  The projection factor (p-factor) is an essential component of the classical
Baade-Wesselink (BW) technique, that is commonly used to determine the
distances to pulsating stars. It is a multiplicative parameter used to convert
radial velocities into pulsational velocities. As the BW distances are linearly
proportional to the p-factor, its accurate calibration for Cepheids is of
critical importance for the reliability of their distance scale. We focus on
the observational determination of the p-factor of the long-period Cepheid RS
Pup (P = 41.5 days). This star is particularly important as this is one of the
brightest Cepheids in the Galaxy and an analog of the Cepheids used to
determine extragalactic distances. An accurate distance of 1910 +/- 80 pc (+/-
4.2%) has recently been determined for RS Pup using the light echoes
propagating in its circumstellar nebula. We combine this distance with new
VLTI/PIONIER interferometric angular diameters, photometry and radial
velocities to derive the p-factor of RS Pup using the code
Spectro-Photo-Interferometry of Pulsating Stars (SPIPS). We obtain p = 1.250
+/- 0.064 (+/-5.1%), defined for cross-correlation radial velocities. Together
with measurements from the literature, the p-factor of RS Pup confirms the good
agreement of a constant p = 1.293 +/- 0.039 (+/-3.0%) model with the
observations. We conclude that the p-factor of Cepheids is constant or mildly
variable over a broad range of periods (3.7 to 41.5 days).
