What size wire should you use for 20 amp service to a building 200 feet from electric supply?

Answer 1

Answer for USA, Canada and countries running a 60 Hz supply service.
Use 10/2 it will handle 30 amps and it wont have a voltage drop.

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But be very careful: before you can get proper advice about the right size wire to use you have to include information not only about about the length of run, you also need to state the intended installation method!

Is it to be hung between buildings in the open air or fixed to a wall, etc. ... ?

Is it to be in a conduit or clipped to a cable tray, or is it running underground, etc. ... ?

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As always, if you are in doubt about what to do, the best advice anyone should give you is to call a licensed electrician to advise what work is needed.

Before you do any work yourself,
on electrical circuits, equipment or appliances,
always use a test meter to ensure the circuit is, in fact, de-energized.

IF YOU ARE NOT ALREADY SURE YOU CAN DO THIS JOB
SAFELY AND COMPETENTLY
REFER THIS WORK TO QUALIFIED PROFESSIONALS.

Answer 2

for 120v 20A 2% voltage drop

or .12 ohms of wire

400' of wire (out and back)

#6 will give you 116 volts at 20 amps 200 feet from the infinite supply

#12 will give you 107volts

a 3/4 hp water pump with a kva class f motor 6A running may not start with #12 wire

Answer 3

12 AWG