Quantum confinement as well as high frequency ε∞ and static εs dielectric profiles are described for nanoplatelets of halide inorganic perovskites CsPbX3 (X = I, Br, Cl) and hybrid organic-inorganic perovskites (HOP) in two-dimensional (2D) and three-dimensional (3D) structures. 3D HOP are currently being sought for their impressive photovoltaic ability. Prior to this sudden popularity, 2D HOP materials were driving intense activity in the field of optoelectronics. Such developments have been enriched by the recent ability to synthesize colloidal nanostructures of controlled size of 2D and 3D HOP. This raises the need to achieve a thorough description of the electronic structure and dielectric properties of these systems. In this work, we go beyond the abrupt dielectric interface model and reach atomic scale description. We examine the influence of the nature of the halogen and of the cation on the band structure and dielectric constants. Similarly, we survey the effect of dimensionality and shape of the perovskite. In agreement with recent experimental results, we show an increase of the band gap and a decrease of ε∞ when the size of a nanoplatelet reduces. By inspecting 2D HOP, we find that it cannot be described as a simple superposition of independent inorganic and organic layers. Finally, the dramatic impact of ionic contributions on the dielectric constant εs is analysed.