Almost all RNAs can fold to form extensive base-paired secondary structures. Many of these structures then modulate numerous fundamental elements of gene expression. Deducing these structure-function relationships requires that it be possible to predict RNA secondary structures accurately. However, RNA secondary structure prediction for large RNAs, such that a single predicted structure for a single sequence reliably represents the correct structure, has remained an unsolved problem. Here, we demonstrate that quantitative, nucleotide-resolution information from a SHAPE experiment can be interpreted as a pseudo-free energy change term and used to determine RNA secondary structure with high accuracy. Free energy minimization, by using SHAPE pseudo-free energies, in conjunction with nearest neighbor parameters, predicts the secondary structure of deproteinized Escherichia coli 16S rRNA (>1,300 nt) and a set of smaller RNAs (75-155 nt) with accuracies of up to 96-100%, which are comparable to the best accuracies achievable by comparative sequence analysis.