Rand says:

The wire gauge needed depends on the demands of the accessory, the composition and length of the wire, and the voltage at the power source. The longer the distance and the lower the source voltage, the thicker the wire needs to be (larger gauge number). While every analogy limps to some degree, it’s like a hose and water (and we’ll assume the entire length of hose is at the same level so gravity is not an additional factor). The water pressure in your house system will push more water per second through a short thick hose than through a long thin one. By increasing the diameter or by shortening the length you decrease the resistance and more water will flow per second.

It’s much the same with wire. With a lot of pressure (voltage) you can push a lot of current (amps) through a very fine wire – so much so that it gets hot and glows, as does the filament in an incandescent light bulb. In model wiring, however, the purpose is to deliver current to accessories, not to make the whole layout glow and burst into flames.

(Because most wire available for model use is copper wire, this reply does not address the differences in resistance between metals.)

There’s a significant difference between gauge 18 and 29 wire. But if distances are less than three feet, either would probably work for most N gauge accessories. On the other hand, gauge 29 wire might be harder to find and possibly more expensive, even though it has less copper. Over six feet, gauge 29 might result in a voltage drop (the resistance would mean that the voltage available at the accessory is not the full voltage available at the power source) and might not be adequate to push enough current through the accessory to activate it. Thicker wire will never hurt an accessory, so long as the source voltage is not higher than the accessory is designed for. Thinner wire will never hurt an accessory, but the accessory might not work because it’s not getting enough current.

I don’t have any formulas to calculate gauge demands, but if you have access to a multi-meter you can check to see if the voltage at the accessory end of the wire is up to the demands of the accessory. Most accessories have a range of voltages at which they will operate, so a small voltage drop is not usually a problem. If the voltage is above that range you could “burst the pipes”; that is, you could burn out the accessory; if the voltage is too low, the accessory won’t work.

Al T. says:

Actually the thicker the wire the lower the wire gauge number for example 18 ga wire is thicker than 20 ga wire.