Abstract: This paper proposed the definition of distribution system security region (DSSR) surface area, and describes the roundness of high-dimensional DSSR in combination with the volume. First, the surface area of DSSR was defined as the whole size of security boundary. Secondly, an algorithm of DSSR surface area based on dimensionality reduction sampling was proposed. Thirdly, the relationship between surface area and volume of DSSR was studied. A new index, volume to surface area ratio (VSR), which can reflect the overall shape characteristics of DSSR, was defined. VSR is the reciprocal of the surface area required to form a unit volume. This paper found that each wiring mode had a fixed volume to surface area ratio, and we obtained the VSR of several typical wiring modes. Geometry also has its own VSR. Isoperimetric theorem proves that the VSR of circle is the largest. Based on the VSR of hyperspheres in high-dimensional space, this paper defined the roundness of DSSR, that is, the degree that the security region is close to the circle in geometry. Finally, the concept and algorithm of this paper were verified by distribution network cases. The physical meaning of related concepts was summarized. In this paper, the degree of approaching circle of DSSR in high-dimensional space was calculated, which has great significance to evaluate and plan secure and efficient distribution system.