# Wire gauge and actual wire diameter

#### Tonyr1084

Joined Sep 24, 2015
6,883
Just looked up a chart on wire gauge and its physical size. I'm wondering just how someone determined that a wire gauge would represent a specific size wire. The chart shows that as wire gauge decreases the difference between each size also decreases.

http://www.firemountaingems.com/res...e+chart&kwid=9e15e20b13204d3ca7aa2da3931ded84

So I'd like to know the formula for calculating gauge. Does anyone have an answer? Still searching Google but no luck so far.

#### wayneh

Joined Sep 9, 2010
17,168
Try 1.1229322^(36-AWG)*5/1000 = inches of wire diameter. That's an Excel formula and the multiplication is done after exponentiation.

#### Tonyr1084

Joined Sep 24, 2015
6,883
Math isn't my strong point. Are you saying 1.1229322 raised to the power of 36 (in your example) multiplied by 5 then divided by 1000?

And I think I'm looking for the revers of that formula. I know a diameter and want to know its gauge without having to look up a chart.

#### wayneh

Joined Sep 9, 2010
17,168
Math isn't my strong point. Are you saying 1.1229322 raised to the power of 36 (in your example) multiplied by 5 then divided by 1000?

And I think I'm looking for the revers of that formula. I know a diameter and want to know its gauge without having to look up a chart.
It's 36 minus the wire gauge in the exponent. Otherwise yes.

You can rearrange the equation to get gauge from a given diameter, however you'll get non-integer values for AWG.

#### Tonyr1084

Joined Sep 24, 2015
6,883
It's 36 minus the wire gauge in the exponent.
Thanks. I'll give that a shot on Excel. See if I can get it to come up with a known wire diameter.

From what I've been reading gauge seems to have something to do with weight. A steel plate one foot square and one inch thick (144 cubic inches) has something to do with it. I'd have to imagine that with different materials, such as steel versus aluminum, a sheet of a particular gauge of aluminum and a sheet of the same gauge rating of steel would be physically different. But for what I'm looking for, your excel formula may serve well enough. Thank you for that.

#### wayneh

Joined Sep 9, 2010
17,168
Thanks. I'll give that a shot on Excel. See if I can get it to come up with a known wire diameter.

From what I've been reading gauge seems to have something to do with weight. A steel plate one foot square and one inch thick (144 cubic inches) has something to do with it. I'd have to imagine that with different materials, such as steel versus aluminum, a sheet of a particular gauge of aluminum and a sheet of the same gauge rating of steel would be physically different. But for what I'm looking for, your excel formula may serve well enough. Thank you for that.
See the Wiki for quite a bit of detail.
https://en.wikipedia.org/wiki/American_wire_gauge

#### WBahn

Joined Mar 31, 2012
26,398
Just looked up a chart on wire gauge and its physical size. I'm wondering just how someone determined that a wire gauge would represent a specific size wire. The chart shows that as wire gauge decreases the difference between each size also decreases.

http://www.firemountaingems.com/res...e+chart&kwid=9e15e20b13204d3ca7aa2da3931ded84

So I'd like to know the formula for calculating gauge. Does anyone have an answer? Still searching Google but no luck so far.
It's basically the same system as the decibel.

I believe the original intent was for

Gauge # = 10 log(R/Ro)

I think that Ro was supposed to be 0.1 mΩ/ft.

If you look at the standard resistance of #0 AWG wire, you find it is 0.09827 mΩ/ft, which is close.

Even closer, if you look at #10 AWG it is 0.9989 mΩ/ft.

But, at some point, two reference points were chosen, namely that #4/0 had a diameter of 0.46" and #36 had a diameter of 0.005", and the areas for the 39 steps between them varied by the same fractional increase per step. Since area varies as the square of the diameter, this means that the diameters vary as the 39th root of 0.46"/0.005" or the 39th root of 92.

#### ElectricSpidey

Joined Dec 2, 2017
2,146
I just bought some "16 gauge" wire from Amazon, but it's a lot closer to 18...so don't sweat it, your not the only one that has problems doing the math.

#### Tonyr1084

Joined Sep 24, 2015
6,883
Thanks all. Appreciate the help.

#### RichardO

Joined May 4, 2013
2,271
If you look at the wire tables you will see that a good rule of thumb is that the resistance changes by a factor of 2 for 3 changes in wire size number.

Note that resistance is proprtional to wire cross section area, not wire diameter.

#### Attachments

• 88.6 KB Views: 2

#### Tonyr1084

Joined Sep 24, 2015
6,883
@RichardO Thanks. Interesting factoid (the resistance doubling every three gauge sizes)

I've come to appreciate that it's related to the cross sectional area of the conductor. I wonder if someone makes a micrometer that automatically converts wire diameter to either its cross sectional area, or whether one is available that reads out in wire gauge.

Since resistance plays a part - does the type of wire make a difference? In other words; would a wire who's dimeter is 0.032 inch be considered a 20 gauge wire in copper but be a different gauge in - say - aluminum?

#### wayneh

Joined Sep 9, 2010
17,168
@RichardO Thanks. Interesting factoid (the resistance doubling every three gauge sizes)

I've come to appreciate that it's related to the cross sectional area of the conductor. I wonder if someone makes a micrometer that automatically converts wire diameter to either its cross sectional area, or whether one is available that reads out in wire gauge.

Since resistance plays a part - does the type of wire make a difference? In other words; would a wire who's dimeter is 0.032 inch be considered a 20 gauge wire in copper but be a different gauge in - say - aluminum?

#### shortbus

Joined Sep 30, 2009
9,370
I just bought some "16 gauge" wire from Amazon, but it's a lot closer to 18...so don't sweat it, your not the only one that has problems doing the math.
I worked where they made automotive wire. They years ago had some concern that the trend toward metric sizes was more and more prevalent, and that they should "switch" to making metric size wire. But last I knew they didn't go that route, may have changed now but don't know. If you look at metric equivalents for wire they are usually a little smaller diameter wise than a corresponding AWG size. Even though they both are rated for the same current carrying capacity.

#### cmartinez

Joined Jan 17, 2007
7,683
I've been doing projects for the automotive wire harness industry for more than a decade now, and yes, all of their wiring is specified in mm² nowadays. They'll reference that even for U.S. brands, such as Chrysler and Ford.

#### wayneh

Joined Sep 9, 2010
17,168
I've been doing projects for the automotive wire harness industry for more than a decade now, and yes, all of their wiring is specified in mm² nowadays. They'll reference that even for U.S. brands, such as Chrysler and Ford.
That's interesting. So there is no "gauge" system that requires translation, the industry uses the actual area value directly?

#### ElectricSpidey

Joined Dec 2, 2017
2,146
This wasn't automotive wire, and I always look for the AWG markings when I order wire.

#### cmartinez

Joined Jan 17, 2007
7,683
That's interesting. So there is no "gauge" system that requires translation, the industry uses the actual area value directly?
Yes... although the values used are tabulated. That is, there's a table of standard values, and any value in between would have to be specially manufactured. I haven't bothered to check, but it wouldn't surprise me if those values were directly translatable into AWG sizes.

#### shortbus

Joined Sep 30, 2009
9,370
I've been doing projects for the automotive wire harness industry for more than a decade now, and yes, all of their wiring is specified in mm² nowadays. They'll reference that even for U.S. brands, such as Chrysler and Ford.
Like I said didn't know if they finally had to switch,GM used the AWG because it was always "slightly" bigger than metric mm/squared value. But that was quite a long time ago, late '80's to early '90's, when I still worked in the wire making plant. With the increased scrutiny on vehicle weight savings they, GM, probably have switched to metric now.