j_martin

If you go to this page, and enter your amps and wire length, then hit the calculate button, it'll do the math for you.

The wires from the old headlight connector to the relay only carry coil current. Without looking it up, I'll say it's less than 0.3 amps. The relay coil isn't that sensitive to voltage drop, so it'll run with 10% loss. the wire could be 22 gauge and 285 feet long and still work fine. 16 or 18g would be a nice size to work with, and very ample.

The wire from the relay to the headlights handles about 5 amps. It could be 16g and carry the load at 2% loss. With 14g the connectors would be less resistive, (lossy), so that would be my choice. 12g would be OK.

What the original design misses is the loss through all the connectors involved. The 14 g wire itself would lose about 1.5%, and the ridiculous 22g ground another 3%. The connectors and switches easily lose another 5%, leaving you with 12.4 V at the lights assuming the battery is at 13.8. That's about a 20% loss in light.

Power is a squared function of voltage. When voltage is reduced, current is also reduced. Power (watts) is voltage times current.

hope it helps.