The importance of fast neutron fission (i.e., fission caused by neutrons before being slowed down) was recognized by Szilard, and calculations similar to the present one have already been carried out by him, Feld, Ashkin, Wheeler, Wigner and others. The purpose of the present paper is to give a general formula for the contribution of fast fission to the multiplication constant, which will include all the cases already considered and will be applicable to more complicated geometries than those considered by the previous writers.