On Sat, 20 Aug 2005 18:43:34 -0500, Don Foreman
wrote:

On Sat, 20 Aug 2005 13:51:53 -0500, "Robert Swinney"
wrote:

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
http://www.geocities.com/mklotz.geo


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