This letter provides an analytical derivation of the probability density function (pdf) of the adjacent channel interference (ACI) in the uplink of a cellular system. The result can be easily extended to co-channel interference (CCI). This derivation obviates the need for Monte Carlo simulations to calculate such results numerically. Universal Mobile Telecommunications System (UNITS) parameters are used for the evaluation. Firstly, the results presented show good agreement between the analytical and Monte Carlo based methods. Secondly, the results suggest that system operators should co-ordinate their cell site selection as ACI can vary significantly depending on the cell topology.