AbstractCorrected formulae for the total energy distribution, the emission current density, and the inversion temperature are derived under the condition that the field‐electron emission takes place from a free‐electron metal. The corrections relate to the series truncation approximating the WKB phase integral inherent in the analytic approximation of the electron tunneling probability. The assumed approximation for the phase integral takes into account not only the zero and first order terms, present in the existing theory, but also the quadratic term. The expression for the total energy distribution, obtained on this basis, is in typical circumstances valid for field emission in the electron energy range of |ε| ≦ 1.5 eV with respect to the Fermi energy. The accuracy of the approximations used is also dis