Arduino Connect Long Wires/Cables
The stepper motor 28byj-48 seems to be a 5V motor (datasheet). I've seen it being used with a A3967 driver, which means that it does not draw more than 750 mA of current.

I'll go with the length you mentioned in the comments:


  for this example lets say 3m


The rest is Physics: the resistance of a wire is

R = p * l/A


where l is the length of the wire and A is the area (dependent on the diameter).

A voltage drop calculator can now tell you how much voltage is left at the end of the wire.

I would have estimated a 0.75 mm² (AWG 18), but you might even be fine with 0.5mm² (AWG 20) according to the calculator. But: better safe than sorry.



Also from the comments:


  i have micro servo SG90 working as expected. my expectation is that the large one will work similarly (of course with more power requirements)


A stepper motor needs a totally different setup than a servo. The servo is connected with simple 4 pins, the stepper needs a motor driver (H-bridge). Connecting the stepper motor directly to the Arduino may destroy your board.