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We present metallicity dependent transformation equations between UBV andSDSS ugr colours for red giants with synthetic data. The ranges of the coloursused for the transformations are 0.400 $\leq(B-V)_{0}\leq$ 1.460, -0.085$\leq(U- B)_{0}\leq$ 1.868, 0.291$\leq(g-r)_{0}\leq$ 1.326, and 1.030$\leq(u -g)_{0}\leq$ 3.316 mag, and cover almost all the observational colours of redgiants. We applied the transformation equations to six clusters with differentmetallicities and compared the resulting $(u - g)_{0}$ colours with the onesestimated by the calibration of the fiducial sequences of the clusters. Themean and standard deviation of the residuals for all clusters are $<\Delta(u -g)_0> =$-0.01 and $\sigma(u - g)_{0} =$0.07 mag, respectively. We showed thatinterstellar reddening plays an important role on the derived colours. Thetransformations can be applied to clusters as well as to field stars. They canbe used to extend the colour range of the red giants in the clusters which arerestricted due to the saturation of SDSS data.

Metallicity Dependent Transformations for Red Giants with Synthetic Colours of UBV and ugr