The 3D perception of the human eye is more impressive in irregular land surfaces than in flat land surfaces. The quantification of this perception would be very useful in many applications. This article presents the first approach to determining the visible volume, which we call the 3D‐viewshed, in each and all the points of a DEM (Digital Elevation Model). Most previous visibility algorithms in GIS (Geographic Information Systems) are based on the concept of a 2D‐viewshed, which determines the number of points that can be seen from an observer in a DEM. Extending such a 2D‐viewshed to 3D space, then to all the DEM‐points, is too expensive computationally since the viewshed computation per se is costly. In this work, we propose the first approach to compute a new visibility metric that quantifies the visible volume from every point of a DEM. In particular, we developed an efficient algorithm with a high data and calculation re‐utilization. This article presents the first total‐3D‐viewshed maps together with validation results and comparative analysis. Using our highly scalable parallel algorithm to compute the total‐3D‐viewshed of a DEM with 4 million points on a Xeon Processor E5‐2698 takes only 1.3 minutes.