In-plane cohesive failure of paperboard was characterized by short-span uniaxial tension tests. Six paperboards’ qualities were experimentally investigated, from which cohesive stress-widening curves were extracted. A fracture energy was defined, expressed in the tensile strength and maximum slope of the cohesive stress-widening relation. Analytical cohesive relations were derived based on the tensile strength and maximum slope, utilizing the Morse potential for diatomic molecules. It was experimentally found that the maximum slope and fracture energy depend on the tensile strength. The ratio of the maximum slope to the elastic modulus (stable length) was shown to be independent of the tensile strength.