The purpose of a rock bolt is to improve the strength capacity of a jointed rock mass. The strengthened arch controlling area can be formed based on the superposition of the controlling influence range of the bolt with the controlling influence angle of rock bolt playing an important role. However, quantitative research on the influence angle is still rare. In this study, numerical simulations and mathematical analysis are used to study the law of stress field distribution and the controlling influence angle through a single bolt, and the following conclusions can be obtained. (1) The compressive stress field is roughly distributed in an "Apple shape" and in a "conical" spatial distribution. (2) The bolt controlling angle is not a constant 45°, and it is influenced by the rock mass strength and bolt parameters. It decreases with the increasing elastic modulus of the bolt, bolt diameter and bolt length. It also increases with the increasing pretension and rock mass strength. The length has less influence on the supporting range. (3) Based on the experimental results, an optimal analytical model to predict the bolt's controlling influence angle was developed. The analytical model includes the influences of the rock mass strength and bolt parameters. (4) A comparison between the model predictions with the results from the Dabei Mining 103 face transportation tunnel and the existing results shows the rationale behind the original support design scheme and an improvement over the existing results.