

The Absolute Magnitudes of Red Horizontal Branch Stars in the ugriz System