The quiet Sun photospheric plasma has a variety of magnetic field strengths going from zero to 1800 G. The empirical characterization of these field strengths requires a probability density function (PDF), i.e., a function P(B) describing the fraction of quiet Sun occupied by each field strength B. We present a method to combine magnetic field strength measurements based on the Zeeman effect and the Hanle effect in order to estimate the true P(B). The application of the method to real observations renders a set of possible PDFs, which outline the general characteristics of the quiet Sun magnetic fields. Their most probable field strength differs from zero. The magnetic energy density is a significant fraction of the kinetic energy of the granular motions at the base of the photosphere (larger than 15 or larger than 2×103 erg cm-3). The unsigned flux density (or mean magnetic field strength) has to be between 130 G and 190 G. A significant part of the unsigned flux (between 10% and 40%) and of the magnetic energy (between 40% and 80%) are provided by the field strengths larger than 1 kG which, however, occupy only a small fraction of the surface (between 1% and 4%). The quiet Sun photosphere has far more unsigned magnetic flux and magnetic energy than the active regions and the network together.