Relative Shannon’s entropy-based statistical web calculator to quantify urban growth for sustainable urban development

Urbanization and its associated environmental impacts are significant global concerns affecting not only metropolitan regions but also small and medium-sized cities. Quantitative assessment of urban sprawl is essential for sustainable urban planning and effective policy formulation. This study presents a web-based Urban Sprawl Calculator (USC) that automates the computation of Relative Shannon’s Entropy (RSE) to quantify spatial urban growth patterns and classify them as compact or sprawling. The tool was validated using real-world built-up area data derived from Landsat-8 imagery, with results cross-verified through manual calculation to ensure computational consistency. By enhancing efficiency, transparency, and reproducibility in entropy-based analysis, the USC supports evidence-based decision-making for sustainable urban development.