REE = 16.318VO2 + 4.602VCO2
This is an adaptation of the abbreviated Weir Equation which states that:
REE = [3.9 (VO2) + 1.1 (VCO2)] 1.44 (KCal/Day)
VO2 = volume of oxygen uptake (mL/min)
VCO2 = volume of carbon dioxide output (mL/min)
So in order to convert from KCal/Day to Joules/Min, the values in the equation should be multiplied by the conversion factor (4184) and then divided by the number of minutes in a day (1440).
REE = [3.9 (VO2) + 1.1 (VCO2)] 1.44 (KCal/Day) = 5.616VCO2 +1.584VO2 (KCal/Day) x 4184 = 23497VCO2 + 6627VO2 (Joules/Day) /1440 = 16.318VCO2 + 4.602VO2 (Joules/Min)