  Context. Gaia is an ESA cornerstone mission launched on 19 December 2013
aiming to obtain the most complete and precise 3D map of our Galaxy by
observing more than one billion sources. This paper is part of a series of
documents explaining the data processing and its results for Gaia Data Release
1, focussing on the G band photometry. Aims. This paper describes the
calibration model of the Gaia photometric passband for Gaia Data Release 1.
Methods. The overall principle of splitting the process into internal and
external calibrations is outlined. In the internal calibration, a
self-consistent photometric system is generated. Then, the external calibration
provides the link to the absolute photometric flux scales. Results. The Gaia
photometric calibration pipeline explained here was applied to the first data
release with good results. Details are given of the various calibration
elements including the mathematical formulation of the models used and of the
extraction and preparation of the required input parameters (e.g. colour
terms). The external calibration in this first release provides the absolute
zero point and photometric transformations from the Gaia G passband to other
common photometric systems. Conclusions. This paper describes the photometric
calibration implemented for the first Gaia data release and the instrumental
effects taken into account. For this first release no aperture losses,
radiation damage, and other second-order effects have not yet been implemented
in the calibration.
