The coating film uniformity of a Newtonian fluid on a spinning disc is analyzed theoretically. The effect of evaporation during the spin coating is also investigated. In this study the perturbation technique has been applied to solve the nonlinear governing equation with or without evaporation, and it can be applied for any initial film thickness contour. The perturbation solution is explicit in film thickness. A dynamic uniformity factor is defined to describe the degree of uniformity with time evolution. In this study a criterion for the effect of evaporation on achieving film uniformity is proposed. It is shown theoretically for the case of small evaporation that the coating film thickness is getting more uniform across the whole disc with increasing spinning time.