Real-time amplification and quantification of specific nucleic acid sequences plays a major role in medical and biotechnological applications. In the case of infectious diseases, such as HIV, quantification of the pathogen-load in patient specimens is critical to assess disease progression and effectiveness of drug therapy. Typically, nucleic acid quantification requires expensive instruments, such as real-time PCR machines, which are not appropriate for on-site use and for low-resource settings. This paper describes a simple, low-cost, reaction-diffusion based method for end-point quantification of target nucleic acids undergoing enzymatic amplification. The number of target molecules is inferred from the position of the reaction-diffusion front, analogous to reading temperature in a mercury thermometer. The method was tested for HIV viral load monitoring and performed on par with conventional benchtop methods. The proposed method is suitable for nucleic acid quantification at point of care, compatible with multiplexing and high-throughput processing, and can function instrument-free.