Abstract:The average-angle method is one of the most generally-used methods for drilling trace calculation. However, there's a defect in the general formula of the average-angle method. When the azimuth difference between two adjacent measuring points exceeds 180°, the corresponding direction of the arithmetic average of azimuth angles used in the general formula is opposite to the actual average azimuth orientation. If we ignore this defect, it may lead to a relatively big calculation error of the horizontal coordinate increments, which may directly affect the borehole positioning accuracy. To solve the defect of the general formula, this paper discussed the relationship between the actual average azimuth orientation and the corresponding direction of the arithmetic average of azimuth angles, and then derived the modified formula from rigorous geometric calculations, and finally use the general formula, the calculation method in Drilling Borehole Quality Control Specification "(SY/T 5088-2008), the modified formula to calculate a certain example respectively. Through the analysis of the calculation results by three methods, we concluded: the modified formula is exactly the same as the Specification method in calculation results, which proved the correctness of the modified formula; when the azimuth difference between two adjacent measuring points is greater than 180 °, the horizontal coordinate increments calculated by the general formula and the modified formula are just opposite, which just verifies the effectiveness of the modified formula's correcting the defect of the general formula. In summary, the modified formula perfectly corrects the defect of the general formula, and overcomes the shortcomings of the Specification method which requires classified discussion meanwhile, which is well worth being popularized.