The goal of this work was to develop an easy and reliable equation for calculating seepage discharge through homogeneous earthen dams that operate with toe drains. For this purpose, many data were generated using (SEEP/W) program depending on the geometrical variables that affect this seepage, such as dam height (h), upstream water depth (H), dam top width (b), upstream and downstream slopes, and base length of toe drain. The seepage discharge quantity for 728 cases was determined using three different values for each of the aforementioned geometric variables. A straightforward and precise equation was created for computing the discharge via a homogeneous earth dam with chimney drain system using the dimensional analysis method and SPSS software, with an (R2) coefficient of 0.986. Then the dimensional analysis was applied to this information. A simple and accurate equation was obtained to calculate the discharge through a homogenous earth dam with a toe drain system with a coefficient (R2) of 0.986. The results indicated that the seepage discharge increases with an increase in the upstream water depth, the toe drain’s base length, and the angle of the upstream and downstream slopes, while it decreases with an increase in the dam top width. Additionally, utilizing the produced data, the artificial neural network model (ANN) was implemented. The results of this model revealed varying percentages of importance for the independent geometrical variables on the seepage quantity, where the upstream water depth (H) has the most important and amounted to 66.9%, while the upstream slope was the least important, where the importance percentage for this factor was 0.7%. The (ANN) model and predicted empirical equation results show excellent agreement when compared.