High entropy alloys (HEA) are a new type of high-performance structural material. Their vast degrees of compositional freedom provide for extensive opportunities to design alloys with tailored properties. However, compositional complexities present challenges for alloy design. Current approaches have shown limited reliability in accounting for the compositional regions of single solid solution and composite phases. For the first time, a phenomenological method analysing binary phase diagrams to predict HEA phases is presented. The hypothesis is that the HEA structural stability is encoded within the phase diagrams. Accordingly, we introduce several phase-diagram inspired parameters and employ machine learning (ML) to classify 600+ reported HEAs based on these parameters. Compared to other large database statistical prediction models, this model gives more detailed and accurate phase predictions. Both the overall HEA prediction and specifically single-phase HEA prediction rate are above 80%. To validate our method, we demonstrated its capability in predicting HEA solid solution phases with or without intermetallics in 42 randomly selected complex compositions, with a success rate of 81%. The presented search approach with high predictive capability can be exploited to interact with and complement other computation-intense methods such as CALPHAD in providing an accelerated and precise HEA design.