<p>Due to rapid urbanization, reinforced concrete hillside buildings, irregular in geometry, have become prevalent in modern construction on hill slopes across several countries. These hillside buildings exhibit a torsionally coupled fundamental mode resulting from coupled structural irregularity from the interaction between plan and elevation irregularities due to their irregular geometry. However, existing building design codes and research have not adequately addressed the quantification of such coupled structural irregularity. Additionally, the empirical formulae provided by design codes for estimating the fundamental natural period, typically based on equivalent building height, lacks clarity and applicability across different prevalent configurations of hillside buildings. Therefore, to address these gaps, an empirical expression is proposed for estimating the fundamental natural period of the hillside buildings, incorporating a robust geometry-based regularity index and a new definition of the equivalent building height based on one of the prevalent configurations of hillside buildings, namely the split-foundation building. This geometry-based regularity index offers a basis for comprehensively assessing the level of coupled structural irregularity and, thereby, the dynamic behaviour of prevalent configurations of hillside buildings. The proposed empirical expressions for the natural period, regularity index, and equivalent building height are validated numerically and compared to existing expressions. Statistical measures, including coefficient of determination, Pearson correlation coefficient, root mean square error, and mean square error, confirm the accuracy and predictive capability of the proposed expressions.</p>