Reimagining Archimedes: An innovative and accurate calculation of volumes and asserting another standard method for defining the surface area of quail and any avian eggs

Egg-related research promises unique opportunities for food science and technology. There is an urgent need to develop non-destructive methodologies for defining key egg parameters, e.g., egg volume (V) and surface area (S), based only on egg images. Herewith, V can be measured using the Archimedes’ principle (i.e., dipping in water), while S can be inferred using formulae that include V as one of its variables. Although the Archimedes’ principle is the best approach for determining V, dipping an egg into water cannot be practicable. In this study, we derived the appropriate mathematical approaches to calculate V and S based on measurements of quail eggs’ linear parameters. The proposed calculation formulae are suitable for eggs of any shape and species. This innovative procedure can be employed as the basis of the most accurate of all existing methods for computing S and is suitable for both analytical and industrial measurements of V.