An exponential functional rigorous calculation (EFRC) method for calculation of the number of theoretical plates in distillation column with the ideal system is proposed. In this method, the complex non-liner function describing the relation between the liquid compositions of arbitrary two theoretical plates is converted into the exponential function. For the sake of the linearization feature of the exponential function in logarithmic coordinates, the number of theoretical plates, feed location and gas or liquid composition of any theoretical plate can be obtained without stepwise plate-to-plate calculations. It can greatly help to improve the efficiency and accuracy of distillation design. And the new model is easier to be solved than Lewis method or Smoker method. The physical significances of the parameters in the EFRC model are analyzed considering the effects of the reflux ratio, relative volatility and feed phase condition, especially for that at limiting conditions. The new method can be applied to distillation design and rating, and is generalized from binary ideal system to multiple one. The EFRC method has been validated. The results indicate that the accuracy of the new method agrees well with that of the plate-to-plate calculations, and is better than that of Gilliland correlation. (C) 2012 Elsevier Ltd. All rights reserved.