We derive a first order linear differential equation describ ing the shape of the probability density function of magnetic field strengths in the quiet Sun (PDF). The modeli ng is very schematic. It considers convective motions which continuously supply and withdraw magnetic structures. In addition, a magnetic amplification mechanism increases the field strength up to a threshold that cannot be exceeded. These three basic ingredi- ents provide PDFs in good agreement with the PDFs produced by realistic numerical simulations of magneto convection, as well as with quiet Sun PDFs inferred from observations. In particular, the distribution is approx- imately lognormal, and it produces an excess of magnetic fiel ds (i.e., a hump in the distribution) right before the maximum field strength. The success of this simple model m ay indicate that only a few basic ingredients shape the quiet Sun PDF. Our approach provides a concise parametric representation of the PDF, as required to develop automatic methods of diagnostics. Subject headings: convection - Sun: magnetic fields - Sun: photosphere