Quantitative diagnostics that are rapid, inexpensive, sensitive, robust, and field-deployable are needed to contain the spread of infectious diseases and inform treatment strategies. While current gold-standard techniques are highly sensitive and quantitative, they are slow and require expensive equipment. Conversely, current rapid field-deployable assays available provide essentially binary information about the presence of the target analyte, not a quantitative measure of concentration. Here, we report the development of a molecular diagnostic test [quantitative recombinase polymerase amplification (qRPA)] that utilizes competitive amplification during a recombinase polymerase amplification (RPA) assay to provide semi-quantitative information on a target nucleic acid. We demonstrate that qRPA can quantify DNA, RNA, and viral titers in HIV and COVID-19 patient samples and that it is more robust to environmental perturbations than traditional RPA. These features make qRPA potentially useful for at-home testing to monitor the progress of viral infections or other diseases.