# Air Line Coax from Brass/Copper Tubing

A project log for The Rise and Fall of Pulses

A project in which I try to go faster and faster

Ted Yapo 09/07/2019 at 23:100 Comments

You know you want to make some air-line coax for an impedance reference from brass hobby tubing. But, what sizes to use? I threw together a quick python script to find the characteristic impedance and cutoff frequencies for all the combinations.

The script uses all the available sizes (metric and inch) of K&S brass tubing. Some sizes are also available in copper, and any of them could be silver plated, although this probably isn't necessary for short sections.

I haven't built any coax this way yet, but now I know which sizes to select.

# Calculations

The characteristic impedance of coax is given by:

where D is the inner diameter of the outer conductor, and d is the outer diameter of the inner conductor. The diameter units cancel.

# Cutoff Frequency

At lower frequencies, waves travel in coax in the so-called transverse electromagnetic mode (TEM), where the electric and magnetic fields are both perpendicular to the direction of travel (i.e. the coax). Above a certain frequency, called the cutoff, higher-order modes can also exist on the cable. These propagate at different speeds, and generally ruin your day.

The cutoff frequency for coax is given by:

with D and d in inches.

In both cases, the code uses Er = 1.00058986, the value for air.

# Code

The python code calculates the characteristic impedance and cutoff frequency for all the combinations of K&R tubing sizes:

```#!/usr/bin/env python3

import numpy as np
from fractions import Fraction

# (name, OD, ID) inches

US_idx = np.linspace(1, 21, 21)
US_tubing = map(lambda x: (str(Fraction(int(x), 32))+'"',
x/32, x/32 - 0.028), US_idx)

mm_idx1 = [1, 1.5, 2, 3, 3.5, 4, 4.5, 5]
mm_idx2 = [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]

mm_tubing1 = map(lambda x: (str(x) + '/0.225 mm', x/25.4, (x-2*0.225)/25.4), mm_idx1)
mm_tubing2 = map(lambda x: (str(x) + '/0.45 mm', x/25.4, (x-2*0.45)/25.4), mm_idx2)

tubing = list(US_tubing) + list( mm_tubing1) + list(mm_tubing2)

Er = 1.00058986

table = []

print('       Inner        Outer   Cutoff     Z0')
print('                             (GHz)   (Ohm)')
print('--------------------------------------------')
for outer in tubing:
for inner in tubing:
if inner[1] >= outer[2]:
continue
Z0 = 138 * np.log10(outer[2]/inner[1])/np.sqrt(Er)
fc = 7.51393 / ((inner[1] + outer[2])*np.sqrt(Er))
table.append((inner[0], outer[0], fc, Z0))

for i in sorted(table, key=lambda x: x[3]):
print('{:>12s}  {:>12s}  {:5.1f}  {:6.2f}'.format(i[0], i[1], i[2], i[3]))

