This paper evaluates the performance degradation incurred by an approximation algorithm (min-sum algorithm) when polar codes under successive cancellation decoding (SCD) are employed. To understand the behavior of the algorithm under the SCD, the error performances of the synthetic channels were evaluated, since different synthetic channels show different levels of degradation, because the numbers of the approximation algorithm applied to the channels and the operating signal-to-noise power ratios (SNRs) of the channels, which also affect the levels of degradation, are different. After evaluation of the synthetic channels, the block error rate performances under the SCD for different coding rates were obtained. The results show that the performance degradation was not significant, even when a coded bit length of 2¹⁴=16384 was used.