Land cover classification and investigation of temporal changes are considered to be common applications of remote sensing. Water/non-water region estimation is one of the most fundamental classification tasks, analyzing the occurrence of water on the Earth`s surface. However, common remote sensing practices such as thresholding, spectral analysis, and statistical approaches are not sufficient to produce a globally adaptable water classification. The aim of this study is to develop a formula with automatically derived tuning parameters using perceptron neural networks for water/non-water region estimation, which we call the Perceptron-Derived Water Formula (PDWF), using Landsat-8 images. Water/non-water region estimates derived from PDWF were compared with three different approaches--Modified Normalized Difference Water Index (MNDWI), Automatic Water Extraction Index (AWEI), and Deep Convolutional Neural Network--using various case studies. Our proposed method outperforms all three approaches, showing a significant improvement in water/non-water region estimation. PDWF performance is consistently better even in cases of challenging conditions such as low reflectance due to hill shadows, building-shadows, and dark soils. Moreover, our study implemented a sunglint correction to adapt water/non-water region estimation over sunglint-affected pixels.