```

# Table

Here are the results. For the really low-Z combinations, although the tubing would fit based on the nominal sizes, it would probably short out due to manufacturing tolerances.

```       Inner        Outer   Cutoff     Z0
(GHz)   (Ohm)
--------------------------------------------
8/0.45 mm        11/32"   11.9    0.15
5/8"        21/32"    6.0    0.31
19/32"          5/8"    6.3    0.33
9/16"        19/32"    6.7    0.35
17/32"         9/16"    7.0    0.37
1/2"        17/32"    7.5    0.39
15/32"          1/2"    8.0    0.41
7/16"        15/32"    8.6    0.44
13/32"         7/16"    9.2    0.48
12/0.45 mm    13/0.45 mm    7.9    0.50
3/8"        13/32"   10.0    0.52
11/0.45 mm    12/0.45 mm    8.6    0.54
11/32"          3/8"   10.9    0.56
10/0.45 mm    11/0.45 mm    9.5    0.60
5/16"        11/32"   12.0    0.62
4.5/0.225 mm    5/0.225 mm   21.1    0.66
9/0.45 mm    10/0.45 mm   10.5    0.66
9/32"         5/16"   13.3    0.69
4/0.225 mm  4.5/0.225 mm   23.7    0.74
4/0.45 mm  4.5/0.225 mm   23.7    0.74
8/0.45 mm     9/0.45 mm   11.9    0.74
4/0.225 mm         3/16"   23.7    0.76
4/0.45 mm         3/16"   23.7    0.76
1/4"         9/32"   14.9    0.77
3.5/0.225 mm    4/0.225 mm   27.1    0.85
7/0.45 mm     8/0.45 mm   13.5    0.85
7/32"          1/4"   17.0    0.88
15/32"    13/0.45 mm    7.9    0.97
3/0.225 mm  3.5/0.225 mm   31.5    0.99
3/0.45 mm  3.5/0.225 mm   31.5    0.99
6/0.45 mm     7/0.45 mm   15.8    0.99
3/16"         7/32"   19.9    1.03
11/0.45 mm        15/32"    8.6    1.05
5/0.225 mm     6/0.45 mm   18.9    1.19
5/0.45 mm     6/0.45 mm   18.9    1.19
5/32"  4.5/0.225 mm   23.8    1.21
5/16"     9/0.45 mm   11.9    1.21
5/32"         3/16"   23.8    1.23
4/0.225 mm     5/0.45 mm   23.6    1.48
4/0.45 mm     5/0.45 mm   23.6    1.48
1/8"         5/32"   29.7    1.54
7/0.45 mm         5/16"   13.4    1.91
5/32"     5/0.45 mm   23.6    1.95
1.5/0.225 mm    2/0.225 mm   62.6    1.96
3/0.225 mm     4/0.45 mm   31.3    1.96
3/0.45 mm     4/0.45 mm   31.3    1.96
3/32"          1/8"   39.4    2.04
10/0.45 mm         7/16"    9.4    2.36
11/32"    10/0.45 mm   10.7    2.48
13/0.45 mm         9/16"    7.2    2.60
1/0.225 mm  1.5/0.225 mm   93.1    2.92
2/0.225 mm     3/0.45 mm   46.5    2.92
2/0.45 mm     3/0.45 mm   46.5    2.92
1/16"         3/32"   58.6    3.04
19/32"        21/32"    6.1    3.38
3/8"    11/0.45 mm    9.7    3.51
9/16"          5/8"    6.5    3.57
17/32"        19/32"    6.8    3.77
12/0.45 mm        17/32"    7.7    3.79
9/0.45 mm        13/32"   10.3    3.91
1/2"         9/16"    7.3    4.00
3/32"    3/0.225 mm   38.7    4.10
3/16"     6/0.45 mm   19.3    4.10
6/0.45 mm         9/32"   15.3    4.17
15/32"        17/32"    7.7    4.26
13/32"    12/0.45 mm    8.9    4.37
4.5/0.225 mm         7/32"   20.4    4.43
7/16"          1/2"    8.3    4.55
13/32"        15/32"    8.9    4.88
3/0.225 mm         5/32"   30.5    4.93
3/0.45 mm         5/32"   30.5    4.93
7/16"    13/0.45 mm    8.2    5.10
11/0.45 mm          1/2"    8.3    5.16
3/8"         7/16"    9.6    5.27
7/32"     7/0.45 mm   16.4    5.59
11/0.45 mm    13/0.45 mm    8.3    5.71
1/0.225 mm     2/0.45 mm   90.9    5.71
11/32"        13/32"   10.4    5.73
8/0.45 mm          3/8"   11.3    5.80
1/32"         1/16"  114.2    5.93
13/0.45 mm        19/32"    7.0    6.00
10/0.45 mm    12/0.45 mm    9.0    6.25
5/16"          3/8"   11.4    6.27
1.5/0.225 mm         3/32"   60.2    6.43
9/16"        21/32"    6.3    6.62
1/8"    4/0.225 mm   28.4    6.69
1/4"     8/0.45 mm   14.2    6.69
10/0.45 mm        15/32"    9.0    6.76
9/0.45 mm    11/0.45 mm   10.0    6.91
9/32"        11/32"   12.6    6.93
17/32"          5/8"    6.7    6.99
5/0.225 mm          1/4"   17.9    7.20
5/0.45 mm          1/4"   17.9    7.20
12/0.45 mm         9/16"    7.5    7.39
1/2"        19/32"    7.0    7.40
4.5/0.225 mm     6/0.45 mm   19.9    7.50
9/32"     9/0.45 mm   12.5    7.53
4/0.225 mm    5/0.225 mm   22.3    7.72
4/0.45 mm    5/0.225 mm   22.3    7.72
8/0.45 mm    10/0.45 mm   11.2    7.72
1/4"         5/16"   14.1    7.75
15/32"         9/16"    7.5    7.86
7/0.45 mm        11/32"   12.7    8.15
5/32"    5/0.225 mm   22.4    8.19
5/16"    10/0.45 mm   11.2    8.19
