A new formula for the fast fission factor is derived, which takes proper account to fast capture. The fission neutron spectrum is divided into two groups with constant fission cross section in one group and zero fission cross section in the other. The average total, elastic, inelastic and capture cross sections in the two groups are calculated. Different assumptions regarding anisotropic and inelastic scattering are investigated. The effects of backscattering from the moderator and fast fission in neighbouring fuel elements are pointed out. Formulas for the fast fission ratio and for the fast conversion ratio are derived. The calculated fast fission ratios are compared with experimental values. Curves are given for the fast fission factor in uranium metal and uranium oxide.