Calculating rates of VO and/or VCO requires knowledge of the flow rates into and out of the chamber, plus fractional concentrations of the gas mixtures into and out of the animal chamber.  In general, metabolic rates are calculated from steady-state conditions (i.e., animal's metabolic rate is assumed to be constant). To know the rates of oxygen consumed, one needs to know the location of the flow meter relative to the animal chamber (if positioned before the chamber, the flow meter is "upstream," if positioned after the chamber, the flow meter is "downstream"), and whether or not reactive gases are present (e.g., CO, water, methane, see inert gas).
For an open system with upstream flow meter, water (e.g., anhydrous calcium sulfate) and CO removed prior to the oxygen analyzer, a suitable equation is
For an open system with downstream flow meter, water and CO removed prior to the oxygen analyzer, a suitable equation is
where
*FR is the volumetric flow rate adjusted to STP (see Standard conditions for temperature and pressure)
*FO is the fractional amount of oxygen present in the incurrent air stream (the baseline or reference), and
*FO is the fractional amount of oxygen present in the excurrent air stream (what the animal has consumed relative to baseline per unit time).
For example, values for BMR of a 20 g mouse (Mus musculus) might be FR = 200 mL/min, and readings of fractional concentration of O from an oxygen analyzer are FO = 0.2095, FO = 0.2072.  The calculated rate of oxygen consumption is 0.58 mL/min or 35 mL/hour.  Assuming an enthalpy of combustion for O of 20.1 joules per milliliter, we would then calculate the heat production (and therefore metabolism) for the mouse as 703.5 J/h.