The demagnetization ‘constant’, N, enters into all theoretical considerations of multidomain remanence. Although most workers believe N to be related simply to the shape of the grain, no theoretical study of N has previously been completed. It is shown in this paper that N monotonically increases with increase in remanence in multidomain grains. Although N can be approximated by a constant in the limit of small displacements of domain walls from their demagnetized sites, this constant critically depends on the domain geometry.