Studies have shown increased flood risks due to climate change and often disproportionate impacts on socially vulnerable populations. The social inequality of flood impacts has been investigated in various levels of detail, but there lacks a general index that can quantitatively measure social inequality across space and time. In this work, we develop a set of social inequality indices based on the Concentration Curve and the CDC/ASTDR Social Vulnerability Index to fill this gap. Following our previous work investigating climate change's impact on the Remnants of Hurricane Ida flooding in 2021, we extend our analysis to measure the social inequality of the estimated exposed population, considering both past and future climate change. The results show that socially vulnerable populations are unequally exposed to Ida flooding. Both historical and projected future warming were found to exacerbate the social inequality of exposure to Ida’s deep flood water (> 1m). Given the simplicity of the inequality measure and accessibility of underlying social vulnerability data in the U.S., these indices can be easily applied elsewhere in the country to assess inequality of exposure to different hazard types. They provide easily interpretable and consistent measures to quantify environmental justice for decision-making.