Whereas the Mohr-Coulomb criterion is widely used in geotechnics, the Drucker-Prager is common in Finite Element Methods software. Another smooth criterion developed in soil mechanics is the Matsuoka-Nakai criterion, which is also a linear function of mean stress. Parameters of the Coulomb criterion are meaningful to engineers and their determination in laboratory is well known. In this paper, we present a method to measure differences between Mohr-Coulomb and "Coulomb" fitting by Drucker-Prager or Matsuoka Nakai. Using some properties of the stress space and of the deviatoric plane, we are able to measure discrepancies between Coulomb and other criteria. We provides results as discrepancies on the friction angle allowing a quick evaluation of the error.