Scaling Accuracy

Scaling accuracy is the degree to which a dietary-assessment method produces nutrient estimates that scale linearly and correctly with portion size. The assumption — often unexamined — is that doubling a portion doubles the calories, halving the portion halves them, and so on. The assumption is usable but not exact, and where it breaks down it breaks in directions that matter for accuracy claims.

Where linear scaling holds

For homogeneous foods — fluids, well-mixed granular items, uniform bulk ingredients — per-gram nutrient figures scale cleanly. Two grams of olive oil have precisely twice the calories of one gram. Twenty-five grams of cooked rice have five times the calories of five grams. For these foods the per-gram figure is a sufficient and accurate parameter.

Where it breaks

Four classes of food violate linear scaling in ways worth naming:

• Items with differentiated surface and interior. A roasted potato has a crust (high-temperature-cooked, lower moisture, higher per-gram calorie density) and an interior (lower-temperature-cooked, higher moisture, lower density). A small potato has a higher surface-to-volume ratio and therefore a higher average calorie density per gram than a large potato. Scaling a "medium potato" entry proportionally to weight overestimates small potatoes and underestimates large ones.
• Items baked in discrete forms. Pizzas, cakes, breads — the edge slices differ from the interior slices in crust proportion. A per-slice figure derived by dividing a whole-pizza total by the number of slices is correct on average but wrong for any specific slice.
• Items with optional components. A sandwich scaled up in size may have proportionally more bread and proportionally less filling, or the other way around. The linear-scaling assumption on the "ham sandwich" entry does not handle this.
• Mixed dishes where ingredient ratio varies by serving. A stew served with a ladle that randomly captures different meat-to-broth ratios across servings gives each serving a different nutrient profile. Linear scaling of a "stew" entry cannot capture the variance.

Magnitude of the non-linearity

A 2020 Journal of Food Composition and Analysis study on portion-scaling accuracy measured per-serving calorie variance across twenty replicate servings of the same stew recipe, served by the same ladle by the same cook; the coefficient of variation was 8 per cent. This is the scaling-error floor for a well-mixed composite dish even when the underlying recipe is known exactly. For less-homogeneous dishes, the variance is larger.

Implications for tracking

Consumer tracking apps handle scaling primarily at the per-gram level — the database entry reports per-gram figures, the user enters the gram weight, the calorie estimate is the product. This is the most defensible scaling convention because it normalises out the discrete-item variability. Apps that allow logging by "item" (one medium apple, one large slice of pizza) inherit the per-item approximation and the accompanying non-linear scaling error.

Users who care about per-meal accuracy should prefer weight-based entry over item-based. A "large pizza slice" at the one-item level may be 250 or 350 kcal depending on slice geometry; weighed and logged at 105 g against a "pizza, pepperoni" per-gram entry it is a tighter number.