Urban sprawl, as one of the fundamental challenges facing contemporary cities, especially in developing countries, has led to excessive land consumption, destruction of agricultural lands, and inefficiency of urban infrastructure. This study aims to disaggregate the contribution of two factors—population growth and sprawl (increase in per capita land consumption)—to the physical expansion of Andimeshk city during the period 2000–2025. For this purpose, the Holdren mathematical model and remote sensing data (Landsat satellite images) were used. The accuracy assessment of image classification using overall accuracy (above 82%) and Kappa coefficient (above 0.76) confirmed the high reliability of the produced maps. The findings indicate that the built-up area of the city grew by 60.45% to reach 1,447.12 hectares, while the population increased by only 32.64%. According to the Holdren model, 59.75% of the physical development was attributed to population growth and 40.25% to sprawl. The analysis of five-year sub-periods shows that the share of sprawl decreased from 74.90% during 2000–2005 to 59.69% during 2005–2010, and during 2010–2015, with a negative share (-38.13%), a turning point toward compactness occurred. During the periods 2015–2020 and 2020–2025, the share of sprawl reached -163.56% and -176.03%, respectively, indicating the continuation and intensification of the urban compactness trend. Rising land and housing prices, along with the institutional discipline of development plans, have been key factors in this shift. Sustaining the current favorable situation requires maintaining the rigidity of the legal boundary, imposing levies on vacant lands, and improving environmental quality in compact neighborhoods.