Density functional theory calculations are performed to study the out-of-plane polarisation in BaTiO3 (BTO) thin films epitaxially grown on platinum. Prior to any polarisation calculation, the stability of the Pt(001)/BaTiO3(001) structure is thoroughly discussed. In particular, the nature of the Pt/BTO and BTO/vacuum interfaces is characterised. The growth of BTO is shown to start with a TiO2 layer while the nature of the surface termination does not broadly modify the stability. Therefore both upper terminations are considered when describing the ferroelectric behaviour in Pt/BTO interfaces. The geometric and electronic effects of the substrate on the polarisation are investigated. To isolate the electronic influence of platinum, the out-of-plane polarisation in Pt/BTO systems is compared to the one in isolated BTO slabs constrained to the same lattice mismatch induced by the epitaxial growth on platinum. The ferroelectric phase is favoured as soon as the thickness is larger than 23 Å, both for isolated and deposited BTO, for the smallest width. The Pt substrate will modify the size of polarisation domains, while an upper BaO layer through the use of asymmetric [TiO2/BaO] systems will induce an increase of the polarisation. One could take advantage of this experimentally.