A new method for calculating paramagnetic susceptibilities from nuclear electromagnetic shieldings is outlined. A distributed origin gauge with origins at nuclei has been used. The quantum mechanical constraints for gauge invariance and charge-current conservation have been written in terms of nuclear shieldings. An extended numerical test on first- and second-row hydrides has been carried out. For a given basis set larger than double zeta the computed paramagnetic susceptibilities are more accurate than those obtained via conventional direct calculations. The results for the largest basis sets are in excellent agreement with near Hartree-Fock paramagnetic susceptibilities from other sources and with available experimental values. It has also been found that polarised 6-31G basis sets provide near Hartree-Fock paramagnetic susceptibilities for the second-row hydrides and satisfy the conservation conditions to high extent.