Hydrogen bond (HB) is an essential interaction in countless phenomena, and regulates the chemistry of life. HBs are characterized by two main features, strength and directionality, with a high degree of heterogeneity across different chemical groups. These characteristics are dependent on the electronic configuration of the atoms involved in the interaction, which, in turn, is influenced strongly by the molecular environment where they are found. Studies based on the analysis of HB in solid phase, such as X-ray crystallography, suffer from significant biases due to the packing forces. These will tend to better describe strong HBs at the expenses of weak ones, which are either distorted or under represented. Using quantum mechanics (QM), we calculated interaction energies for about a hundred acceptor and donors, in a rigorously defined set of geometries. We performed about 180,000 independent QM calculations, covering all relevant angular components, and mapping strength and directionality in a context free from external biases, with both single-site and cooperative HBs. We show that by quantifying directionality, there is not correlation with strength, and therefore these two components need to be addressed separately. Results demonstrate that there are very strong HB acceptors (e.g.,DMSO) with nearly isotropic interactions, and weak ones (e.g.,thioacetone) with a sharp directional profile. Similarly, groups can have comparable directional propensity, but be very distant in the strength spectrum (e.g., thioacetone and pyridine). These findings have implications for biophysics and molecular recognition, providing new insight for chemical biology, protein engineering, and drug design. The results require rethinking the way directionality is described, with implications for the thermodynamics of HB.