Background: Recent experimental efforts of CRISPR-Cas9 systems have shown that off-target binding and cleavage are a concern for the system and that this is highly dependent on the selected guide RNA (gRNA) design. Computational predictions of off-targets have been proposed as an attractive and more feasible alternative to tedious experimental efforts. However, accurate scoring of the high number of putative off-targets plays a key role for the success of computational off-targeting assessment. Results: We present an approximate binding energy model for the Cas9-gRNA-DNA complex, which systematically combines the energy parameters obtained for RNA-RNA, DNA-DNA, and RNA-DNA duplexes. Based on this model, two novel off-target assessment methods for gRNA selection in CRISPR-Cas9 applications are introduced: CRISPRoff to assign confidence scores to predicted off-targets and CRISPRspec to measure the specificity of the gRNA. We benchmark the methods against current state-of-the-art methods and show that both are in better agreement with experimental results. Furthermore, we show significant evidence supporting the inverse relationship between the on-target cleavage efficiency and specificity of the system, in which introduced binding energies are key components. Conclusions: The impact of the binding energies provides a direction for further studies of off-targeting mechanisms. The performance of CRISPRoff and CRISPRspec enables more accurate off-target evaluation for gRNA selections, prior to any CRISPR-Cas9 genome-editing application. For given gRNA sequences or all potential gRNAs in a given target region, CRISPRoff-based off-target predictions and CRISPRspec-based specificity evaluations can be carried out through our webserver at https://rth.dk/resources/crispr/.