Density functional theory based on hybrid functionals and localized atomic type basis sets is employed to calculate the exchange couplings in the layered three-dimensional compound Cu-2(OH)(3)NO3. We assign accurate values to the six different in-plane exchange couplings. Interlayer exchange interactions through hydrogen bonds are also quantified. The calculated exchange coupling constants are then employed to perform quantum Monte Carlo simulations to yield magnetic susceptibility data, which compare successfully with experiments. Our approach sets the foundations of a viable methodology to extract reliable magnetic susceptibilities from density functional data.