Non-sinusoidal magnetic induction variation pattern (IVP) makes the estimation of iron loss a challenging step of designing a trapezoidal back-EMF machine. Commercially available finite element analysis (FEA) based machine design tools fail to accurately estimate core losses in such situations. Previously proposed methods to address that problem either compromise too much on accuracy, or are too time-consuming to be applied to every design-iteration. This paper proposes a simple theoretical approach to address this problem. Flux density variations under both no-load and loaded conditions were studied and their relations with the machine's design details were derived. The complete approach was verified by 2D time stepped FEA. The loss expressions presented were verified by experiments on a sample material. © 2016 IEEE.