This research explores the stability of ferroelectric phases in (Ba,Sr)TiO3 thin films on GdScO3 substrates. Investigating the interplay of temperature, composition, and strain-state, the study aims to simplify complexities by focusing on one substrate. Computational simulations, varying temperature, composition, and strain contribute to a temperature-composition phase diagram. The phase diagram reveals stable ferroelectric phases in specific regions, forming distinctive patterns. The significance lies in advancing understanding and control of BSTO, a pivotal ferroelectric material with diverse applications.