For a feature of finite length, linewidth roughness leads to variations in the mean feature width. Typically, numerical simulations are used to explore this relationship. An analytical approach is used. Starting with a common expression for the power spectral density, an analytical expression relating critical dimension uniformity to linewidth roughness is derived. The derived expression matches simulation results extremely well and can be used to understand more fully the detrimental impact of feature roughness on lithographic results. Finally, based on this expression, a new metric of linewidth roughness is proposed.