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The dihedral angle of a retroreflector, which directly determines the quality of velocity aberration compensation, is usually detected using a Zygo interferometer. However, since the software is effectively a black box, the user is unable to determine the method and approach that is used to process the data. This also adds further difficulty of determining the error inherent in the retroreflector. From the perspective of phase distribution, a mathematical model is built between rectangular error and phase distribution. Combining the original data and area boundaries provided by Zygo interferometer, and a numerical fitting method, the dihedral angle value of the retroreflector is computed, and then compared with the value provided by the interferometer. Results show that the maximum difference between the two values is 0.2". Considering that the measurement tolerance of the Zygo interferometer is 0.2", this suggests that the computed value is consistent with the value given by the interferometer. Thus, computing method provides a new basis and approach for dihedral angle detection for retroreflector manufacturers and users.