Wire size is dictated by two things, voltage drop and temperature rise of the wire. Heating of the wiring is difficult to calculate, since it is dependent on many things, like number of wires in the bundle, ambient temperature, routing of the wire within the bundle and in the environment. So rules of thumb are usually used for the temperature rise. Voltage drop is the main driver for lighting.
Voltage drop is easy to figure, since it is equal to ohms law V = IR (where V = voltage, I = current, and R = resistance). So the longer the run of the wire or more current the higher the voltage drop. I have heard for normal house wiring a 3% loss in the wire is used for sizing the wire gauge. For Christmas lighting, the full color RGB controllers generally support a ±5-10% variance in power. If you account for the ±2-3% variance in the power supply outputs, this gives you 7-8% voltage drop. I would tend to be conservative and use the wire size at a 5% drop in voltage. Additional pages have been included to show charts of the voltage drop for 5V and 12V power versus the current load. It is also recommend to verify in the data sheet for your controller how much voltage tolerance is acceptable.
For AC power the underwriters laboratory (UL) provides guidelines for extension cords, which is shown in the list below. Please verify the rating for your extensions cords, the table below is just for reference.
- 25/50 feet : 1-13 amperes 16 gauge wire
- 25/50 feet : 14-15 amperes 14 gauge wire
- 25/50 feet : 16-20 amperes 10/12 gauge wire
- 100 feet : 1-10 amperes 16 gauge wire
- 100 feet : 11-13 amperes 14 gauge wire
- 100 feet : 14-15 amperes 12 gauge wire
- 100 feet : 16-20 amperes 10 gauge wire
- 150 feet : 1-7 amperes 14 gauge wire
- 150 feet : 8-10 amperes 12 gauge wire
- 150 feet : 11-15 amperes 10 gauge wire