Derive the MET equation for caloric expenditure estimate

Question

A Metabolic Equivalent of Task (METs) is:

1 MET := Consumption of 3.5 mL_O2/kg/min ~= 1 kcal/kg/hr

Most online calculators that use MET to estimate caloric burn use:

Eq. 1) Cal_kcal = Duration_min * (Mets_MET * 3.5 * Mass_kg / 200)

But none of them derive it or provide a proof to get from 3.5 mL_O2/kg/min => 1 kcal/kg/hr! Where did "200" come from? Intuitively, knowing the units of MET kcal/kg/hr, you'd likely simply perform this following conversion instead:

Eq. 2) Cal_kcal = Duration_hr * Mets_MET * Mass_kg

But this differs by 5% from Eq. 1. Please derive Eq. 1 and explain all units/constants so that we may understand why it is used in almost all MET calculator (and not Eq. 2).

• https://www.healthline.com/health/what-are-mets#calorie-connection
• https://howdyhealth.tamu.edu/use-metabolic-equivalents-mets-to-calculate-calories-burned/
• https://captaincalculator.com/health/calorie/calories-burned-running-calculator/
• https://www.cmsfitnesscourses.co.uk/blog/using-mets-to-calculate-calories-burned/
• https://www.omnicalculator.com/sports/calories-burned
• https://blog.nasm.org/metabolic-equivalents-for-weight-loss
• https://www.acefitness.org/resources/pros/expert-articles/6434/5-things-to-know-about-metabolic-equivalents/
• https://www.gymondo.com/magazin/en/workout/what-are-mets-and-how-to-calculate-them-to-burn-more-calories
• https://www.convertcalculator.com/templates/met-calculator/

Hint

These links are the closest I've ever seen to a derivation: Metabolic Equations for Anaerobic Exercise? and https://fitness.stackexchange.com/a/25564/40079. However, there is no source, explanation of why 5/1000 is used (vs 4.X), or what the units all are. Even more confusing, they both conclude by using Eq. 2 not Ex. 1 like all online calculators!

Answer 1

You won't get to eqn 1 starting from your definition of MET.

MET is VO2 in milliliters per minute per kilogram body mass divided by 3.5. So using the conventional value of: 1 liter of O2 consumed is roughly equivalent to burning 5 kcal we get:

a) E = MET * 3.5 / 1000 ml/l * 5 kcal * duration_min * mass_kg

which is

b) E = MET * 3.5 / 200 ml/l*kcal * duration_min * mass_kg

which is eqn 1 in your question. That is why you get a deviation of 5% since its not 1 kcal/kg/h per MET as given by your definition but 1.05 kcal/kg/h per MET.