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Thread: Numbered drills - wherefrom?

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    mklotz mklotz's Avatar
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    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.

    ----------------------
    * 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
    ---
    Regards, Marv


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  2. The Following 4 Users Say Thank You to mklotz For This Useful Post:

    Big Mike71 (01-02-2017), Frank S (01-02-2017), PJs (11-04-2016), Toolmaker51 (11-05-2016)

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    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.


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