  The first Gaia data release unlocked the access to the photometric
information of 1.1 billion sources in the $G$-band. Yet, given the high level
of degeneracy between extinction and spectral energy distribution for large
passbands such as the Gaia $G$-band, a correction for the interstellar
reddening is needed in order to exploit Gaia data. The purpose of this
manuscript is to provide the empirical estimation of the Gaia $G$-band
extinction coefficient $k_G$ for both the red giants and main sequence stars,
in order to be able to exploit the first data release DR1. We selected two
samples of single stars: one for the red giants and one for the main sequence.
Both samples are the result of a cross-match between Gaia DR1 and 2MASS
catalogues; they consist of high quality photometry in the $G$-, $J$- and
$Ks$-bands. These samples were complemented by temperature and metallicity
information retrieved from, respectively, APOGEE DR13 and LAMOST DR2 surveys.
We implemented a Markov Chain Monte Carlo method where we used $(G-Ks)_0$ vs
$T_\mathrm{eff}$ and $(J-Ks)_0$ vs $(G-Ks)_0$ calibration relations to estimate
the extinction coefficient $k_G$ and we quantify its corresponding confidence
interval via bootstrap resampling method. We tested our method on samples of
red giants and main sequence stars, finding consistent solutions. We present
here the determination of the Gaia extinction coefficient through a completely
empirical method. Furthermore we provide the scientific community a formula for
measuring the extinction coefficient as a function of stellar effective
temperature, the intrinsic colour $(G-Ks)_0$ and absorption.
