Initial susceptibility is frequently used as a palaeoclimatic indicator in sediments, but its grain size dependence is not well established. We measured initial magnetic susceptibility chi(0) in grown and natural magnetite crystals ranging from 0.09 mu m to 6 mm in grain size. Over these five decades of grain diameter, the presented initial susceptibilities are essentially independent of grain size with a mean value of 3.1 SI and a standard deviation of +/-0.4 SI. Numerical results of micromagnetic calculations for cylindrical particles in the size range 0.06 mu m < d < 0.120 mu m agree well with the experimental data. Initial susceptibilities of grown synthetic and natural magnetite crystals larger than 80 mu m can be explained with demagnetizing factors N approximate to 1/3 and large intrinsic susceptibility (chi(i) > 200) using the relation chi(0) = chi(i)(1 + N chi(i)) The observed number of magnetic domains in magnetite grains between 50 mu m and 1000 mu m is too low for the required demagnetizing factor of about 0.33. In a lamellar domain model one needs a higher number of domains than those observed, to obtain a demagnetizing factor of 0.33. A simple lamellar stripe domain model without closure domains is therefore not a good approximation for large magnetite grains. Remanent coercive force of grown magnetite grains shows a weak dependence on grain diameter. The remanent coercive force H-cr decreases gradually from about 35 mT to 10 mT between 0.09 mu m and 6 mm. A noticeable drop in H-cr occurs at a grain size of about 110 mu m, which is interpreted as the transition from pseudo-single-domain to multidomain grains. The remanent coercive force of magnetite grains is not a sensitive indicator of grain size, unlike coercive force or saturation remanent magnetization.