Numbered drills - wherefrom?

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. (See mathematical details 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.

The last fellow who inquired about this also wanted to know the origin of the numbered drills. That set me off to do a bit of research and I decided to pass my findings along.

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 drawing it through successively smaller dies. This is done again and again to produce the finer wire sizes. Now, the folks who run wire mills decided to start labeling their wire by the number of times it's been drawn. This might have made sense in the mill but, unfortunately into the outside world and came into common use. If ever there was an argument for adopting the sensible 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 Inferial* 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 folks 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 Inferial 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 drill nomenclature.

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* The USA does not use the Imperial system. The correct name for our system is the American Customary Units. Of course, ACU is derived from the Imperial system with some uniquely American confusions thrown in to trap the unwary. I prefer to refer to our system as the "inferial" system, my own portmanteau of "inferior" or "infuriating" and "Imperial".

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

Fantastic explanation! After reading it several times and devoting my best logic and expertise, I simplify the question.
Should I use the big drill bit or the little one? A little humor is good for my soul.