The quantification of roof covering in the early stages of building project estimation remains a critical challenge, particularly in projects funded by Nigeria's Tertiary Education Trust Fund (TETFund). Inaccurate estimations often lead to budget overruns and project delays, undermining the efficiency of fixed-sum contracts common to TETFund projects. This study developed a regression-based predictive model for quantifying roof-covering in TETFund projects across universities in Anambra State. Data was collected from twenty-five TETFund buildings at Nnamdi Azikiwe University, Awka, and Chukwuemeka Odumegwu Ojukwu University through physical measurements and secondary sources. Key variables, including gross floor area, external blockwork centerline girth, and roof pitch, were analyzed using correlation and regression techniques. The developed model enables reliable roof covering area estimation, mitigating risks associated with cost misallocation and enhancing project efficiency. The findings provide a robust framework for improving estimation practices, ensuring cost alignment, and bolstering the operational effectiveness of TETFund projects.