MicroRNAs (miRNAs) act within Argonaute proteins to guide repression of messenger RNA targets. Although various approaches have provided insight into target recognition, the sparsity of miRNA-target affinity measurements has limited understanding and prediction of targeting efficacy. Here, we adapted RNA bind-n-seq to enable measurement of relative binding affinities between Argonaute-miRNA complexes and all sequences ≤12 nucleotides in length. This approach revealed noncanonical target sites specific to each miRNA, miRNA-specific differences in canonical target-site affinities, and a 100-fold impact of dinucleotides flanking each site. These data enabled construction of a biochemical model of miRNA-mediated repression, which was extended to all miRNA sequences using a convolutional neural network. This model substantially improved prediction of cellular repression, thereby providing a biochemical basis for quantitatively integrating miRNAs into gene-regulatory networks.