Hello everybody.
I'm using rack & pinion drive system.I need help from you guys to calculate step per mm correctly

.
I saw calculation
example in INCH. I used same calculation calculating steps per mm. But I getting wrong step count.
My calculation:
circle pitch 25.4mm (1")
25.4 * pi = 79.796453
79.796453 / 3 = 26.598817 (reduction)
26.598817 / 200 = 0.132994 (mm per step)
1 / 0.132994 = 7.51913 (steps per mm)
7.51913 * 16 = 120.30609 (16x microstepping)
I used mach 3 steps per unit calibration, and come out with pretty accurate results - ~ 57.6 steps per mm.
So I'm wondering where I miscalculated ? I need to calculate it accurately

Thank you guys for help !