7/16"        17/32"    8.0    8.39
9/0.45 mm         7/16"    9.8    8.67
11/32"    11/0.45 mm   10.1    8.73
3.5/0.225 mm  4.5/0.225 mm   25.3    8.74
7/0.45 mm     9/0.45 mm   12.6    8.74
3.5/0.225 mm         3/16"   25.3    8.76
7/32"         9/32"   15.9    8.77
13/32"          1/2"    8.6    8.99
11/0.45 mm        17/32"    8.0    9.00
3/8"    12/0.45 mm    9.3    9.17
13/0.45 mm          5/8"    6.8    9.22
3.5/0.225 mm     5/0.45 mm   25.1    9.48
13/32"    13/0.45 mm    8.5    9.54
3/8"        15/32"    9.2    9.68
17/32"        21/32"    6.5   10.05
3/0.225 mm    4/0.225 mm   29.1   10.09
3/0.45 mm    4/0.225 mm   29.1   10.09
6/0.45 mm     8/0.45 mm   14.6   10.09
3/16"          1/4"   18.3   10.12
11/32"         7/16"   10.0   10.49
1/2"          5/8"    6.8   10.62
12/0.45 mm        19/32"    7.2   10.80
10/0.45 mm          1/2"    8.7   10.87
8/0.45 mm        13/32"   10.8   10.97
6/0.45 mm         5/16"   14.4   11.14
15/32"        19/32"    7.3   11.27
10/0.45 mm    13/0.45 mm    8.6   11.42
5/16"        13/32"   10.9   11.44
4/0.225 mm         7/32"   21.6   11.48
4/0.45 mm         7/32"   21.6   11.48
5/0.225 mm     7/0.45 mm   17.2   11.91
5/0.45 mm     7/0.45 mm   17.2   11.91
5/32"         7/32"   21.6   11.95
7/16"         9/16"    7.7   12.00
13/0.45 mm        21/32"    6.6   12.28
2/0.225 mm          1/8"   42.7   12.50
2/0.45 mm          1/8"   42.7   12.50
9/0.45 mm    12/0.45 mm    9.5   12.57
9/32"          3/8"   12.0   12.59
11/0.45 mm         9/16"    7.8   12.61
13/32"        17/32"    8.3   12.83
9/0.45 mm        15/32"    9.4   13.08
4.5/0.225 mm          1/4"   18.8   13.52
1/2"        21/32"    6.7   13.68
3/8"          1/2"    8.9   13.78
7/0.45 mm          3/8"   12.1   13.80
8/0.45 mm    11/0.45 mm   10.5   13.97
1/4"        11/32"   13.3   13.99
12/0.45 mm          5/8"    7.0   14.02
3/8"    13/0.45 mm    8.8   14.34
11/32"    12/0.45 mm    9.6   14.38
5/16"    11/0.45 mm   10.6   14.44
15/32"          5/8"    7.0   14.49
9/32"    10/0.45 mm   11.7   14.50
2/0.225 mm    3/0.225 mm   41.9   14.56
2/0.45 mm    3/0.225 mm   41.9   14.56
4/0.225 mm     6/0.45 mm   21.0   14.56
4/0.45 mm     6/0.45 mm   21.0   14.56
1/8"  4.5/0.225 mm   26.4   14.58
1/4"     9/0.45 mm   13.2   14.58
1/8"         3/16"   26.4   14.60
7/32"     8/0.45 mm   15.1   14.69
10/0.45 mm        17/32"    8.4   14.71
3/32"  3.5/0.225 mm   35.1   14.83
3/16"     7/0.45 mm   17.6   14.83
11/32"        15/32"    9.6   14.89
5/32"     6/0.45 mm   21.0   15.03
5/0.225 mm         9/32"   16.7   15.09
5/0.45 mm         9/32"   16.7   15.09
1/8"     5/0.45 mm   26.2   15.32
7/16"        19/32"    7.5   15.40
3.5/0.225 mm    5/0.225 mm   23.7   15.72
7/0.45 mm    10/0.45 mm   11.9   15.72
8/0.45 mm         7/16"   10.4   15.73
7/32"         5/16"   14.9   15.75
3/32"     4/0.45 mm   34.8   15.80
11/0.45 mm        19/32"    7.5   16.01
5/16"         7/16"   10.4   16.20
13/32"         9/16"    8.0   16.44
1/32"  1.5/0.225 mm  103.5   16.76
1/16"     3/0.45 mm   51.7   16.76
12/0.45 mm        21/32"    6.8   17.08
9/0.45 mm          1/2"    9.1   17.18
6/0.45 mm        11/32"   13.6   17.39
15/32"        21/32"    6.8   17.55
3/8"        17/32"    8.6   17.62
9/0.45 mm    13/0.45 mm    9.0   17.73
9/32"        13/32"   11.4   17.75
3/0.225 mm  4.5/0.225 mm   27.1   17.98
3/0.45 mm  4.5/0.225 mm   27.1   17.98
6/0.45 mm     9/0.45 mm   13.5   17.98
3/0.225 mm         3/16"   27.1   18.00
3/0.45 mm         3/16"   27.1   18.00
3/16"         9/32"   17.0   18.01
4.5/0.225 mm     7/0.45 mm   18.0   18.23
10/0.45 mm         9/16"    8.1   18.32
7/16"          5/8"    7.3   18.62
3/0.225 mm     5/0.45 mm   26.9   18.72
3/0.45 mm     5/0.45 mm   26.9   18.72
3/32"         5/32"   33.8   18.77
7/0.45 mm        13/32"   11.5   18.97
11/32"          1/2"    9.2   19.00
11/0.45 mm          5/8"    7.3   19.23
3.5/0.225 mm         7/32"   22.9   19.48
11/32"    13/0.45 mm    9.2   19.55
1/32"     2/0.45 mm  100.8   19.55
8/0.45 mm    12/0.45 mm   10.0   19.62
1/4"          3/8"   12.6   19.64
13/32"        19/32"    7.7   19.84
5/16"    12/0.45 mm   10.0   20.09
8/0.45 mm        15/32"    9.9   20.13
1.5/0.225 mm     3/0.45 mm   53.0   20.16
4/0.225 mm          1/4"   19.8   20.57
