Based on the union bound, formulas to estimate the BER distribution of channel codes are derived. By using these formulas, the BER for every position in the information sequence can be estimated. Appling the formulas to Turbo codes, several examples were given, and the results are also compared with simulation results. The results show that the derived formulas can give out good estimations of the BER distributions for Turbo codes. Therefore this would be helpful for the BER analysis, especially the unequal error protection analysis of Turbo codes.