Recipe scaling is straightforward mathematically — multiply every ingredient by the ratio of desired to original servings — but the science of cooking reveals why this linear approach fails for many ingredients and techniques. Leavening agents (baking powder, baking soda, yeast) cannot be scaled linearly: doubling a cake recipe requires only 1.5-1.75x the leavening, not 2x, because doubling leavening can cause baked goods to over-rise and then collapse. Spices and seasonings generally scale more conservatively than 1:1 because volatile aromatic compounds intensify disproportionately in concentration. Experienced bakers know these adjustments intuitively; recipe scaling calculators provide the starting math while noting where judgment is required.

Cooking time does not scale with batch size. A roast that takes 3 hours for 3 pounds doesn't take 6 hours for 6 pounds — it takes approximately 4.5-5 hours, because cooking time is determined by the distance heat must penetrate to the center, which scales with volume's cube root rather than linearly. The same principle applies to cake layers, bread loaves, and any other item where internal temperature must be reached. Surface-to-volume ratio decreases as size increases, slowing heat transfer. This is why doubling a recipe in the same pan (rather than two separate pans) typically under-bakes the center while over-browning the exterior.

Restaurant scaling operates on principles fundamentally different from home cooking. Professional kitchens use standardized recipes expressed in weights (not volumes) because weight measurements are more precise and scale exactly — one cup of flour can vary by 30-50 grams depending on packing, while 120 grams is always 120 grams. The transition from volume to weight recipes is itself a form of scaling up: professional recipe scaling begins with converting to weight measurements. For large-scale production (catering, food manufacturing), batch size also affects emulsification, heat distribution in commercial ovens, and mixing dynamics in ways that require empirical testing, not just arithmetic.

The square-cube law underlying cooking scaling has historical engineering applications. Galileo first described it in 1638: as an object's size doubles, its surface area quadruples (square) but its volume octuples (cube). This means large animals need proportionally heavier bones than small animals; large ships can carry proportionally more cargo per unit hull material than small ships; and large batches of food cook differently than small ones. Understanding this law isn't just culinary — it's fundamental to engineering, biology, and physics. Cooks who internalize the surface-to-volume relationship develop an intuition for why thin cookies crisp faster than thick ones, and why restaurant portions of braised short ribs taste more intensely flavored than a small home batch.