When a high-intensity laser pulse hits a solid target, its pedestal creates a preplasma. The interaction of the main laser pulse, linearly polarized, with this preplasma produces relativistic electrons. These electrons subsequently penetrate inside the target, with high atomic number, and produce bremsstrahlung emission, which constitutes an x-ray source that may be used in various applications such as radiography of high area density objects, photonuclear studies or positron production. This x-ray source is mainly defined by its photon dose, which depends upon the laser, preplasma and target characteristics. In new facilities the radioprotection layout design can be obtained by numerical simulations, which are somewhat tedious. A simple model giving the photon dose per laser energy unit is obtained by using the mean bremsstrahlung cross section of electrons interacting with the atoms of the conversion target. It is expressed versus the fraction eta(e1) of the laser energy absorbed into the forward hot electrons, their mean kinetic energy E, the photon lobe emission mean angular aperture (theta) over bar and the target characteristics, i. e. thickness, element, atomic mass and atomic number. The parameters eta(e1) , E and (theta) over bar are analysed by applying the energy and momentum flux conservation laws during the laser-plasma interaction in the relativistic regime in an underdense and overdense plasma, including the hole-boring effect. In addition, these quantities are parametrized versus the normalized laser vector potential a(0) and the preplasma scale length L-p by using a full set of numerical simulations, in the laser intensity domain 10(18)-10(21)Wcm(-2) and preplasma scale length range 0.03-400 mu m. These simulations are done in two-and three-dimensional geometry with the CALDER particle-in-cell code, which computes the laser-plasma interaction, and with the MCNP Monte Carlo code, which calculates the bremsstrahlung emission. The present model is compared with the simulations and with experimental results.