Hello for all metalworking men ;-) The newbie's strange question of the day : in many web links some lengths are in inch and there is no problem to convert them in millimeters (for me) but some dimensions are notified by a number - so I've seen a drill bit with #45 or #57 Can you give me the way to calculate them (in inch) ?

There is a formula that I can't put my hands on at the moment. If you have a set of numbered drills, the box should be marked with the diameters, otherwise pick up a pocket machinists handbook at a local welding supply. It will have a lot of basic, useful data on drills and taps. Bugs

So, Gil - your question wasn't answered. No one gave a specific formula relating numbered drill sizes and lettered drill sizes to "inches". AFAIK, the actual formula (if there is one) has faded into antiquity. Just get a good table and go with it.

Below is a note on this subject that I wrote for the members of my metalworking club.

Regards, Marv

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29 January 2005

Via my web page, I get frequent requests for a formula that relates numbered drill size to the number designation. This typically from the poor benighted souls who think that there should be some sort of logical relationship in American metalworking so-called 'standards'. I respond to these people by saying that it is possible to fit a practical (i.e., first order) least squares equation but the maximum error for a particular drill size runs as high as 10% which is just too much for precision metalworking. (If you're curious, the fit is included below.) Higher order fits can decrease this error slightly but the resulting fifth or sixth order polynominal is just too complex to be practical in a shop environment. That's why everyone uses a table for these drill sizes.

You may hear oldtimers referring to the numbered drills as 'wire gage' drills. This gives us a hint of where to start looking. Perhaps the numbers are related to a particular wire gage 'standard'. Now the nice thing about standards is the fact that there are so many of them. There are literally dozens of so-called 'standards' for wire sizes.

Wire is made by taking an ingot and pulling it through a die. This is done again and again to produce the finer wire sizes. Now, the idiots who run wire mills decided to start labeling their wire by the number of times it's been drawn. It's hard to understand how anyone would be dumb enough to use such a stupid system. If ever there was an argument for adopting the Metric System approach of labeling things by their size, wire (and sheet) gage numbers are it.

Labeling by the number of times drawn explains why the higher numbers correspond to smaller sizes. Not only is the system stupid, it's backwards as well! However, in keeping with the anything-to-maximize-confusion nature of the Imperial system, I must point out that there *are* wire gages where the size *increases* with the gage number. Music wire makers especially seem to favor this approach. I'm frankly surprised that these cretins didn't label their wire with the notes of the musical scale so one could run around measuring wire by 'twanging' it.

At any rate, some judicious Googling led me to the Stub's *steel* wire gage. In the table below, this 'standard' is compared side-by-side with the numbered drill sizes. They're close (but, of course, not quite equal) across the full range from 1 to 80 gage numbers. Since an agreement this close doesn't exist for any of the other 'gage' standards, I can only conclude that the numbered drill series was derived from the Stub's *steel* wire gage, with a bit of finagling thrown in to prevent any accidental total agreement, and thus preserve the sacred illogic and confusion of the Imperial system of measurement.

Should you decide to research this further, note that there is also a Stub's

*iron* wire gage. By this time, it will probably not come as a surprise to learn that it's not the same as the Stub's *steel* wire gage.

Finally, before you ask, I don't have a clue about the origin of the letter drills. I can, however, picture some boffin in a post-colonial New England factory muttering to himself, "Blimey, nobody will ever need more than

26 drill sizes. Let's just label the blighters with letters."

Comparison of Stub's steel wire gage and numbered drill series:

A = gage/index number B = Stub's *steel* wire gage diameter (in) C = standard numbered drill diameter (in)

Well ... the problem with this technique is that the pitch produced is dependent on both the length being "twanged" and the tension applied to the wire. Otherwise, you could not get different notes by pressing a string down to a fret to shorten its effective length.

I suspect that the finagling was to shift them away from fractional sizes in the same range (in 1/32" increments).

[ ... ]

Note that those start (with 'A') where the number sizes leave off. I guess that it was better than using negative numbers.

Note that these number-sized and letter-sized drills *do* serve a purpose. They provide a finer fit for tap drills for many screw threads which would not be well served by the fractional sized sets which came first.

And consider what happens with the number size *screws* -- which of course bear no logical relationship to the drill sizes. After #1 (quite small), there is a #0, followed by a #00, a #000, and finally a #0000. Below that, the diameter becomes negative. And there *is* a formula for the number sized screws.

From a posting by Ted Edwards in this newsgroup some number of years ago:

A related and useful piece of info: A #N machine screw has a nominal diameter of 0.060"+0.013"*N. Actual diameter is slightly smaller than this due to the flats at the top of the threads. e.g. A #6 screw has nominal OD of 0.060+0.013*6 = 0.138".

And to extend it below #0, you have to turn the multi-zero ones into negative values of "N" above, so a #0000 is a #-3 screw. :-)

I wrote a small C program some years ago to calculate the number sized screws based on that formula -- with a bit of trickery to handle the multi-zero sizes, and some sanity checking to avoid sizes beyond #0000 -- those would have negative diameters. :-)

You're right of course. Any shop formula is only a close approximation To the actual pubkished sizes. There are also separate gauging systems for iron wire and nonferrous metals [Brown & Sharp, Stub's, U.S. Steel wire, Imperial, Music wire, and those are just the standards that survived to modern times.] Some of them are based on the weight of a plate with a given thickness [gauge]. Get a handbook already! Bugs

I found the equation, which is for U.S./Brown & Sharp gage for wire. It is accurate to 0.0001" over the whole range from 7/0 to 50 gage. B & S pioneered the use of accurate mathematical models for standardization. The 0,00,000 . . . series are put into the formula as negative numbers,

00 corresponding to -1. INVLOG(-.05035 * GAGE# - .48825) = T [Thickness in Inches] You can apply metric conversion to the formula by multiplying by 25.4. Numbered drill sizes do not follow a formula and regression yields a variance of +/- 0.009", which isn't very useful. You need a reference chart for those. Bugs

Hmm ... nothing seems to work out for me with this. I have a few questions:

1) the part in the parens is ambiguous, and will give different results in different computer languages. Could you add an extra layer of parens to force the order of evaluation? E.g.:

((-0.05035 * Gauge# ) - 0.48825)

or

(-0.05035 * (Gauge# - 0.48825))

2) Which log is your "INVLOG()" function? Base-10 or Base-e?

No matter which set of assumptions I try, I can't get anything close to the values in _Machinery's Handbook_.

I was going to throw together a quick computer program to handle it (with some tricks for the multi-'0' gauges), as I have done with number sized screws.

An added option for the program when the inital part of it is working properly.

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