Surfactant film rigidity is a ubiquitous general concept that is quantified in two different units. We show here how to convert the bending rigidity from reduced units of a virtual infinitely thin film (not made of molecules) into the chemical unit (kJ.mol-1) of a realistic film of monomolecular thickness. In most cases molecular lengths are not negligible versus curvature radius. Two bending constants for the elasticity of thin-shelled solids can be defined, as introduced by Gauss, whereas only one physical bending constant taking into account that the film cannot be teared has been introduced in the nineties by Hyde and Ninham. The explicit conversion depends on the topology and is different in the quasi-planar approximation, as well as the “direct” o/w or “reverse” w/o case of spherical or cylindrical micelles. We show some examples for classical and nonclassical micelles and microemulsions of different topologies in (H,N coordinates).