  The three Advanced Virgo and LIGO gravitational wave detectors participated
to the third observing run (O3) between 1 April 2019 15:00 UTC and 27 March
2020 17:00 UTC,leading to several gravitational wave detections per month. This
paper describes the Advanced Virgo detector calibration and the reconstruction
of the detector strain $h(t)$ during O3, as well as the estimation of the
associated uncertainties. For the first time, the photon calibration technique
as been used as reference for Virgo calibration, which allowed to
cross-calibrate the strain amplitude of the Virgo and LIGO detectors. The
previous reference, so-called free swinging Michelson technique, has still been
used but as an independent cross-check. $h(t)$ reconstruction and noise
subtraction were processed online, with good enough quality to prevent the need
for offline reprocessing, except for the two last weeks of September 2019. The
uncertainties for the reconstructed $h(t)$ strain, estimated in this paper in a
20-2000~Hz frequency band, are frequency independent: 5% in amplitude, 35 mrad
in phase and 10 $\mu$s in timing, with the exception of larger uncertainties
around 50 Hz.
