Although a catalogue of synthetic RGB magnitudes, providing photometric data for a sample of 1346 bright stars, has been recently published, its usefulness is still limited due to the small number of reference stars available, considering that they are distributed throughout the whole celestial sphere, and the fact that they are restricted to Johnson V < 6.6 mag. This work presents synthetic RGB magnitudes for ~15 million stars brighter than Gaia G = 18 mag, making use of a calibration between the RGB magnitudes of the reference bright star sample and the corresponding high quality photometric G, G_BP and G_RP magnitudes provided by the Gaia EDR3. The calibration has been restricted to stars exhibiting -0.5 < G_BP - G_RP < 2.0 mag, and aims to predict RGB magnitudes within an error interval of $pm 0.1$ mag. Since the reference bright star sample is dominated by nearby stars with slightly undersolar metallicity, systematic variations in the predictions are expected, as modelled with the help of stellar atmosphere models. These deviations are constrained to the $pm 0.1$ mag interval when applying the calibration only to stars scarcely affected by interstellar extinction and with metallicity compatible with the median value for the bright star sample. The large number of Gaia sources available in each region of the sky should guarantee high-quality RGB photometric calibrations.
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