We model energy demand across five end-use sectors and 15 energy products in Saudi Arabia, generating comprehensive price and income elasticity estimates. Using the Structural Time Series Model, we demonstrate that the trends underlying energy demand are generally stochastic, underscoring the importance of using such models for estimating unbiased elasticities. Our estimates reveal that energy demand in Saudi Arabia is price inelastic in all cases and income inelastic in most cases, with industrial natural gas and electricity being the only exceptions. Nevertheless, we find extensive variation in the elasticities across sectors and energy products, highlighting the importance of using sector- and product-specific elasticity values and not assuming they are similar in the same country. We then use our estimated elasticities to conduct a welfare analysis of the energy price reforms implemented in 2016 and 2018. Our analysis reveals that the 2016 reform delivered a total annual welfare gain of 11.6 billion 2010 United States Dollars (USD) in 2016. Following the 2018 reform, the annual welfare gain increased to 17.0 billion 2010 USD in 2018. We also estimate the cumulative carbon dioxide emissions avoided between 2016 and 2018 due to energy price reform at 164 million tonnes.