dimensions notified by numbers

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

Note that there are also letter drills.

Steve

Gil HASH wrote:

Here's an on-line table:

Mike

Thanks for all links

There are 25.4 millimeters to the inch, so convert the inch fractions to decimal inches and multiply. E.G. 1-3/4" = 1.75" x 25.4 = 44.45mm.

There is a drill chart (and tons of other neat stuff)here:

----------------------------------------- Jack Kevorkian for Congressional physician!

Wondrous Website Design =================================================

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.

According to WikaPedia, there isn't and never was a formula.

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

Regards, Marv

Home Shop Freeware - Tools for People Who Build Things

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)

A B C

1 0.227 0.2280 2 0.219 0.2210 3 0.212 0.2130 4 0.207 0.2090 5 0.204 0.2055 6 0.201 0.2040 7 0.199 0.2010 8 0.197 0.1990 9 0.194 0.1960 10 0.191 0.1935 11 0.188 0.1910 12 0.185 0.1890 13 0.182 0.1850 14 0.180 0.1820 15 0.178 0.1800 16 0.175 0.1770 17 0.172 0.1730 18 0.168 0.1695 19 0.164 0.1660 20 0.161 0.1610 21 0.157 0.1590 22 0.155 0.1570 23 0.153 0.1540 24 0.151 0.1520 25 0.148 0.1495 26 0.146 0.1470 27 0.143 0.1440 28 0.139 0.1405 29 0.134 0.1360 30 0.127 0.1285 31 0.120 0.1200 32 0.115 0.1160 33 0.112 0.1130 34 0.110 0.1110 35 0.108 0.1100 36 0.106 0.1065 37 0.103 0.1040 38 0.101 0.1015 39 0.099 0.0995 40 0.097 0.0980 41 0.095 0.0960 42 0.092 0.0935 43 0.088 0.0890 44 0.085 0.0860 45 0.081 0.0820 46 0.079 0.0810 47 0.077 0.0785 48 0.075 0.0760 49 0.072 0.0730 50 0.069 0.0700 51 0.066 0.0670 52 0.063 0.0635 53 0.058 0.0595 54 0.055 0.0550 55 0.050 0.0520 56 0.045 0.0465 57 0.042 0.0430 58 0.041 0.0420 59 0.040 0.0410 60 0.039 0.0400 61 0.038 0.0390 62 0.037 0.0380 63 0.036 0.0370 64 0.035 0.0360 65 0.033 0.0350 66 0.032 0.0330 67 0.031 0.0320 68 0.030 0.0310 69 0.029 0.0292 70 0.027 0.0280 71 0.026 0.0260 72 0.024 0.0250 73 0.023 0.0240 74 0.022 0.0225 75 0.020 0.0210 76 0.018 0.0200 77 0.016 0.0180 78 0.015 0.0160 79 0.014 0.0145 80 0.013 0.0135

--------------------------------------------------------

polynomial fit Y = A0 + A1*X + A2*X^2 + A3*X^3 + ... order of polynomial fit requested = 1

