Context. The Baade-Wesselink (BW) method, also known as the pulsation parallax 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. This method also provides a way of determining mean radii of pulsating stars. Aims. 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 the mean radius-period relations for these stars. Methods. Our calibrations for RR Lyrae stars are based on photometric data gathered at the Cerro Murphy Observatory and parallaxes from the Data Release 3 of the Gaia space mission. We obtained spectroscopic data specifically for this project using high-resolution spectrographs. We used the infrared surface brightness (IRSB) version of the method that relies on a surface brightness-color relation that is dependent on the ( V − K ) color. It allows us to estimate stellar angular diameters, while tracing variations of the stellar radius using measurements of the stellar radial velocity obtained from spectroscopy. We present results based on four different empirical surface brightness-color relations, with three relations for dwarfs and subgiants and one for classical Cepheids. Results. We present our calibration of projection factors and determination of the mean radii for nine Galactic RR Lyrae stars. We obtained a spread of p -factors of around 0.07–0.08 for our sample of RR Lyrae stars from the solar neighborhood. However, depending on a given SBCR, we also found relations between the p -factor and the pulsation period for RRab stars with a root mean square (rms) scatter around the relation of around 0.05, but with relatively large uncertainty on the relation parameters. We also present relations between the mean radius and period for RR Lyrae pulsating in the fundamental mode with an rms scatter around the relation of 0.012 R ⊙ . We observe a clear offset between p -factors obtained using the IRSB technique (with a mean p value between 1.39 and 1.45) and values inferred using the SPIPS tool. This confirms that different implementations of the BW method are sensitive to various components of the p -factor. On the other hand, we obtain a similar scatter for p , as observed in a previous study based on the SPIPS tool. Our period-radius relations are in a good agreement with both the inference based on SPIPS and theoretical predictions.