Micromagnetic simulations of the ground state magnetization patterns of rectangular gadolinium thin film elements were performed and the effects of aspect ratio, size, and thickness of the island on net long axis moment were investigated. Highly remanent states were found in 15 nm thick gadolinium islands with high aspect ratios, 8:1 or greater, as well as in smaller islands with aspect ratios down to 5:1. The thickness of the island was also critical for the ability of a gadolinium island to maintain a highly remanent ground state; islands with thickness greater than or equal to 30 nm showed increased multidomain formation. These results provide information and guidance on what dimensions are suitable for fabrication of single-domain gadolinium nanostructures – a feat not yet achieved in literature. The proposed dimensions most suitable for experimental realisation of a single domain gadolinium element are 500nm×50nm×15nm500nm×50nm×15nm, lying within the range found in this investigation to be energetically favoured single domains.