# Derive the MET equation for caloric expenditure estimate

``````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).

#### 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!