Parents hardly ever spot obesity in their children, resulting in damaging consequences for health, doctors warn.
In a study of 2,976 families in the UK, only four parents thought their child was very overweight. Medical assessments put the figure at 369.
The researchers, writing in the British Journal of General Practice, said obesity had become the new normal in society.
Experts said the study showed the "enormity" of the obesity epidemic.
Around one in five children in Year 6 is obese and a further 14% are overweight, the National Child Measurement Programme shows.
The team, from the London School of Hygiene and Tropical Medicine and the UCL Institute of Child Health, gave questionnaires to nearly 3,000 families asking if their child was obese, overweight, underweight or a healthy weight.
The results showed that nearly a third, 31%, of parents underestimated the weight of their child.
An accurate diagnosis kicked in only at the very high end of the scales.
Prof Russell Viner, from the Institute of Child Health, told the BBC News website: "Modern parents don't recognise children as obese.
"If parents don't recognise a child is obese then they're very unlikely to do anything to help their child move to a more healthy weight.
"Then it's a potential major public health crisis being stored up."
The main explanation for parents not identifying their child's weight problem is that society as a whole has become so fat we have collectively lost our sense of a healthy weight.
The chief medical officer, Dame Sally Davies, raised this issue of overweight becoming the new norm in her annual report last year.
"We need to find some tool to educate parents, when their child is born, what they should expect a child's size to be and not to be afraid of talking to parents over fears they, or the child, will react badly," Prof Viner said.
Commenting on the findings, the chief executive of the Royal Society for Public Health, Shirley Cramer, said: "School education from a young age should focus on the importance of active lifestyles and healthy diets to ensure our society is one that understands the relationship between diet and good health.
"Parents are key role models for their children and it is imperative they are aware of all the factors that can influence health.
"However, it is not just the role of the parents, society as a whole needs to help enforce messages about eating well."
She said restricting junk food advertising would help as would better calorie labelling on food.
Tam Fry, from the Child Growth Foundation, told the BBC: "To the obesity specialist it is incomprehensible that parents cannot tell if their children are overweight.
"You sometimes have to wonder if they are in total denial, but when you realise that even health professionals may often have difficulty in recognising obesity in their patients, the enormity of our obesity epidemic sinks in.
"The knock-on risk of extreme overweight to the individual's and country's health cannot be emphasised enough."