When we get poor sleep, our bodies go into survival mode. This is likely wrought by evolution: Little sleep, in prehistoric days, was probably associated with danger or scarcity.
Scientists now know that sleep deprivation sets off a chain of metabolic responses to ensure our survival: Namely, it makes us hungrier (so we have more energy to face the threat).
In ancient times, this would have helped us stay alive. But in these times of abundant calories, it seems to just propel us to overeat.
A recent meta-analysis of 11 studies finds evidence that, overall, sleep deprivation seems to cause a person to eat an average of 385 extra calories the next day. (For reference, there are about 380 calories in a medium French fries at McDonald's, and generally people should aim to eat around 2,000 to 2,500 calories per day.)
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It's not a ton of extra food, but perhaps enough to start tipping the scale.