Shannon's capacity result has often been used as a benchmark to compare the performance of practical codes. Shannon's theorem helps us to calculate the maximum rate at which data can be transferred without making any errors. Most of the practical codes never achieve this zero error bound. Moreover most of the digital data like audio and video can tolerate various amount of errors. In this paper we introduce the notion of distorted channel capacity - the maximum rate at which data can be transferred when we allow certain amount of error in the recovered bits. We also calculate the distorted channel capacity for a gaussian channel and a fading channel.