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The geopotential height is usually calculated with the measured temperature,pressure and humidity, and the calculation formula is called barometric height formula. In this paper,we analyze the derivation of the formula and point out that the origin of the simplified formula. The errors caused by the simplification are calculated quantitatively. The analysis shows that the gravitational acceleration in the barometric height formula should be the local actual variable value instead of the current constant value,and the replacement can reduce errors of the potential height calculation.