Accurately Measure Calories Burned in Time Period

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DavidSnider
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What is the most accurate way of measuring the amount of calories a person has burned in a certain time period?
 
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You measure the metabolic rate over time.

Breath Respirometry - measure VO2 and VCO2 - the rate of consumption/transport of Oxygen and the production/transport of Carbon Dioxide.

Oxygen is required to fully "burn" energy sources, Carbon Dioxide is the end product of burning Calories.

If you are really interested in Respirometry and measuring metabolic rates see:
"Measuring Metabolic Rates" By John R. B. Lighton It mentions other methodologies.