Protein-ligand dissociation constants, K(d), are determined precisely and down to the picomolar range from reaction-diffusion (RD) concentration profiles created by proteins diffusing through hydrogels functionalized with protein ligands. The RD process effectively amplifies the molecular-scale binding events into macroscopic patterns visible to the naked eye. The method is applicable to various protein-ligand pairs and does not require any prior knowledge about the protein structure.