Self-assembled monolayers (SAMs) are fundamental building blocks of molecular electronics and find numerous applications in organic (opto)electronic devices. Their properties are decisively determined by their response to electric fields, which are either applied externally (e.g., when biasing devices) or originate from within the monolayer itself in case it consists of dipolar molecules (which are used to tune charge-injection barriers). This response is typically described by the dielectric constant of the monolayer. In this work it is explicitly show that there is no "general" dielectric constant that simultaneously applies to both cases. This is first derived on the basis of density-functional theory (DFT) calculations for substituted biphenyl-thiol SAMs at varying packing densities. Depolarization effects, which play a crucial role for the dielectric properties of the monolayers, are Subsequently analyzed on the basis of packing-dependent charge rearrangements. Finally, the DFT results are rationalized using all electrostatic model. In this context, the importance of finite-size effects is highlighted and a connection between the macroscopic dielectric properties and the Molecular polarizability is established providing a monolayer equivalent to the Clausius-Mossotti relationship. This allows deriving general trends for the packing-density dependent dielectric response of monolayers to both external and internal electric fields.