My layout is 33 ft x 38 ft, so not quite a large as yours. My challenge, however, was due to where I had to locate the control center with all the transformers (*), switches, etc. , which was rather distant from where I needed to route the power.
A wire run from my control center to the center of one of the two main portions of my layout was about 120 feet as it had to go around the perimeter of the room, and around several obstacles. After I installed several of these runs, I decided to run the wires up the wall next to the control center (inside PVC pipe), and down at the center of the area to be powered. This saved me about 40 feet, so now these runs were 80 feet.
(*) I have six remote control wall outlets on the layout room walls, and these feed local power supplies for lighting. Not only is this a convenient way to turn on and off the street lights, building lights, and some accessories, but also cut down on the lengths of the wires.
What wire gauge (AWG) should you use? This depends on how long your wire runs will be, and the expected amperage (current) they will carry. As an example, let’s look at my track wiring.
My track wiring consists of eight 12 AWG wires, each 80 feet long, from the transformers to the TIU’s – four from each ZW-L. Each of the TIU’s supplies four distribution blocks (relays) via 14 AWG wires that are 20 feet long or shorter. Each distribution block supplies power to six track districts (mains, sidings, or spurs) via 16 AWG wires that are 12 feet long or shorter. Average current draw at any one time from any channel is about 3 amps, but this can be higher occasionally.
You can easily calculate the voltage drop across the wire if you know the wire material (usually copper), the resistance for the wire for the given length, and the wire gauge. But an easier way yet is using this calculator:
Once you have entered the parameters, you will get the voltage drop and the resulting voltage at the end of the wire. Some transformers sense the current draw and raise the output to maintain a somewhat constant voltage, but there can be a drop nevertheless.
With the information provided by the calculator, you can decide what voltage you want to have available for your trains, and select the proper AWG to get there.