Water under soft nanoconfinement features physical and chemical properties fundamentally different from bulk water; yet, the multitude and specificity of confining systems and geometries mask any of its potentially universal traits. Here, we advance in this quest by resorting to lipidic mesophases as an ideal nanoconfinement system, allowing inspecting the behavior of water under systematic changes in the topological and geometrical properties of the confining medium, without altering the chemical nature of the interfaces. By combining Terahertz absorption spectroscopy experiments and molecular dynamics simulations, we unveil the presence of universal laws governing the physics of nanoconfined water, recapitulating the data collected at varying levels of hydration and nanoconfinement topologies. This geometry-independent universality is evidenced by the existence of master curves characterizing both the structure and dynamics of simulated water as a function of the distance from the lipid-water interface. Based on our theoretical findings, we predict a parameter-free law describing the amount of interfacial water against the structural dimension of the system (i.e., the lattice parameter), which captures both the experimental and numerical results within the same curve, without any fitting. Our results offer insight into the fundamental physics of water under soft nanoconfinement and provide a practical tool for accurately estimating the amount of nonbulk water based on structural experimental data.