Empirical Modeling of Speech Clarity C50 as a Function of Distance and Reverberation Time T30

The acoustic design of learning spaces is commonly carried out using geometrical acoustics simulations or analytical calculations. While 3D simulations provide high accuracy, they are time-consuming and resource-intensive, whereas analytical calculations are limited to reverberation time. This study proposes a set of empirical regression formulas for estimating the speech clarity index C50 from the reverberation time T30 and the source–receiver distance r. The models are intended for design verification, allowing a quick assessment of whether a proposed acoustic solution meets speech clarity criteria without using numerical simulations. A total of 455 measurement entries from 28 rooms were analyzed, representing three categories of acoustic conditions. Polynomial and logarithmic regression models were developed and evaluated using three statistical criteria: the adjusted coefficient of determination (Radj2), the Akaike Information Criterion (AIC), and the root mean square error (RMSE). The results show that logarithmic models generally provide better fit consistency across room types, whereas polynomial models describe lower frequency bands more accurately. The proposed relationships demonstrate practical potential for predicting C50 for mid–high frequencies in real rooms using analytically obtained T30 values and geometric distances. The proposed models are intended for early-stage building and classroom design, where numerical simulations are not yet available.