The WUP method, thus . measures urban sprawl by integrating these three dimensions into a single metric. WUP = UP * w1(DIS) * w2(UD) Where UP = Urban Permeation, w1(DIS) = Weighting1(Dispersion), and w2(UD) = Weighting2(Utilization Density). Since the utilization density and dispersion are weighted with the weighting functions w2(UD) and w1(DIS) , this metric of urban sprawl is referred to as Weighted Urban Proliferation (WUP). UP = (size of built up area /reporting unit) * dispersion UP is expressed in urban permeation units per m2 of land (UPU/m2). Within the framework of the WUP method, built-up areas are defined as areas where buildings are located. Since roads, railway lines, and parking lots, etc. are not buildings, they are disregarded in the WUP method of measuring urban sprawl. The third component of the WUP model is utilization density (UD). This component is based on the premise that as more people and jobs are located in the built-up area, the more efficient the utilization of the land becomes.Naghmeh Nazarnia, Christian Schwick, Miroslav Kopecky, Tomas Soukup, Erika Orlitova, Felix Kienast, Jochen A.G. Jaeger. 2016: Urban Sprawl Metrics (USM) Toolset – User Manual-First edition UD = (number of Inhabitants + number of jobs)/size of built up area
The WUP method, thus , measures urban sprawl by integrating these three dimensions into a single metric. Since the utilization density and dispersion are weighted with the weighting functions and , this metric of urban sprawl is referred to as Weighted Urban Proliferation (WUP). UP is expressed in urban permeation units per m2 of land (UPU/m2). Within the framework of the WUP method, built-up areas are defined as areas where buildings are located. Since roads, railway lines, and parking lots, etc. are not buildings, they are disregarded in the WUP method of measuring urban sprawl. The third component of the WUP model is utilization density (UD). This component is based on the premise that as more people and jobs are located in the built-up area, the more efficient the utilization of the land becomes.Naghmeh Nazarnia, Christian Schwick, Miroslav Kopecky, Tomas Soukup, Erika Orlitova, Felix Kienast, Jochen A.G. Jaeger. 2016: Urban Sprawl Metrics (USM) Toolset – User Manual-First edition 
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.
,
D
WUP = UP * w1(DIS) * w2(UD)
D
Where UP = Urban Permeation, w1(DIS) = Weighting1(Dispersion), and w2(UD) = Weighting2(Utilization Density).
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w2(UD) and w1(DIS)
and
D
= (size of built up area /reporting unit) * dispersion
D
UP
D
UD = (number of Inhabitants + number of jobs)/size of built up area