Abstract : The calculation of the current in an electron gun structure is one of the main investigations involved in the electron gun physics understanding. In particular, various simulation codes exist but often present some important discrepancies with experiments. Moreover, those differences cannot be reduced because of the lack of physical information in these codes. We present a simple physical three-dimensional model, valid for all kinds of gun geometries. This model presents a better precision than all the other simulation codes and models encountered and allows the real understanding of the electron gun physics. It is based only on the calculation of the Laplace electric field at the cathode, the use of the classical Child-Langmuir's current density, and a geometrical correction to this law. Finally, the intensity versus voltage characteristic curve can be precisely described with only a few physical parameters. Indeed, we have showed that only the shape of the electric field at the cathode without beam, and a distance of an equivalent infinite planar diode gap, govern mainly the electron gun current generation.