What wire size is needed for 50 amp service at 300 ft?

6 AWG is the nominal wire size in copper for 50 amps. 300 feet of 6 AWG has a resistance of .12 ohms. At 50 amps the voltage drop across .12 ohms would be about 6 volts. As a rule of thumb you want to keep voltage drop to no more than 10% of the supply voltage. So it you were using 120 volts you are okay at 300 ft with 6 AWG since the drop is only 5% of the supply. If you were at 240 volts it would be even better since the drop would be 2.5%.