Wide-scope mathematical relationships have been established between the C-13-NMR of liquid polycondensation resins, such as urea-formaldehyde and phenol-formaldehyde resins, and the strength of the network formed by the same resin when hardened under well-defined conditions, the thermomechanical analysis deflection, the number average molecular mass and the number of degrees of freedom of the average polymer segment between crosslinking nodes in the hardened resin network, the resin network glass transition temperature, its solid-phase C-13-NMR proton-rotating frame spin-lattice relaxation time, and the homogeneous and heterogeneous polymer segment/polymer segment interfacial interaction energy calculated by molecular mechanics. These mathematical relationships allow the calculation of any of these parameters from any of the techniques listed, provided that all of the systems are used under well-defined conditions. Under different conditions, the values of the numerical coefficients involved change; and, whereas the equations are still valid, a different set of coefficients needs to be recalculated.