4/0.45 mm          1/4"   19.8   20.57
5/16"        15/32"   10.0   20.60
9/32"    11/0.45 mm   11.1   20.75
5/0.225 mm     8/0.45 mm   15.8   21.01
5/0.45 mm     8/0.45 mm   15.8   21.01
9/0.45 mm        17/32"    8.8   21.02
5/32"          1/4"   19.9   21.04
3/8"         9/16"    8.3   21.23
4.5/0.225 mm         9/32"   17.5   21.41
1/8"    5/0.225 mm   24.7   21.56
1/4"    10/0.45 mm   12.3   21.56
7/16"        21/32"    7.0   21.68
10/0.45 mm        19/32"    7.8   21.72
7/0.45 mm    11/0.45 mm   11.2   21.97
7/32"        11/32"   14.1   21.99
5/0.225 mm         5/16"   15.6   22.07
5/0.45 mm         5/16"   15.6   22.07
11/0.45 mm        21/32"    7.1   22.29
9/32"         7/16"   10.9   22.51
3.5/0.225 mm     6/0.45 mm   22.2   22.56
7/32"     9/0.45 mm   14.0   22.58
11/32"        17/32"    8.9   22.84
6/0.45 mm          3/8"   12.9   23.04
13/32"          5/8"    7.5   23.06
7/0.45 mm         7/16"   11.0   23.73
3/32"    4/0.225 mm   32.2   23.93
3/16"     8/0.45 mm   16.1   23.93
8/0.45 mm          1/2"    9.5   24.24
9/0.45 mm         9/16"    8.5   24.63
3/8"        19/32"    8.0   24.64
5/16"          1/2"    9.6   24.71
8/0.45 mm    13/0.45 mm    9.5   24.79
1/4"        13/32"   12.0   24.81
10/0.45 mm          5/8"    7.6   24.94
3/0.225 mm    5/0.225 mm   25.3   24.96
3/0.45 mm    5/0.225 mm   25.3   24.96
6/0.45 mm    10/0.45 mm   12.6   24.96
3/16"         5/16"   15.9   24.98
5/16"    13/0.45 mm    9.5   25.26
2/0.225 mm  3.5/0.225 mm   37.8   25.28
2/0.45 mm  3.5/0.225 mm   37.8   25.28
4/0.225 mm     7/0.45 mm   18.9   25.28
4/0.45 mm     7/0.45 mm   18.9   25.28
1/8"         7/32"   23.8   25.32
5/32"     7/0.45 mm   18.9   25.75
13/32"        21/32"    7.3   26.12
1/0.225 mm    2/0.225 mm   74.8   26.26
2/0.225 mm     4/0.45 mm   37.4   26.26
2/0.45 mm     4/0.45 mm   37.4   26.26
1/16"          1/8"   47.1   26.34
9/32"    12/0.45 mm   10.5   26.40
11/32"         9/16"    8.6   26.45
9/32"        15/32"   10.4   26.92
4.5/0.225 mm     8/0.45 mm   16.4   27.32
7/0.45 mm    12/0.45 mm   10.5   27.62
7/32"          3/8"   13.3   27.64
1/4"    11/0.45 mm   11.6   27.81
3/8"          5/8"    7.7   27.86
10/0.45 mm        21/32"    7.4   28.00
9/0.45 mm        19/32"    8.2   28.04
8/0.45 mm        17/32"    9.2   28.08
7/0.45 mm        15/32"   10.5   28.13
6/0.45 mm        13/32"   12.2   28.21
5/0.225 mm        11/32"   14.7   28.31
5/0.45 mm        11/32"   14.7   28.31
4.5/0.225 mm         5/16"   16.3   28.38
1/16"    3/0.225 mm   46.1   28.40
1/8"     6/0.45 mm   23.1   28.40
4/0.225 mm         9/32"   18.3   28.46
4/0.45 mm         9/32"   18.3   28.46
5/16"        17/32"    9.2   28.55
3.5/0.225 mm          1/4"   20.9   28.57
3/0.225 mm         7/32"   24.3   28.72
3/0.45 mm         7/32"   24.3   28.72
5/0.225 mm     9/0.45 mm   14.6   28.90
5/0.45 mm     9/0.45 mm   14.6   28.90
5/32"         9/32"   18.3   28.93
2/0.225 mm         5/32"   36.3   29.23
2/0.45 mm         5/32"   36.3   29.23
7/32"    10/0.45 mm   13.0   29.56
1/4"         7/16"   11.4   29.57
1.5/0.225 mm          1/8"   48.1   29.73
11/32"        19/32"    8.3   29.85
1/0.225 mm         3/32"   71.5   30.73
3/8"        21/32"    7.5   30.92
9/32"          1/2"   10.0   31.02
6/0.45 mm    11/0.45 mm   11.9   31.20
3/16"        11/32"   14.9   31.23
9/0.45 mm          5/8"    7.9   31.26
9/32"    13/0.45 mm    9.9   31.57
8/0.45 mm         9/16"    8.8   31.69
1.5/0.225 mm    3/0.225 mm   47.1   31.79
3/0.225 mm     6/0.45 mm   23.6   31.79
3/0.45 mm     6/0.45 mm   23.6   31.79
3/32"  4.5/0.225 mm   29.7   31.82
3/16"     9/0.45 mm   14.8   31.82
3/32"         3/16"   29.7   31.84
5/16"         9/16"    8.9   32.16
7/0.45 mm          1/2"   10.0   32.24
3/32"     5/0.45 mm   29.4   32.56
7/0.45 mm    13/0.45 mm   10.0   32.79
7/32"        13/32"   12.6   32.81
6/0.45 mm         7/16"   11.6   32.96
11/32"          5/8"    8.0   33.07
3.5/0.225 mm     7/0.45 mm   19.9   33.28
1/4"    12/0.45 mm   10.9   33.46
5/0.225 mm          3/8"   13.8   33.96
5/0.45 mm          3/8"   13.8   33.96
1/4"        15/32"   10.9   33.97
9/0.45 mm        21/32"    7.6   34.31
2/0.225 mm    4/0.225 mm   34.4   34.38
2/0.45 mm    4/0.225 mm   34.4   34.38
4/0.225 mm     8/0.45 mm   17.2   34.38
