Respiration chamber estimates of metabolizable energy intakes and diet metabolizability for ruminants cannot be used directly to check existing metabolizable energy requirements, because of the definition of ME concentrations of feeds used in the ARC (1980) energy requirement models. These were constructed so that the amounts of net energy available for the synthesis of milk or body tissue was predicted from ME intake as defined. Reversal of the calculations requires that both metabolizability measured at the maintenance plane and feeding level as a multiple of maintenance requirement, which is also a function of diet metabolizability, are available, which is not usually the case with calorimetry studies. In the case of dairy cows, two functions were derived, both quadratic in nature, which were solved to give the required estimates of ME intake measured at the maintenance level of feeding. Use of either of the quadratic functions on test data showed the procedures to be accurate. Mean differences in ME requirement of the order of 25 MJ/d above current standards were found with the first procedure. The second procedure developed was sensitive to the estimate of fasting metabolism adopted. Using recent estimates of the latter, the mean value for ME intake measured at the maintenance level of feeding obtained indicated that no level of feeding correction was necessary to get an accurate fit of the model to the test data. Also, that the 5% safety margin adopted in AFRC (1993) was not required. The exponential energy retention model for growing beef cattle of ARC (1980) cannot be reversed; it generates a transcendental equation with no algebraic solution. The linear model of ARC (1965), with a feeding level correction dependent upon diet metabolizability is shown to be a good fit to the exponential model, and its use is suggested if estimates of depressions in diet metabolizability by growing beef cattle are required. The derived equation was cubic in nature. The Newton-Raphson method was used to obtain solutions numerically, using suitable test calorimetry data. Testing of the solutions obtained showed the equation derived was reliable, and that the AFRC (1993) ME requirements for growing beef cattle are accurate.