A0 = 0.224840 A1 = -0.003150

index xdata ydata ycalc error err%

0 1.00E+000 2.28E-001 2.22E-001 -6.31E-003 -2.77E+000 ** 1 2.00E+000 2.21E-001 2.19E-001 -2.46E-003 -1.11E+000 2 3.00E+000 2.13E-001 2.15E-001 2.39E-003 1.12E+000 3 4.00E+000 2.09E-001 2.12E-001 3.24E-003 1.55E+000 4 5.00E+000 2.06E-001 2.09E-001 3.59E-003 1.75E+000 5 6.00E+000 2.04E-001 2.06E-001 1.94E-003 9.49E-001 6 7.00E+000 2.01E-001 2.03E-001 1.79E-003 8.89E-001 7 8.00E+000 1.99E-001 2.00E-001 6.36E-004 3.20E-001 8 9.00E+000 1.96E-001 1.96E-001 4.85E-004 2.48E-001 9 1.00E+001 1.94E-001 1.93E-001 -1.65E-004 -8.53E-002 10 1.10E+001 1.91E-001 1.90E-001 -8.16E-004 -4.27E-001 11 1.20E+001 1.89E-001 1.87E-001 -1.97E-003 -1.04E+000 12 1.30E+001 1.85E-001 1.84E-001 -1.12E-003 -6.04E-001 13 1.40E+001 1.82E-001 1.81E-001 -1.27E-003 -6.96E-001 14 1.50E+001 1.80E-001 1.78E-001 -2.42E-003 -1.34E+000 15 1.60E+001 1.77E-001 1.74E-001 -2.57E-003 -1.45E+000 16 1.70E+001 1.73E-001 1.71E-001 -1.72E-003 -9.93E-001 17 1.80E+001 1.70E-001 1.68E-001 -1.37E-003 -8.08E-001 18 1.90E+001 1.66E-001 1.65E-001 -1.02E-003 -6.14E-001 19 2.00E+001 1.61E-001 1.62E-001 8.30E-004 5.16E-001 20 2.10E+001 1.59E-001 1.59E-001 -3.20E-004 -2.01E-001 21 2.20E+001 1.57E-001 1.56E-001 -1.47E-003 -9.37E-001 22 2.30E+001 1.54E-001 1.52E-001 -1.62E-003 -1.05E+000 23 2.40E+001 1.52E-001 1.49E-001 -2.77E-003 -1.82E+000 24 2.50E+001 1.50E-001 1.46E-001 -3.42E-003 -2.29E+000 25 2.60E+001 1.47E-001 1.43E-001 -4.07E-003 -2.77E+000 ** 26 2.70E+001 1.44E-001 1.40E-001 -4.22E-003 -2.93E+000 ** 27 2.80E+001 1.41E-001 1.37E-001 -3.87E-003 -2.76E+000 28 2.90E+001 1.36E-001 1.33E-001 -2.52E-003 -1.86E+000 29 3.00E+001 1.29E-001 1.30E-001 1.83E-003 1.42E+000 30 3.10E+001 1.20E-001 1.27E-001 7.17E-003 5.98E+000 ** 31 3.20E+001 1.16E-001 1.24E-001 8.02E-003 6.92E+000 ** 32 3.30E+001 1.13E-001 1.21E-001 7.87E-003 6.97E+000 ** 33 3.40E+001 1.11E-001 1.18E-001 6.72E-003 6.06E+000 34 3.50E+001 1.10E-001 1.15E-001 4.57E-003 4.16E+000 35 3.60E+001 1.07E-001 1.11E-001 4.92E-003 4.62E+000 36 3.70E+001 1.04E-001 1.08E-001 4.27E-003 4.11E+000 37 3.80E+001 1.02E-001 1.05E-001 3.62E-003 3.57E+000 38 3.90E+001 9.95E-002 1.02E-001 2.47E-003 2.48E+000 39 4.00E+001 9.80E-002 9.88E-002 8.20E-004 8.37E-001 40 4.10E+001 9.60E-002 9.57E-002 -3.30E-004 -3.44E-001 41 4.20E+001 9.35E-002 9.25E-002 -9.81E-004 -1.05E+000 42 4.30E+001 8.90E-002 8.94E-002 3.69E-004 4.15E-001 43 4.40E+001 8.60E-002 8.62E-002 2.18E-004 2.54E-001 44 4.50E+001 8.20E-002 8.31E-002 1.07E-003 1.30E+000 45 4.60E+001 8.10E-002 7.99E-002 -1.08E-003 -1.34E+000 46 4.70E+001 7.85E-002 7.68E-002 -1.73E-003 -2.21E+000 47 4.80E+001 7.60E-002 7.36E-002 -2.38E-003 -3.14E+000 48 4.90E+001 7.30E-002 7.05E-002 -2.53E-003 -3.47E+000 49 5.00E+001 7.00E-002 6.73E-002 -2.68E-003 -3.83E+000 50 5.10E+001 6.70E-002 6.42E-002 -2.83E-003 -4.23E+000 51 5.20E+001 6.35E-002 6.10E-002 -2.49E-003 -3.91E+000 52 5.30E+001 5.95E-002 5.79E-002 -1.64E-003 -2.75E+000 53 5.40E+001 5.50E-002 5.47E-002 -2.86E-004 -5.21E-001 54 5.50E+001 5.20E-002 5.16E-002 -4.37E-004 -8.40E-001 55 5.60E+001 4.65E-002 4.84E-002 1.91E-003 4.11E+000 56 5.70E+001 4.30E-002 4.53E-002 2.26E-003 5.26E+000 57 5.80E+001 4.20E-002 4.21E-002 1.12E-004 2.66E-001 58 5.90E+001 4.10E-002 3.90E-002 -2.04E-003 -4.97E+000 59 6.00E+001 4.00E-002 3.58E-002 -4.19E-003 -1.05E+001 **

correlation coefficient = 9.966944E-001

[ ... ] [ ... ]

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. :-)

Enjoy, DoN.

[snipped]

Wonderful to read!

Nick

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

"Bravo" for this link, filled with a lot of treasures (a smile for Human Assisted Machine)

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.

Thanks, DoN.

Never mind! I got it going eventually. THe first syntax turned out to be the correct one, and it was antilog base 10, or in C:

T = pow( 10, calculated-value);

Thanks, DoN.