4/0.45 mm     8/0.45 mm   17.2   34.38
1/8"          1/4"   21.6   34.41
4.5/0.225 mm        11/32"   15.2   34.62
5/32"     8/0.45 mm   17.2   34.85
9/32"        17/32"    9.6   34.86
8/0.45 mm        19/32"    8.5   35.09
4.5/0.225 mm     9/0.45 mm   15.1   35.22
4/0.225 mm         5/16"   17.0   35.44
4/0.45 mm         5/16"   17.0   35.44
5/16"        19/32"    8.6   35.56
7/32"    11/0.45 mm   12.2   35.81
5/0.225 mm    10/0.45 mm   13.5   35.88
5/0.45 mm    10/0.45 mm   13.5   35.88
5/32"         5/16"   17.0   35.91
7/0.45 mm        17/32"    9.6   36.08
11/32"        21/32"    7.7   36.13
3.5/0.225 mm         9/32"   19.2   36.46
6/0.45 mm    12/0.45 mm   11.2   36.86
3/16"          3/8"   14.1   36.88
6/0.45 mm        15/32"   11.1   37.37
7/32"         7/16"   12.0   37.57
3/0.225 mm          1/4"   22.1   37.81
3/0.45 mm          1/4"   22.1   37.81
1/4"          1/2"   10.4   38.08
8/0.45 mm          5/8"    8.2   38.31
9/32"         9/16"    9.2   38.47
1/4"    13/0.45 mm   10.3   38.63
5/16"          5/8"    8.3   38.78
3/32"    5/0.225 mm   27.5   38.80
3/16"    10/0.45 mm   13.8   38.80
1/16"  3.5/0.225 mm   41.1   39.12
1/8"     7/0.45 mm   20.6   39.12
5/0.225 mm        13/32"   13.1   39.13
5/0.45 mm        13/32"   13.1   39.13
7/0.45 mm         9/16"    9.3   39.69
1/32"    2/0.225 mm   81.4   40.10
1/16"     4/0.45 mm   40.7   40.10
4.5/0.225 mm          3/8"   14.3   40.28
8/0.45 mm        21/32"    8.0   41.37
7/32"    12/0.45 mm   11.5   41.46
6/0.45 mm          1/2"   10.6   41.47
4/0.225 mm        11/32"   15.9   41.68
4/0.45 mm        11/32"   15.9   41.68
5/16"        21/32"    8.0   41.84
9/32"        19/32"    8.9   41.88
1/4"        17/32"   10.0   41.92
7/32"        15/32"   11.4   41.97
6/0.45 mm    13/0.45 mm   10.5   42.03
3/16"        13/32"   13.3   42.05
5/0.225 mm    11/0.45 mm   12.6   42.13
5/0.45 mm    11/0.45 mm   12.6   42.13
5/32"        11/32"   15.9   42.15
4.5/0.225 mm    10/0.45 mm   14.0   42.19
2/0.225 mm  4.5/0.225 mm   31.5   42.27
2/0.45 mm  4.5/0.225 mm   31.5   42.27
4/0.225 mm     9/0.45 mm   15.8   42.27
4/0.45 mm     9/0.45 mm   15.8   42.27
2/0.225 mm         3/16"   31.5   42.29
2/0.45 mm         3/16"   31.5   42.29
1/8"         9/32"   19.9   42.30
3.5/0.225 mm     8/0.45 mm   18.0   42.38
1.5/0.225 mm  3.5/0.225 mm   41.9   42.52
3/0.225 mm     7/0.45 mm   21.0   42.52
3/0.45 mm     7/0.45 mm   21.0   42.52
3/32"         7/32"   26.4   42.56
5/32"     9/0.45 mm   15.8   42.74
2/0.225 mm     5/0.45 mm   31.3   43.01
2/0.45 mm     5/0.45 mm   31.3   43.01
1/16"         5/32"   39.4   43.07
7/0.45 mm        19/32"    8.9   43.09
3.5/0.225 mm         5/16"   17.8   43.44
1.5/0.225 mm     4/0.45 mm   41.5   43.49
5/0.225 mm         7/16"   12.4   43.89
5/0.45 mm         7/16"   12.4   43.89
1/0.225 mm     3/0.45 mm   61.5   44.45
1/32"         3/32"   77.4   44.57
3/16"    11/0.45 mm   12.8   45.04
9/32"          5/8"    8.6   45.10
6/0.45 mm        17/32"   10.2   45.31
4.5/0.225 mm        13/32"   13.5   45.44
1/4"         9/16"    9.6   45.53
3/32"     6/0.45 mm   25.5   45.63
3/0.225 mm         9/32"   20.2   45.70
3/0.45 mm         9/32"   20.2   45.70
7/32"          1/2"   10.9   46.08
7/0.45 mm          5/8"    8.6   46.31
1.5/0.225 mm         5/32"   40.1   46.46
7/32"    13/0.45 mm   10.8   46.63
3/16"         7/16"   12.6   46.80
4/0.225 mm          3/8"   14.9   47.33
4/0.45 mm          3/8"   14.9   47.33
5/0.225 mm    12/0.45 mm   11.9   47.78
5/0.45 mm    12/0.45 mm   11.9   47.78
5/32"          3/8"   14.9   47.80
9/32"        21/32"    8.3   48.15
1/16"    4/0.225 mm   37.1   48.22
1/8"     8/0.45 mm   18.6   48.22
5/0.225 mm        15/32"   11.8   48.29
5/0.45 mm        15/32"   11.8   48.29
4.5/0.225 mm    11/0.45 mm   13.1   48.44
6/0.45 mm         9/16"    9.7   48.92
1/4"        19/32"    9.2   48.93
2/0.225 mm    5/0.225 mm   29.1   49.25
2/0.45 mm    5/0.225 mm   29.1   49.25
4/0.225 mm    10/0.45 mm   14.6   49.25
4/0.45 mm    10/0.45 mm   14.6   49.25
1/8"         5/16"   18.3   49.28
7/0.45 mm        21/32"    8.3   49.37
3.5/0.225 mm        11/32"   16.6   49.68
5/32"    10/0.45 mm   14.6   49.72
7/32"        17/32"   10.4   49.92
4.5/0.225 mm         7/16"   12.8   50.20
