Purpose: This study aimed to evaluate the relative efficiencies of the state universities in Sri Lanka from 2017 to 2019 and their capacity to enroll more students. Design/methodology/approach: Data envelopment analysis (DEA) method was used to measure the relative efficiencies. Annual data on expenditure, academic staff, non-academic staff, student enrollments, graduate output and publications in indexed journals were used. Findings: Results from both input oriented DEA and output oriented DEA showed that seven out of 15 (47%) state universities were constantly performing efficiently from 2017 to 2019. Well-established universities are apparently more efficient than emerging universities. Six universities were constantly inefficient. Excess staff and the deficiencies in enrollments, graduate output and publications were the main causes of the inefficiencies. In particular, the total enrollments can be increased by 23%. Research limitations/implications: The outcomes are thoroughly based on DEA with a selected set of variables and data. Owing to the limitations in the DEA method, variables and data, the results may not reflect the actual efficiencies of the universities. However, this study indicates that the universities can improve their relative efficiencies by accommodating more students and increasing research output. Originality/value: This study is the first proper investigation of the relative efficiencies of the state universities in Sri Lanka using DEA. This is also the first quantitative assessment of the capacity of Sri Lankan Universities to increase student enrollments.