convert AWG to mm and reverse

[dinges]

A while ago, after a discussion on IRC about AWG wiresizes and the annoyance of having to convert from AWG to mm (or reverse), a few of us dived into the matter.

It appeared there was a relatively simple equation to convert from AWG to mm:

dia [mm] = 0.127 * 92 ^ ((36-#AWG)/39)

Ross implemented it in the bot in IRC, I programmed it in my calculator so as to be always available. After a short while of re-arranging the equation, I also got the reverse equation, to convert from mm to AWG:

#AWG = - ((ln (dia[mm]/0.127)) / (ln 92)) * 39  + 36

Since others may hate the looking up in conversion tables too (besides, I don't always have these tables on me; the calculator I have), these equations may come in handy.

Hope the above is useful for others too.

Regards,

Peter.

[vawtman]

Peter just found this

http://www.simetric.co.uk/siwire_elect.htm

[Murlin]

.03936 is the majak number.....

Divide or multiply, depending on whether converting mm to inches or inches to mm...

Murlin

[richhagen]

Peter, quite a while ago I wrote this wire resistance calculator:

http://www.otherpower.com/images/scimages/742/WIRECALC.exe

It is written in Visual Basic 6, so its basically for Windows computers.    

One thing you can do with it is plug in the wire size with what you have, AWG, or mm or a few others that I programmed in at the time, enter some arbitrary length, calculate the resistance and then empty out the units field leaving the length and resistance alone, set the units to whatever you want to convert to, and recalculate.  It is not exactly what I designed it for, but it works for me when I am curious about what an equivelant wire would approximately be.  Rich Hagen

[alancorey]

I don't know if anyone else has tried these, but that second equation,

#AWG = - ((ln (dia[mm]/0.127)) / (ln 92)) * 39  + 36

doesn't work for me.  If I put in 1 mm I get 53 AWG, and if I put in 2 mm I get 59 AWG.  Not only are the values wacky, but the AWG is going in the wrong direction: up as the physical size gets bigger.

Looking at the equation, the mm value is in the top which makes more sense with the way it's working than the way it should be.  I'm sort of ignoring the minus sign after the equals, but I'm not getting negative AWG values.  If this is a typo and there's supposed to be some number before the - that might explain it.

I was programming these in JavaScript to make a simple HTML page with calculators on it, but when the second one didn't work I tried it with a real calculator.

  Alan

[alancorey]

I Googled and found this at http://www.rcgroups.com/forums/showthread.php?t=596219&page=3&pp=15

  AWG = 18.24 - (19.89 * log(mm))

It seems to work, at least in the few cases I tried.  I really didn't want try making my own inverse to the first function because I was a Calculus dropout twice, the last time over 10 years ago.

JavaScript version in a day or two when I get back to it.

  Alan

[alancorey]

OK, an initial ugly JavaScript version: http://128.119.200.7/awg.html

It also has GPM <-> liters/second and MPH <-> meters/second.

Suggestions for other calculations to add to it welcome.

  Alan

[dinges]

Hi Alan,

Ah, a calculus dropout. That explains...

The equations are ok but stuffed with brackets; this may be causing the problem. One of the reasons I love RPN.

I tried the equation again, and 1mm gives 18.2 AWG; 2mm gives 12.2 AWG.

The steps:

 - ln ( diameter/.127)

divide the above by ln(92)

multiply it all by 39

add 36 to the above result.

In RPN:

(diameter in mm on the stack, as input value)

.127



ln

92

ln

/

+- (reverse polarity)

39

*

36

+

(RETURN or END)

It leaves the wire size in AWG on the stack.

Most likely you have made a mistake with the brackets, i.e. correct order of operations. The one you found is a bit easier though (haven't checked yours for accuracy though; my problem has been solved by the equations in my original post  )

BTW, easy to remember: 1.5mm = AWG 15.

Regards,

[dinges]

You have forgotten the 'minus' sign at the beginning of the equation (just after the 'equals' sign). Both equations have been tested by me and others and are correct.

Regards,

[alancorey]

I didn't forget the minus sign, I just left it out because it didn't make sense to me there.  I expected to get a negative AWG because of leaving it out, but that didn't happen.  I see why now.

Now I see that your equation:

#AWG = - ((ln (dia[mm]/0.127)) / (ln 92)) * 39  + 36

Could also be written as:

#AWG = 36 - ((ln (dia[mm]/0.127)) / (ln 92)) * 39

just by moving the 36 to the beginning and that way the minus isn't orphaned.

But that wasn't the problem.  I was probably doing ln(dia[mm])/0.127 instead of ln(dia[mm]/0.127).  No such thing as too many parenthesis, just need to pay attention to them.  Now it works.  I didn't try it for AWG > 36 though.

I think I'm going to Google to get some formulas for resistance per circular mils and write some resistance calculator stuff in JavaScript.  Also like to do something for winding with n-in-hand being equivalent to what larger sizes.  I've got spools of #22 and #26 that I realize weren't such a great investment now that I've wound a generator with 28 ohms/phase resistance.  Too expensive to not use it for something though.

  Alan