3.5/0.225 mm     9/0.45 mm   16.4   50.27
3/16"    12/0.45 mm   12.0   50.70
3/16"        15/32"   12.0   51.21
1.5/0.225 mm    4/0.225 mm   37.8   51.62
3/0.225 mm     8/0.45 mm   18.9   51.62
3/0.45 mm     8/0.45 mm   18.9   51.62
3/32"          1/4"   23.8   51.65
1/4"          5/8"    8.9   52.15
6/0.45 mm        19/32"    9.4   52.33
5/0.225 mm          1/2"   11.2   52.40
5/0.45 mm          1/2"   11.2   52.40
4/0.225 mm        13/32"   14.0   52.50
4/0.45 mm        13/32"   14.0   52.50
3/0.225 mm         5/16"   18.7   52.67
3/0.45 mm         5/16"   18.7   52.67
5/0.225 mm    13/0.45 mm   11.2   52.95
5/0.45 mm    13/0.45 mm   11.2   52.95
5/32"        13/32"   14.1   52.97
2/0.225 mm         7/32"   27.9   53.01
2/0.45 mm         7/32"   27.9   53.01
7/32"         9/16"   10.0   53.53
1/0.225 mm          1/8"   55.1   54.03
4.5/0.225 mm    12/0.45 mm   12.2   54.10
4.5/0.225 mm        15/32"   12.2   54.61
1/4"        21/32"    8.6   55.21
3/16"          1/2"   11.4   55.31
3.5/0.225 mm          3/8"   15.5   55.33
4/0.225 mm    11/0.45 mm   13.5   55.50
4/0.45 mm    11/0.45 mm   13.5   55.50
1/8"        11/32"   17.0   55.52
6/0.45 mm          5/8"    9.0   55.55
3/16"    13/0.45 mm   11.3   55.87
5/32"    11/0.45 mm   13.6   55.97
1/0.225 mm    3/0.225 mm   53.7   56.09
2/0.225 mm     6/0.45 mm   26.9   56.09
2/0.45 mm     6/0.45 mm   26.9   56.09
1/16"  4.5/0.225 mm   33.8   56.11
1/8"     9/0.45 mm   16.9   56.11
1/16"         3/16"   33.8   56.13
5/0.225 mm        17/32"   10.7   56.24
5/0.45 mm        17/32"   10.7   56.24
3/32"     7/0.45 mm   22.5   56.36
1/16"     5/0.45 mm   33.5   56.85
7/32"        19/32"    9.6   56.93
3.5/0.225 mm    10/0.45 mm   15.1   57.25
4/0.225 mm         7/16"   13.2   57.26
4/0.45 mm         7/16"   13.2   57.26
5/32"         7/16"   13.3   57.73
1/32"     3/0.45 mm   65.9   58.29
6/0.45 mm        21/32"    8.7   58.61
4.5/0.225 mm          1/2"   11.6   58.71
3/0.225 mm        11/32"   17.3   58.92
3/0.45 mm        11/32"   17.3   58.92
3/16"        17/32"   10.9   59.15
4.5/0.225 mm    13/0.45 mm   11.5   59.26
1.5/0.225 mm  4.5/0.225 mm   34.4   59.51
3/0.225 mm     9/0.45 mm   17.2   59.51
3/0.45 mm     9/0.45 mm   17.2   59.51
1.5/0.225 mm         3/16"   34.4   59.53
3/32"         9/32"   21.6   59.54
5/0.225 mm         9/16"   10.3   59.85
5/0.45 mm         9/16"   10.3   59.85
7/32"          5/8"    9.2   60.15
1.5/0.225 mm     5/0.45 mm   34.1   60.25
3.5/0.225 mm        13/32"   14.6   60.50
4/0.225 mm    12/0.45 mm   12.6   61.15
4/0.45 mm    12/0.45 mm   12.6   61.15
1/8"          3/8"   15.9   61.17
5/32"    12/0.45 mm   12.7   61.62
4/0.225 mm        15/32"   12.6   61.66
4/0.45 mm        15/32"   12.6   61.66
2/0.225 mm          1/4"   25.0   62.10
2/0.45 mm          1/4"   25.0   62.10
5/32"        15/32"   12.6   62.13
4.5/0.225 mm        17/32"   11.0   62.55
3/16"         9/16"   10.4   62.76
1/16"    5/0.225 mm   31.1   63.09
1/8"    10/0.45 mm   15.5   63.09
7/32"        21/32"    8.9   63.21
5/0.225 mm        19/32"    9.9   63.25
5/0.45 mm        19/32"    9.9   63.25
3.5/0.225 mm    11/0.45 mm   14.0   63.50
3/0.225 mm          3/8"   16.2   64.57
3/0.45 mm          3/8"   16.2   64.57
3.5/0.225 mm         7/16"   13.7   65.26
3/32"     8/0.45 mm   20.1   65.46
4/0.225 mm          1/2"   11.9   65.77
4/0.45 mm          1/2"   11.9   65.77
4.5/0.225 mm         9/16"   10.6   66.16
3/16"        19/32"   10.0   66.17
5/32"          1/2"   12.0   66.24
4/0.225 mm    13/0.45 mm   11.9   66.32
4/0.45 mm    13/0.45 mm   11.9   66.32
1/8"        13/32"   14.9   66.34
5/0.225 mm          5/8"    9.5   66.47
5/0.45 mm          5/8"    9.5   66.47
1.5/0.225 mm    5/0.225 mm   31.5   66.49
3/0.225 mm    10/0.45 mm   15.8   66.49
3/0.45 mm    10/0.45 mm   15.8   66.49
3/32"         5/16"   19.9   66.51
5/32"    13/0.45 mm   11.9   66.79
1/0.225 mm  3.5/0.225 mm   47.1   66.81
2/0.225 mm     7/0.45 mm   23.6   66.81
2/0.45 mm     7/0.45 mm   23.6   66.81
1/16"         7/32"   29.7   66.85
1/0.225 mm     4/0.45 mm   46.5   67.79
1/32"          1/8"   58.6   67.87
3.5/0.225 mm    12/0.45 mm   13.1   69.15
1/8"    11/0.45 mm   14.4   69.34
3/16"          5/8"    9.6   69.39
5/0.225 mm        21/32"    9.1   69.53
