Reappraisal of the Weir equation for calculation of metabolic rate

In 1949 Weir (3) demonstrated that the metabolic rate calculated from respiratory gas exchange measurements is to a close approximation proportional to the difference in percentage oxygen content between inspired and expired air. Although values for the energy equivalent of oxygen consumed and for the respiratory quotient for the oxidation of various nutrients have been revised since 1949, we show that the error in the calculation remains generally below 0.5% for the oxidation of dietary carbohydrate, fat, and protein. Where the original equation is uncritically applied to situations in which other nutrients are being oxidized, the error may reach 3%, although alternative methods for calculating the metabolic rate may be similarly in error. We give the derivation from first principles of the general mathematical solution to the calculation of the metabolic rate following Weir's method. Examples are provided of the subsequent derivation of specific equations for the more precise calculation of the metabolic rate where different combinations of nutrients are being oxidized.