I have a 24VDC power supply, and have a Radar sensor at about 700' away. It is metered from a Allen Bradley PLC. I am trying to figure out what size wire I would need for the signal to travel the distance needed. Is there any formula that I can use to find this out?

 

I found a good voltage drop calculator at the following site:
http://www.bulkwire.com/wireresistance.asp

I would probably suggest 24 gauge twisted pair, shielded.

 

Ohm's law.

the analog input will have a certain dropping resistor, and the wire will account for the rest of the resistance in the loop.

generally with 4-20mA loops about 500 Ohms is the maximum loop impedance but you will have to check the instrument's manual and see what it actually is.

 

As correctly said by Bob Peterson, you have to consider both analog circuits, i.e. sensor end and PLC input resistance. Also overall loop impedance in most cases is 500 to 750 ohms.

You have to refer your RADAR sensor and PLC manual for correct matching. In some cases you may need to include a series resistance to get correct loop impedance.

for the wire size as recommended by PaulyD you can use multi stranded 24 gauge twisted pair, shielded cable of good quality.