This paper identifies uncertainties and problems in the practical application of the ICNIRP low frequency basic restriction on current density. This quantity should be averaged over a cross-section of 1 cm(2) perpendicular to the current direction. The rationale and the sensitivity of the current density average are investigated. There are difficulties in finding a square centimetre of spinal cord over which to average. The consequences of including neighbouring tissues in the averages are investigated in the male and female voxel models NORMAN and NAOMI for applied uniform electric and magnetic fields at 50 Hz. Also the case of the non-uniform magnetic field from a horizontal current carrying conductor adjacent to the back of the body is investigated. The maximum and 99th percentile current density values are compared with the 1 cm(2) average in the derivation of external field reference levels. For more information on this article, see medicalphysicsweb.org.