5/0.45 mm        21/32"    9.1   69.53
4.5/0.225 mm        19/32"   10.1   69.57
4/0.225 mm        17/32"   11.4   69.61
4/0.45 mm        17/32"   11.4   69.61
3.5/0.225 mm        15/32"   13.0   69.66
3/0.225 mm        13/32"   15.1   69.74
3/0.45 mm        13/32"   15.1   69.74
1/32"    3/0.225 mm   57.1   69.93
1/16"     6/0.45 mm   28.5   69.93
2/0.225 mm         9/32"   22.6   69.99
2/0.45 mm         9/32"   22.6   69.99
5/32"        17/32"   11.4   70.08
1.5/0.225 mm         7/32"   30.1   70.25
1/0.225 mm         5/32"   44.8   70.76
1/8"         7/16"   14.1   71.10
3/16"        21/32"    9.2   72.45
3/0.225 mm    11/0.45 mm   14.6   72.73
3/0.45 mm    11/0.45 mm   14.6   72.73
3/32"        11/32"   18.3   72.76
4.5/0.225 mm          5/8"    9.7   72.79
4/0.225 mm         9/16"   10.9   73.22
4/0.45 mm         9/16"   10.9   73.22
1.5/0.225 mm     6/0.45 mm   28.9   73.32
3/32"     9/0.45 mm   18.2   73.35
5/32"         9/16"   10.9   73.69
3.5/0.225 mm          1/2"   12.3   73.77
3.5/0.225 mm    13/0.45 mm   12.2   74.32
3/0.225 mm         7/16"   14.2   74.49
3/0.45 mm         7/16"   14.2   74.49
1/8"    12/0.45 mm   13.4   74.99
1/8"        15/32"   13.3   75.50
4.5/0.225 mm        21/32"    9.3   75.84
1/0.225 mm    4/0.225 mm   41.9   75.91
2/0.225 mm     8/0.45 mm   21.0   75.91
2/0.45 mm     8/0.45 mm   21.0   75.91
1/16"          1/4"   26.4   75.94
4/0.225 mm        19/32"   10.4   76.62
4/0.45 mm        19/32"   10.4   76.62
2/0.225 mm         5/16"   20.7   76.97
2/0.45 mm         5/16"   20.7   76.97
5/32"        19/32"   10.4   77.09
3.5/0.225 mm        17/32"   11.7   77.61
3/0.225 mm    12/0.45 mm   13.5   78.39
3/0.45 mm    12/0.45 mm   13.5   78.39
3/32"          3/8"   17.0   78.41
3/0.225 mm        15/32"   13.4   78.90
3/0.45 mm        15/32"   13.4   78.90
1.5/0.225 mm          1/4"   26.7   79.34
1/8"          1/2"   12.6   79.61
4/0.225 mm          5/8"   10.0   79.84
4/0.45 mm          5/8"   10.0   79.84
1/8"    13/0.45 mm   12.5   80.16
5/32"          5/8"   10.0   80.31
3/32"    10/0.45 mm   16.6   80.32
1/32"  3.5/0.225 mm   49.6   80.65
1/16"     7/0.45 mm   24.8   80.65
3.5/0.225 mm         9/16"   11.2   81.22
1/32"     4/0.45 mm   49.0   81.63
4/0.225 mm        21/32"    9.6   82.90
4/0.45 mm        21/32"    9.6   82.90
3/0.225 mm          1/2"   12.7   83.00
3/0.45 mm          1/2"   12.7   83.00
2/0.225 mm        11/32"   19.0   83.21
2/0.45 mm        11/32"   19.0   83.21
5/32"        21/32"    9.6   83.37
1/8"        17/32"   12.0   83.45
3/0.225 mm    13/0.45 mm   12.6   83.56
3/0.45 mm    13/0.45 mm   12.6   83.56
3/32"        13/32"   15.9   83.58
1/0.225 mm  4.5/0.225 mm   37.8   83.80
2/0.225 mm     9/0.45 mm   18.9   83.80
2/0.45 mm     9/0.45 mm   18.9   83.80
1/0.225 mm         3/16"   37.8   83.82
1/16"         9/32"   23.8   83.83
1.5/0.225 mm     7/0.45 mm   25.1   84.05
1/0.225 mm     5/0.45 mm   37.4   84.54
1/32"         5/32"   47.1   84.60
3.5/0.225 mm        19/32"   10.7   84.62
3/32"    11/0.45 mm   15.3   86.57
3/0.225 mm        17/32"   12.1   86.84
3/0.45 mm        17/32"   12.1   86.84
1/8"         9/16"   11.4   87.06
1.5/0.225 mm         9/32"   24.1   87.23
3.5/0.225 mm          5/8"   10.2   87.84
3/32"         7/16"   14.9   88.33
2/0.225 mm          3/8"   17.6   88.86
2/0.45 mm          3/8"   17.6   88.86
1/32"    4/0.225 mm   43.9   89.75
1/16"     8/0.45 mm   22.0   89.75
3/0.225 mm         9/16"   11.5   90.45
3/0.45 mm         9/16"   11.5   90.45
1/8"        19/32"   10.9   90.46
1/0.225 mm    5/0.225 mm   34.4   90.78
2/0.225 mm    10/0.45 mm   17.2   90.78
2/0.45 mm    10/0.45 mm   17.2   90.78
1/16"         5/16"   21.6   90.81
3.5/0.225 mm        21/32"    9.8   90.90
3/32"    12/0.45 mm   14.2   92.23
3/32"        15/32"   14.1   92.74
1.5/0.225 mm     8/0.45 mm   22.2   93.15
1/8"          5/8"   10.4   93.68
3/0.225 mm        19/32"   11.0   93.86
3/0.45 mm        19/32"   11.0   93.86
2/0.225 mm        13/32"   16.4   94.03
2/0.45 mm        13/32"   16.4   94.03
1.5/0.225 mm         5/16"   21.9   94.20
1/0.225 mm         7/32"   32.6   94.54
1/8"        21/32"   10.0   96.74
3/32"          1/2"   13.3   96.84
2/0.225 mm    11/0.45 mm   15.8   97.03
