The Longest-Lived Bar: Soap Bar Dimensions That Maximise Washes per Gram at Fixed Mass

This study examines a practical question in everyday hygiene by explicit arithmetic from stated assumptions. At 100 g the best grippable block found, 5.6 x 5.0 x 3.4 cm, lasted 916 washes, while the thinnest admissible slab lasted 417 washes and a typical oval approximated as a 22 mm thick tablet lasted 584 washes. The best block therefore delivers 56.8% more washes than the typical tablet from the same mass of soap, at a modelled cost of 0.1 US cents per wash against 0.15 cents. Storing the typical tablet on its smallest face raised its life to 584 washes, recovering part but not all of the geometric penalty. Surface area at first use ranged from 128.1 to 161.9 square centimetres across the grid, and washes tracked initial surface area closely throughout. The proposed arrangement is as follows. The design rule that emerges is to choose the thickest, most nearly cubic block the grip constraints allow, and to store any bar on its smallest face on a draining rack. Thickness is the governing variable: doubling thickness at fixed mass roughly halves the surface-to-mass ratio in the relevant range, and washes rise accordingly. All results are derived from the accompanying simulation script, in which every assumption appears as a named, replaceable value. SIMULATED, NOT MEASURED.