For the study, researchers with the Max Planck Institute for Human Development in Berlin visited 305 German families that included at least one child between the ages of 6 and 12. Each child’s body mass index was calculated, and the parent who planned and provided most family meals — usually, but not always, the mother — completed a simple computer quiz. The parents were asked to estimate the sugar content in various foods and beverages; these included orange juice, yogurt, pizza and ketchup, all of which are common in the diets of young children. To help the parents visualize sugar volumes, they were told to think in terms of sugar cubes and that each cube contains roughly 3 grams of sugar.

About three-quarters of the parents underestimated the total amount of sugar in the foods — in some cases radically, with the biggest divergences happening around foods commonly seen as “healthful.” More than 90 percent of the study participants underestimated the sugar in yogurt, for instance, by an average of seven cubes, or about 60 percent of the total sugar in each serving. More concerning, these misjudgments turned out to be related to children’s body weights: Those with the highest B.M.I.s tended to have parents with the largest underestimates.