The rapid growth of high-power light-emitting diode (LED) technologies has gained momentum in developing accurate tools and methods to measure performances of such products. For instance, it is widely recognized that confirming the photobiological safety is extremely important since the light of the high-power products may be shone directly into people's eyes. For many years, the international standard organizations, such as CIE, and researchers have been developing guidelines and/or improving methods for measuring the LED radiation patterns, respectively. However, the difficulties in LED measurements have been still highlighted by discrepancies in the experimental results among different laboratories. In this paper, we first propose a mathematical formulation for the existing approaches, such as those using two- and three-dimensional goniometers. Then, generalization of the measurement methods is presented to improve the system measurement accuracy, through making a connection between a predicted accuracy and the parameters of the optical setups (such as aperture size and working distance). To verify the effectiveness of our approach, the experiments are conducted to evaluate and compare the performances of the proposed approach. The measurement results indicate that our approach is consistent from theory to practice.