Visibility represents the size of a space that people visually perceive. An isovist is a spatial concept and measure to illustrate visibility and its visual characteristics in the built environment. For measuring openness within an urban area, the isovist has been widely used as a representative measure. Since actual perception of urban space is based on the three-dimensional (3D) form, the conventional two-dimensional analysis of an isovist has been sought to extend to 3D isovist measures. In this paper, we define a new measure for a 3D urban environment that is directly applicable to a standard range sensor measurement. Upon developing volumetric and angular openness indexes in the three-dimensional coordinate systems, the findings in this paper emphasize that the viewing angle is critical in measuring 3D openness while closely connected to the range measurements. By mutually considering the angle and the range simultaneously, the proposed 3D isovist captures a viewpoint from pedestrians for more realistic openness evaluation. Additionally, we validate the proposed method in both simulated environments and real point cloud sensor data. The proposed, straightforward, point-based method is expected to be applicable to measure a real urban environment with a mobile mapping system with 3D point clouds and LiDAR.