A new approach to quantify hydrogen bond strengths based on interaction coordinates (HBSBIC) is proposed and is very promising. In this research, it is assumed that the projected force field of the fictitious three atoms fragment (DHA) where D is the proton donor and A is the proton acceptor from the full molecular force field of the H-bonded complex characterizes the hydrogen bond. The "interaction coordinate (IC)" derived from the internal compliance matrix elements of this three-atom fragment measures how the DH covalent bond (its electron density) responds to constrained optimization when the HA hydrogen bond is stretched by a known amount (its electron density is perturbed by a specified amount). This response of the DH bond, based on how the IC depends on the electron density along the HA bond, is a measure of the hydrogen bond strength. The inter- and intramolecular hydrogen bond strengths for a variety of chemical and biological systems are reported. When defined and evaluated using the IC approach, the HBSBIC index leads to satisfactory results. Because this involves only a three-atom fragment for each hydrogen bond, the approach should open up new directions in the study of "appropriate small fragments" in large biomolecules.