# How can I calculate length of wire, given its gauge and resistance?

As the title suggests; I am trying to calculate the length of a wire given its gauge and resistance in ohms per 1000 feet. I also have the amount of voltage drop, which is 1.1 V.

Specifications
Gauge: 14 AWG
Resistance (per 1000 feet): 2.525 ohms


I researched briefly and found this equation:

Vdrop = IR


However, I don't have an amperage value, so is it possible to calculate cable length without amperage? This is a DC system.

EDIT: I may be confusing some people. I'm looking for Total Length of the Cable.

The ohms/1000 feet value came from this table here, not from me.

• 2.525 Ohms / 1000 feet. Pretty simple. You don't need to know voltage drop or current. – R Drast Nov 2 '18 at 12:00
• @RDrast This gives the resistance per foot does it not? I'm looking for total length of wire in feet. The resistance value that I quote is a standard value for 14 AWG cable, it wasn't measured by myself. – Jay Nov 2 '18 at 12:07
• What are you trying to get here? You are asking for the length, given the gauge and resistance. But you have the length of 1000 ft (304.8 meters), and resistance of 2.525 ohms. – Puffafish Nov 2 '18 at 12:16
• Without another fixing value, there are many lengths with appropriate current values that can give a voltage drop of 1.1V – Solar Mike Nov 2 '18 at 12:37
• @Puffafish I'm trying to get total cable length. The ohm/1000ft number is from a table I found online, please see my edit at the bottom of the post – Jay Nov 2 '18 at 16:55

$$\Delta V = \frac {R_{1000}}{1000} l I$$

where $$\ \Delta V \$$ is the voltage drop, $$\ R_{1000} \$$ is the resistance per 1000 feet, $$\ l \$$ is the length in feet and $$\ I \$$ is the current.

There are four variables. You can find any one of them if you have the other three. You only have two variables, $$\ \Delta V \$$ and $$\ R_{1000} \$$ so you can't solve for $$\l\$$ or $$\I\$$.

One other thing: don't forget that the loop resistance will be twice that of a single core.

You're missing a few points. The most important thing is the actual length of the wire. What is it? If it's 100 feet, then the actual resistance of the wire is 2.525 ohms divided by 10.

As you realize, without knowing the current you cannot apply Ohm's Law to derive voltage. What you can do (once you've specified the wire length) is determine the maximum current which will fit your voltage drop.

V = iR means that i = V/R. Once you have calculated the resistance of the wire (see above), you can combine this with a voltage of 1.1 volts to determine the current which produces that voltage.

Once you have that number, any current less than that will produce a voltage less than 1.1 volts, and a current greater than that will produce a voltage larger than 1.1 volts.

• I'm attempting to find the length of the wire. Is there no way to calculate the length given what I know at the moment? – Jay Nov 2 '18 at 16:56
• @Jay, without more info, there is no way to isolate one single length : there are many possibilities that mathematically solve to the voltage drop you state... – Solar Mike Nov 2 '18 at 17:38