This article proposes the Differential Entropy-based Compactness Index (DECI), a novel metric for synthetically describing the spatial distribution of point clouds. The index is based on the calculation of the differential entropy of each point in the point clouds. If the point clouds represent a spatial distribution of moving objects, making them time-dependent, one of the key advantages of DECI is its capability for real-time monitoring. Moreover, analyzing historical data enables the study of DECI trends, point dynamics, and average values within specific intervals. It also allows for the comparison of two or more point clouds. While DECI primarily characterizes the spatial distribution of points, the paper proposes several practical applications. Notably, DECI can serve as a measure of risk and congestion, making it relevant in various engineering domains, particularly in controlling maritime, aerial, and road traffic (including autonomous driving) and identifying areas in need of infrastructure improvements. It is also applicable for assessing crowd density and risks in public, outdoor, and indoor spaces. The versatility of DECI extends to the health and biological fields, and it holds significance in team sports analysis, where it can examine the influence of compactness on match results. The ability of DECI to capture real-time dynamics and historical models makes it invaluable for decision-making and optimizing various aspects of system management. Additionally, this index could be considered a valuable feature for Machine Learning applications.