AbstractA parametric representation of the effectiveness factor for a first‐order, nonisothermal irreversible reaction in a catalyst pellet has geen devised that amply covers the realistic range of parameters for the exothermic case. Given the Thiele modulus, Prater temperature, and dimensionless activation energy, the effectiveness factor can be recovered in about 1/1000 sec. (CDC 6600) to an accuracy of better than 5% over most of the range. When heat and mass transfer resistance at the surface is added the time required is about 0.03 sec. This makes fixed bed calculations more than 50 times faster than would otherwise be possible.