The respiratory quotient (RQ) is the ratio:
RQ = CO / O
where the term "eliminated" refers to carbon dioxide (CO) removed from the body.
In this calculation, the CO and O must be given in the same units, and in quantities proportional to the number of molecules. Acceptable inputs would be either moles, or else volumes of gas at standard temperature and pressure.
Many metabolized substances are compounds containing only the elements carbon, hydrogen, and oxygen. Examples include fatty acids, glycerol, carbohydrates, deamination products, and ethanol. For complete oxidation of such compounds, the chemical equation is
CHO + (x + y/4 - z/2) O 
→ x CO + (y/2) HO
and thus metabolism of this compound gives an RQ of x/(x + y/4 - z/2).
For glucose, with the molecular formula, CHO, the complete oxidation equation is CHO + 6 O 
→ 6 CO + 6 HO. Thus, the RQ= 6 CO/ 6 O=1.
For fats, the RQ depends on the specific fatty acids present.  Amongst the commonly stored fatty acids in vertebrates, RQ varies from 0.692 (stearic acid) to as high as 0.759 (docosahexaenoic acid).  Historically, it was assumed that average fat had an RQ of about 0.71, and this holds true for most mammals including humans.  However, a recent survey showed that aquatic animals, especially fish, have fat that should yield higher RQs on oxidation, reaching as high as 0.73 due to high amounts of docosahexaenoic acid.
The range of respiratory coefficients for organisms in metabolic balance usually ranges from 1.0 (representing the value expected for pure carbohydrate oxidation) to ~0.7 (the value expected for pure fat oxidation). In general, molecules that are more oxidized (e.g., glucose) require less oxygen to be fully metabolized and, therefore, have higher respiratory quotients. Conversely, molecules that are less oxidized (e.g., fatty acids) require more oxygen for their complete metabolism and have lower respiratory quotients. See BMR for a discussion of how these numbers are derived. A mixed diet of fat and carbohydrate results in an average value between these numbers.
RQ value corresponds to a caloric value for each liter (L) of CO produced. If O consumption numbers are available, they are usually used directly, since they are more direct and reliable estimates of energy production.
RQ as measured includes a contribution from the energy produced from protein. However, due to the complexity of the various ways in which different amino acids can be metabolized, no single RQ can be assigned to the oxidation of protein in the diet.
Insulin, which increases lipid storage and decreases fat oxidation, is positively associated with increases in the respiratory quotient. A positive energy balance will also lead to an increased respiratory quotient.