What wire size do you need for a 20 amp circuit at 300 feet?
At 120 volts, a full 20 amp load 300 feet out needs roughly 4 AWG copper to stay inside 3 percent voltage drop. At 240 volts the same load needs about 8 AWG. Voltage drop is not an NEC requirement, it is an informational note, but it is a real performance problem and most engineers and many local amendments treat 3 percent on the branch circuit as a design rule.
The calculation
For a single phase circuit, the drop equals 2 times K times I times D divided by the circular mil area, where K is about 12.9 for copper, I is the current in amps, and D is the one way distance in feet. Three percent of 120 volts is 3.6 volts. Rearranged for circular mils: 2 times 12.9 times 20 times 300 divided by 3.6 gives 43,000 circular mils. From Chapter 9 Table 8, 6 AWG is 26,240 circular mils and 4 AWG is 41,740, so 4 AWG is the honest answer and even it is a hair short. Three AWG at 52,620 clears it with margin.
On 240 volts the allowable drop doubles to 7.2 volts while the current for the same power halves, so the required area falls to roughly 10,750 circular mils. Eight AWG at 16,510 circular mils covers it comfortably. That is why running a 240 volt circuit to a remote building is so much cheaper in copper than running two 120 volt circuits.
Design the load, not the breaker
The 20 amp figure assumes the circuit runs at its full rating. If the actual load is a few lights and a receptacle drawing 5 amps, the drop scales down proportionally and 12 AWG may be perfectly adequate. Calculate on the real connected load where you know it, and on the full circuit rating where you do not. A subpanel feeder is a different calculation again, because 215.2(A)(1) Informational Note 2 recommends 3 percent on the feeder with a combined 5 percent to the farthest outlet.
What the code does require
Section 210.19(A) Informational Note 4 and 215.2(A)(1) Informational Note 2 are the voltage drop references, and informational notes are not enforceable under 90.5(C). What is enforceable is 240.4(D), which caps 12 AWG copper at 20 amps regardless of how large you go for voltage drop. Upsizing the ungrounded conductors also triggers 250.122(B): where conductors are increased in size for any reason, the equipment grounding conductor must be increased proportionally by the same ratio of circular mil area. Going from 12 AWG at 6,530 circular mils to 4 AWG at 41,740 is a factor of 6.4, which turns a 12 AWG equipment grounding conductor into roughly 5 AWG, so use 4 AWG.
Terminations
Four AWG will not land on a standard 20 amp receptacle or breaker. Run the large conductors to a junction box near the load and transition to 12 AWG pigtails there with listed connectors, or feed a small panel at the far end. Section 110.14(A) requires terminals to be identified for the conductor size and material being connected.
Field takeaway
Four AWG copper for 20 amps at 300 feet on 120 volts, 8 AWG on 240 volts, upsize the equipment grounding conductor proportionally per 250.122(B), and transition to 12 AWG at a box near the load.