A Two-Parameter Geometric Model for Volume Estimation and Grade Classification of ISA Brown Eggs

Commercial egg grading remains anchored to weight-based thresholds, a single metric that incompletely represents internal composition and is automated only through industrial graders too costly for small and medium-sized enterprises. Existing parametric egg models treat volume in isolation from grading and rely on parameters that are difficult to extract from simple measurements. We propose a two-parameter geometric framework adapting Smart’s parametric egg profile to the ISA Brown breed, in which the egg asymmetry is encoded through a single dimensionless shape parameter and the volume is obtained in closed form as a solid of revolution from only the maximum length and maximum width. The model is validated on 120 ISA Brown eggs against fluid-displacement ground truth, attaining a Pearson correlation of 0.894 and a mean absolute percentage error of 6.02%; a single closed-form correction factor, derived from the model’s own b2-dependence, reduces the error to 3.09%, below that of an empirically fitted formula. A closed-form linear discriminant on the same two measurements recovers the commercial grade with 92.0% cross-validated accuracy, and the product H·W2 alone classifies 93.3% by a single arithmetic rule. The shape parameter and whole-egg density are essentially invariant across grades, establishing a geometric self-similarity that reduces the framework to breed-level constants.