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We used the updated [Fe/H] abundances of 168 F-G type dwarfs and calibrated them to a third order polynomial in terms of reduced ultraviolet excess, δ 0.41 defined with ugr data in the SDSS. We estimated the M g absolute magnitudes for the same stars via the re-reduced Hipparcos parallaxes and calibrated the absolute magnitude offsets, ∆M g , relative to the intrinsic sequence of Hyades to a third order polynomial in terms of δ 0.41 . mean of the residuals and the corresponding standard deviation for the metallicity calibration are 0 and 0.137 mag; while, for the absolute magnitude calibration they are 0 and 0.179 mag, respectively. We applied our procedures to 23,414 dwarf stars in the Galactic field with the Galactic coordinates 85• and size 78 deg 2 . We estimated absolute magnitude M g dependent vertical metallicity gradients as a function of vertical distance Z. The gradients are deep in the range of 0 < Z ≤ 5 kpc, while they are very small positive numbers beyond Z = 5 kpc. All dwarfs with 5 < M g ≤ 6 mag are thin-disc stars and their distribution shows a mode at (g − r) 0 ≈ 0.38 mag, while the absolute magnitudes 4 < M g ≤ 5 are dominated by thick disc and halo stars, i.e. the apparently bright ones (g 0 ≤ 18 mag) are thick-disc stars with a mode at (g − r) 0 ∼ 0.38 mag, while the halo population is significant in the faint stars (g 0 > 18 mag).

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The transformation equations from BV R c to g r i magnitudes and vice versa for the giants were established from a sample of 80 stars collected from Soubiran et al. (2010) with confirmed surface gravity (2 ≤ log g (cm s−2 ) ≤ 3) at effective temperatures 4000 < T e f f (K) < 16000. The photometric observations, all sample stars at g r i and 65 of them at BV R c , were obtained at TÜBİTAK National Observatory (TUG) 1m (T100) telescope, on the Taurus Mountains in Turkey. The M V absolute magnitudes of the giant stars were estimated from the absolute magnitude-temperature data for the giant stars by Sung et al. (2013) using the T e f f from the intrinsic colours considered in this study. The transformation equations could be considered to be valid through the ranges of the following magnitudes and colours involved: 7.10 < V 0 < 14.50, 7.30 < g 0 < 14.85, −0.20

We derive transformation equations between GALEX and UBV colours by using the reliable data of 556 stars. We present two sets of equations: as a function of (only) luminosity class and as a function of both luminosity class and metallicity. The metallicities are provided from the literature, while the luminosity classes are determined by using the PARSEC mass tracks in this study. Small colour residuals and high squared correlation coefficients promise accurate derived colours. The application of the transformation equations to 70 stars with reliable data shows that the metallicity plays an important role in estimation of more accurate colours.