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Many believe almost no calories are used during sleep, but that is incorrect. While the body rests during sleep and energy consumption is not high, it is a long way from 0.
A convenient way to measure energy use is the “metabolic equivalent”. This essentially normalizes energy use numbers across body types and physiologies. A metabolic equivalent is defined as the rate of energy use by a person sitting and awake and not exercising – the “resting metabolic rate”. A person bicycling may be using 5 metabolic equivalents. A runner can be at 9 or more metabolic equivalents. The metabolic equivalent number for any activity depends on fitness level and intensity.
A sleeping person uses about 0.9 metabolic equivalents. So we burn calories when we are asleep about 90% as fast as we while sitting on the couch watching television.
As far as order of magnitude, a metabolic equivalent is about 1 kcal/kg hr. A kcal is what nutritionists call a dietary calorie. So an adult weighing 70 kg (about 154 lb) uses about 70 dietary calories per hour while resting, while awake and about 60 while sleeping.
The National Cancer Institute (the US government publishes a list of estimated MET for common activities. http://appliedresearch.cancer.gov/atus-met/met.php Housework is listed at about 3 MET and yard work at 3 to 4. Sleeplessness – lying in bed unable to get to sleep – is a MET of 1, the same as sitting on the couch watching television.
Note the Basal Metabolic Rate is different from Resting Metabolic Rate. The Basal rate is even lower and just the minimum to stay alive.
In REM the large skeletal muscles are paralyzed. In stages 1 and 2 sleepers are more active than in deep sleep, but overall, differences in energy consumption from one sleep stage to another is minimal.
One reason we know the purpose of sleep is not simply to rest is that energy consumption is not much lower than it is in simple waking rest. The brain does many different things during sleep as compared to waking,