The problem of fluctuation-induced digital errors in a rapid single flux quantum (RSFQ) circuit has been a very important issue. In this work, we calculated the bit error rate of an RSFQ switch used in superconductive arithmetic logic unit (ALU). RSFQ switch should have a very low error rate in the optimal bias. Theoretical estimates of the RSFQ error rate are on the order of $10^{-50}$ per bit operation. In this experiment, we prepared two identical circuits placed in parallel. Each circuit was composed of 10 Josephson transmission lines (JTLs) connected in series with an RSFQ switch placed in the middle of the 10 JTLs. We used a splitter to feed the same input signal to both circuits. The outputs of the two circuits were compared with an RSFQ exclusive OR (XOR) to measure the bit error rate of the RSFQ switch. By using a computerized bit-error-rate test setup, we measured the bit error rate of $2.18{ imes}10^{-12}$ when the bias to the RSFQ switch was 0.398 mA that was quite off from the optimum bias of 0.6 mA.