  The Baade-Wesselink method allows us to estimate distances to individual
pulsating stars. Accurate geometric parallaxes obtained by the Gaia mission
serve us in the calibration of the method and in the determination of its
precision. The method also provides a way of determining mean radii of
pulsating stars. The main aim of this work is to determine the scatter and
possible dependence of p- factors of RR Lyrae stars on their pulsation periods.
The secondary objective is to determine mean radius - period relations for
these stars. Our calibrations for RR Lyrae stars are based on photometric data
gathered at the Cerro Murphy Observatory. We obtained spectroscopic data
specifically for this project using high resolution spectrographs. We use the
Infrared Surface Brightness (IRSB) version of the method that relies on a
surface brightness - color relation dependent on the (V-K) color. We obtain the
spread of p- factors of around 0.07-0.08 for our sample of 9 RR Lyrae stars
from the solar neighborhood. However, we also find relations between the
p-factor and the pulsation period for RRab stars with the rms scatter around
the relation of around 0.05, but with relatively large uncertainty of
relations' parameters. We present relations between the mean radius and period
for RR Lyrae pulsating in the fundamental mode with the rms scatter around the
relation of $0.012R_{\odot}$. We observe a clear offset between p- factors
obtained using the IRSB technique (with mean p between 1.39 and 1.45) and
values inferred by Bras et al. (2024) using the SPIPS tool (M\'erand et al.
2015). On the other hand, we obtain a similar scatter of p of as observed by
Bras et al. (2024). Our period-radius relations are in a good agreement with
both the inference of Bras et al. (2024) based on SPIPS and theoretical
predictions of Marconi et al. (2005, 2015)