2/0.45 mm    11/0.45 mm   15.8   97.03
1/16"        11/32"   19.9   97.05
3/0.225 mm          5/8"   10.5   97.08
3/0.45 mm          5/8"   10.5   97.08
3/32"    13/0.45 mm   13.2   97.40
1/0.225 mm     6/0.45 mm   31.3   97.62
1/32"  4.5/0.225 mm   39.4   97.64
1/16"     9/0.45 mm   19.7   97.64
1/32"         3/16"   39.4   97.66
1/32"     5/0.45 mm   39.0   98.38
2/0.225 mm         7/16"   15.4   98.79
2/0.45 mm         7/16"   15.4   98.79
3/0.225 mm        21/32"   10.1  100.14
3/0.45 mm        21/32"   10.1  100.14
1.5/0.225 mm        11/32"   20.0  100.45
3/32"        17/32"   12.6  100.68
1.5/0.225 mm     9/0.45 mm   19.9  101.04
2/0.225 mm    12/0.45 mm   14.6  102.68
2/0.45 mm    12/0.45 mm   14.6  102.68
1/16"          3/8"   18.3  102.70
2/0.225 mm        15/32"   14.5  103.19
2/0.45 mm        15/32"   14.5  103.19
1/0.225 mm          1/4"   28.7  103.63
3/32"         9/16"   12.0  104.29
1/32"    5/0.225 mm   35.7  104.62
1/16"    10/0.45 mm   17.9  104.62
1.5/0.225 mm          3/8"   18.5  106.10
2/0.225 mm          1/2"   13.6  107.30
2/0.45 mm          1/2"   13.6  107.30
3/32"        19/32"   11.4  107.70
2/0.225 mm    13/0.45 mm   13.5  107.85
2/0.45 mm    13/0.45 mm   13.5  107.85
1/16"        13/32"   17.0  107.87
1.5/0.225 mm    10/0.45 mm   18.0  108.02
1/0.225 mm     7/0.45 mm   26.9  108.34
1/32"         7/32"   33.8  108.38
1/16"    11/0.45 mm   16.3  110.87
3/32"          5/8"   10.9  110.92
2/0.225 mm        17/32"   12.9  111.14
2/0.45 mm        17/32"   12.9  111.14
1.5/0.225 mm        13/32"   17.2  111.27
1/32"     6/0.45 mm   32.4  111.46
1/0.225 mm         9/32"   25.7  111.52
1/16"         7/16"   15.9  112.63
3/32"        21/32"   10.4  113.98
1.5/0.225 mm    11/0.45 mm   16.4  114.26
2/0.225 mm         9/16"   12.2  114.75
2/0.45 mm         9/16"   12.2  114.75
1.5/0.225 mm         7/16"   16.0  116.02
1/16"    12/0.45 mm   15.0  116.52
1/16"        15/32"   14.9  117.03
1/0.225 mm     8/0.45 mm   23.6  117.44
1/32"          1/4"   29.7  117.47
2/0.225 mm        19/32"   11.7  118.15
2/0.45 mm        19/32"   11.7  118.15
1/0.225 mm         5/16"   23.2  118.50
1.5/0.225 mm    12/0.45 mm   15.1  119.92
1.5/0.225 mm        15/32"   15.0  120.43
1/16"          1/2"   14.1  121.14
2/0.225 mm          5/8"   11.1  121.37
2/0.45 mm          5/8"   11.1  121.37
1/16"    13/0.45 mm   13.9  121.69
1/32"     7/0.45 mm   27.7  122.18
2/0.225 mm        21/32"   10.6  124.43
2/0.45 mm        21/32"   10.6  124.43
1.5/0.225 mm          1/2"   14.1  124.53
1/0.225 mm        11/32"   21.2  124.74
1/16"        17/32"   13.3  124.98
1.5/0.225 mm    13/0.45 mm   14.0  125.09
1/0.225 mm     9/0.45 mm   21.0  125.33
1/32"         9/32"   26.4  125.36
1.5/0.225 mm        17/32"   13.4  128.37
1/16"         9/16"   12.6  128.59
1/0.225 mm          3/8"   19.4  130.39
1/32"     8/0.45 mm   24.2  131.28
1.5/0.225 mm         9/16"   12.7  131.98
1/16"        19/32"   12.0  131.99
1/0.225 mm    10/0.45 mm   18.9  132.31
1/32"         5/16"   23.8  132.34
1/16"          5/8"   11.4  135.21
1.5/0.225 mm        19/32"   12.0  135.39
1/0.225 mm        13/32"   18.0  135.56
1/16"        21/32"   10.9  138.27
1/0.225 mm    11/0.45 mm   17.2  138.56
1/32"        11/32"   21.6  138.58
1.5/0.225 mm          5/8"   11.4  138.61
1/32"     9/0.45 mm   21.5  139.17
1/0.225 mm         7/16"   16.7  140.32
1.5/0.225 mm        21/32"   10.9  141.67
1/0.225 mm    12/0.45 mm   15.8  144.21
1/32"          3/8"   19.9  144.23
1/0.225 mm        15/32"   15.6  144.72
1/32"    10/0.45 mm   19.3  146.15
1/0.225 mm          1/2"   14.7  148.83
1/0.225 mm    13/0.45 mm   14.6  149.38
1/32"        13/32"   18.3  149.40
1/32"    11/0.45 mm   17.5  152.40
1/0.225 mm        17/32"   13.8  152.67
1/32"         7/16"   17.0  154.16
1/0.225 mm         9/16"   13.1  156.28
1/32"    12/0.45 mm   16.0  158.05
1/32"        15/32"   15.9  158.56
1/0.225 mm        19/32"   12.4  159.68
1/32"          1/2"   14.9  162.67
1/0.225 mm          5/8"   11.8  162.90
1/32"    13/0.45 mm   14.8  163.22
1/0.225 mm        21/32"   11.3  165.96
1/32"        17/32"   14.1  166.51
1/32"         9/16"   13.3  170.12
1/32"        19/32"   12.6  173.52
1/32"          5/8"   12.0  176.74
1/32"        21/32"   11.4  179.80
```