MicroRNAs (miRNAs) suppress gene expression by forming a duplex with a target messenger RNA (mRNA), blocking translation or initiating cleavage. Computational approaches have proven valuable for predicting which mRNAs can be targeted by a given miRNA, but currently available prediction methods do not address the extent of duplex formation under physiological conditions. Some miRNAs can at low concentrations bind to target mRNAs, whereas others are unlikely to bind within a physiologically relevant concentration range. Here we present a novel approach in which we find potential target sites on mRNA that minimize the calculated free energy of duplex formation, compute the free energy change involved in unfolding these sites, and use these energies to estimate the extent of duplex formation at specified initial concentrations of both species. We compare our predictions to experimentally confirmed miRNA-mRNA interactions (and non-interactions) in Drosophila melanogaster and in human. Although our method does not predict whether the targeted mRNA is degraded and/or its translation to protein inhibited, our quantitative estimates generally track experimentally supported results, indicating that this approach can be used to predict whether an interaction occurs at specified concentrations. Our approach offers a more-quantitative understanding of post-translational regulation in different cell types, tissues, and developmental conditions.