DNA stores our genetic information and is ubiquitous in applications, where it interacts with binding partners ranging from small molecules to large macromolecular complexes. Binding is modulated by mechanical strains in the molecule and can change local DNA structure. Frequently, DNA occurs in closed topological forms where topology and supercoiling add a global constraint to the interplay of binding-induced deformations and strain-modulated binding. Here, we present a quantitative model with a straight-forward numerical implementation of how the global constraints introduced by DNA topology modulate binding. We focus on fluorescent intercalators, which unwind DNA and enable direct quantification via fluorescence detection. Our model correctly describes bulk experiments using plasmids with different starting topologies, different intercalators, and over a broad range of intercalator and DNA concentrations. We demonstrate and quantitatively model supercoiling-dependent binding in a single-molecule assay, where we directly observe the different intercalator densities going from supercoiled to nicked DNA. The single-molecule assay provides direct access to binding kinetics and DNA supercoil dynamics. Our model has broad implications for the detection and quantification of DNA, including the use of psoralen for UV-induced DNA crosslinking to quantify torsional tension in vivo, and for the modulation of DNA binding in cellular contexts.