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

Gil HASH wrote:
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) ?


http://en.wikipedia.org/wiki/Drill_bit_sizes

http://users.ticnet.com/mikefirth/drill.htm

Note that there are also letter drills.

Steve

Gil HASH wrote:

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) ?

"Gil HASH" wrote in message
...
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) ?

Here's an on-line table:

http://www.rfcafe.com/references/gen...s_numbered.htm

Mike

Thanks for all links

On Sat, 20 Aug 2005 14:18:11 +0400, the opaque "Gil HASH"
clearly wrote:

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 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)he
http://www.engineersedge.com/Calulators_Online.shtml


-----------------------------------------
Jack Kevorkian for Congressional physician!
http://www.diversify.com 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.

Bob Swinney
"Gil HASH" wrote in message
...
Thanks for all links

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.

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

In article ,
Marvin W. Klotz wrote:
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.

[ ... ]

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.

[ ... ]

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.

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.

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.

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

[ ... ]

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."

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.

--
Email: | Voice (all times): (703) 938-4564
(too) near Washington D.C. | http://www.d-and-d.com/dnichols/DoN.html
--- Black Holes are where God is dividing by zero ---

Marvin W. Klotz wrote:

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

Wonderful to read!


Nick

--
Motormodelle / Engine Models:
http://www.motor-manufaktur.de
Ellwe 2FB * VTM 87 * DLM-S3a * cubic
more to come ...

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

Home Shop Freeware - Tools for People Who Build Things
http://www.geocities.com/mklotz.geo


"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

In article . com,
Bugs wrote:
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]

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.

You can
apply metric conversion to the formula by multiplying by 25.4.

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

Thanks,
DoN.
--
Email: | Voice (all times): (703) 938-4564
(too) near Washington D.C. | http://www.d-and-d.com/dnichols/DoN.html
--- Black Holes are where God is dividing by zero ---

In article ,
DoN. Nichols wrote:
In article . com,
Bugs wrote:
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]

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_.

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.

--
Email: | Voice (all times): (703) 938-4564
(too) near Washington D.C. | http://www.d-and-d.com/dnichols/DoN.html
--- Black Holes are where God is dividing by zero ---