  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 show
how to combine magnetic field strength measurements based on the Zeeman effect
and the Hanle effect to estimate an unbiased 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 10^{3} 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 50%) and of the
magnetic energy (between 45% and 85%) are provided by the field strengths
larger than 500 G which, however, occupy only a small fraction of the surface
(between 1% and 10%). The fraction of kG fields in the quiet Sun is even
smaller, but they are important for a number of reasons. The kG fields still
trace a significant fraction of the total magnetic energy, they reach the high
photosphere, and they appear in unpolarized light images. The quiet Sun
photosphere has far more unsigned magnetic flux and magnetic energy than the
active regions and the network all together.
