WIT Press

A Scale For Architectural Design Compactness: A Mathematical Approach


Free (open access)

Paper DOI






Page Range

397 - 408




3599 kb


M. M. Saeed


The topic of compactness is significantly connected to sustainability, due to its impact in understanding and managing the process of shape-space formation, which may lead to an energy efficient design. This paper is a complement to a research delivered to a scientific conference of the Iraqi University of Technology in 1999 by the same researcher, discussing the concept of architectural design compactness, its prospects and development, the recent paper distinguishes between the shape compactness and the design compactness, and suggests a scale for the latter. The methodology adopted in this paper is, after defining the function of the architectural design compactness, reviewing all the relevant available scales and discussing their function to find whether they are sufficient to measure the design compactness. Discovering the contradictions of these scales results, lead to the necessity of deriving an objective and quantitative scale for the latter which is the aim of this paper. By analyzing the function of the architectural design compactness as a dependent variable, the independent variables which the latter relatively varies accordingly were devised, and then the scale is mathematically derived. Reliability of the scale has been verified by comparing the computed design compactness values of various building systems with their subjective evaluation; it shows a remarkable consistence with them. A model of abstract plans representing various design systems is prepared to evaluate their compactness to be used as guidelines for designers. The derived scale can be developed in a subsequent paper to establish a system for evaluating the compactness of multi-storey buildings by taking into account the rate of change for all external surfaces (walls and roofs). Keywords: architectural design, compactness, shape factor, perimeter, surface area, volume, space, form.


architectural design, compactness, shape factor, perimeter, surfacearea, volume, space, form.