Self-assembly is an important process by which nontrivial structures are formed on the sub-micron scales. Such processes are governed by chemical and physical principles that dictate how the molecular interactions affect the supramolecular geometry. Currently there is no general framework that links between molecular properties and the supramolecular morphology with its size parameters. Here we introduce a new paradigm for the description and analysis of supramolecular structures that self-assemble via short-range interactions. Analysis of molecular interactions determines inputs to the theory of incompatible elasticity, which provides analytic expressions for supramolecular shape and fluctuations. We derive quantitative predictions for specific amphiphiles that self-assembled into chiral nanoribbons. These are quantitatively confirmed experimentally, revealing unique shape evolution, unusual mechanics and statistics, proving that the assemblies are geometrically incompatible. The success in predicting equilibrium and statistics suggests the approach as a new framework for quantitative study of a large variety of self-assembled nanostructures.