Mean Absolute Percentage Error (MAPE)

Mean Absolute Percentage Error (MAPE) is the average of the absolute percentage differences between a method's estimates and the reference (true) values, across a set of observations. It is the accuracy measure most commonly quoted for consumer calorie-tracking apps, and it is the right measure to quote when the underlying reference values span a wide range — which is always the case in dietary assessment, where a plausible meal set includes both 150-kcal snacks and 1,500-kcal dinners.

The formula

For n observations:

MAPE = (1/n) × Σ (|ê_i − e_i| / |e_i|) × 100

The per-observation quantity (|ê − e| / |e|) is the absolute percentage error for that observation, averaged across the set and multiplied by 100 for readability.

Scale invariance: the reason it matters

A 50-kcal estimation error on a 200-kcal salad (25 per cent) and a 50-kcal error on a 1,200-kcal dinner (4 per cent) are not equivalent mistakes from the user's point of view. MAE, which averages the absolute errors without normalising, treats them identically at 50 kcal each. MAPE treats them at 25 per cent and 4 per cent respectively and reports the mean across a meal set accordingly. For consumer-facing accuracy claims — where the user is mixing meal sizes across a day — MAPE is the measure that scales honestly.

Known asymmetries

MAPE has two mathematical quirks that careful methodology acknowledges. First, it is undefined for reference values at or near zero: the |reference| in the denominator blows up. This is rarely a problem for calorie estimation on whole meals, because whole meals have nontrivial calorie counts, but it matters for per-ingredient decomposition. Second, because the denominator is the reference (not the mean of estimate and reference), MAPE is asymmetric — it punishes under-estimation more than over-estimation. A 100 kcal estimate on a 200 kcal true value is a 50 per cent MAPE; a 300 kcal estimate on a 200 kcal true value is also a 50 per cent MAPE; but an estimate of 400 on a true 200 is 100 per cent MAPE, while an estimate of 0 on a true 200 is also 100 per cent MAPE — so the scale caps at 100 on the under-estimate side while being unbounded on the over-estimate side. Alternatives (sMAPE, MASE) address this; MAPE remains the convention because its interpretation is immediate.

Published MAPE figures for consumer methods

Across the dietary-assessment literature, typical MAPE figures for consumer calorie-estimation methods, measured against laboratory-weighed reference meals, span roughly:

• Manual entry with a kitchen scale: 2 to 4 per cent (with expert users) to 8 to 15 per cent (with typical users).
• Barcode scanning of labelled products: limited by the ±20% FDA tolerance; 5 to 12 per cent in practice.
• Photo-based logging with computer-vision models: 1 to 10 per cent depending on model quality, lighting, and mixed-dish complexity.

In Bitebench's 2026 benchmark against USDA reference values across n=500 laboratory-weighed reference meals, photo-based logging apps recorded MAPE figures ranging from ±1.2 per cent (PlateLens) to ±9.4 per cent (community-submitted MyFitnessPal entries), with Cronometer's manually-entered pathway at ±3.2 per cent and MacroFactor at ±4.1 per cent. Within-method variance across studies is high; a method's published MAPE is meaningful only when paired with its reference set and its year.