The present invention relates to a gear mesh testing instrument in which the transmission error occurring between the two gears to be tested (the driving gear and the driven gear) is measured while both gears are rotating while intermeshed with each other. A pulse generator is connected to the rotating shaft of the driving gear, and of the driven gear, respectively, so as to produce two pulse signals having frequencies proportional to the number of the rotation of the gears. Then, the two pulse signals are introduced into the gear number compensating circuit so as to be converted into two pulse signals having a same frequency. The transmission error is proportional to the phase difference between the two pulse signals having the same frequency, which phase difference is proportional to the ratio of the phase difference time between the two pulse signals to the period of pulse signal. As a consequence, the phase difference time is converted into a clock pulse number by means of the time difference calculation circuit, while at the same time the reciprocal of the period is calculated by means of a reciprocal calculation circuit. The clock pulse number and reciprocal of the period are multiplied in a multiplier so as to obtain the phase difference.