The neutron detection efficiency of a DEMON detector, averaged over the whole volume, was calculated using GEANT and applied to determine neutron multiplicities in an intermediate heavy ion reaction. When a neutron source is set at a distance of about 1m from the front surface of the detector, the average efficiency, ϵav, is found to be significantly lower (20–30%) than the efficiency measured at the center of the detector, ϵ0. In the GEANT simulation the ratio R=ϵav/ϵ0 was calculated as a function of neutron energy. The experimental central efficiency multiplied by R was then used to determine the average efficiency. The results were applied to a study of the 64Zn+112Sn reaction at 40 A MeV which employed 16 DEMON detectors. The neutron multiplicity was extracted using a moving source fit. The derived multiplicities are compared well with those determined using the neutron ball in the NIMROD detector array in a separate experiment. Both are in good agreement with multiplicities predicted by a transport model calculation using an antisymmetric molecular dynamics (AMD) model code.