Formulas and Tables (From the “Pocket Companion,” published by the Carnegie Steel Co.)
Reading edition
1. Weights
The average weight of wrought iron is 480 pounds per cubic foot. A bar 1 inch square and 3 feet long weighs, therefore, exactly 10 pounds. The weight of steel is 2 per cent greater than the weight of wrought iron, or 489.6 pounds. Cast iron weighs 450 pounds to the cubic foot.
2. Lengths
Circumference of circle = diameter × 3.1416. Diameter of circle = circumference × 0.3183. Side of square of equal periphery as circle = diameter × 0.7854. Diameter of circle of equal periphery as square = side × 1.2732. Side of an inscribed square = diameter of circle × 0.7071. Length of arc = number of degrees × diameter × 0.008727.
3. Areas
Triangle = base × half altitude. Parallelogram = base × altitude. Trapezoid = half the sum of the parallel sides × altitude. Trapezium, found by dividing into two triangles. Circle = square of diameter × 0.7854; or, = square of circumference × 0.07958. Sector of circle = length of arc × half radius.
4. Standard Dimensions of Nuts and Bolts
Short diameter of rough nut = 11⁄2 × diameter of bolt + 1⁄8 inch. Short diameter of finished nut = 11⁄2 × diameter of bolt + 1⁄16 inch. Thickness of rough nut = diameter of bolt. Thickness of finished nut = diameter of bolt − 1⁄16 inch. Short diameter of rough head = 11⁄2 × diameter of bolt + 1⁄8 inch. Short diameter of finished head = 11⁄2 × diameter of bolt + 1⁄16 inch. Thickness of rough head = 1⁄2 short diameter of head. Thickness of finished head = diameter of bolt − 1⁄16 inch.
5. Decimals of an Inch for each 1⁄64th
1⁄32ds. 1⁄64ths. Decimal Fraction
1 .015625
1 2 .03125
3 .046875
2 4 .0625 1⁄16
5 .078125
3 6 .09375
7 .109375
4 8 .125 1⁄8
9 .140625
5 10 .15625
11 .171875
6 12 .1875 3⁄16
13 .203125
7 14 .21875
15 .234375
8 16 .25 1⁄4
17 .265625
9 18 .28125
19 .296875
10 20 .3125 5⁄16
21 .328125
11 22 .34375
23 .359375
12 24 .375 3⁄8
25 .390625
13 26 .40625
27 .421875
14 28 .4375 7⁄16
29 .453125
15 30 .46875
31 .484375
16 32 .5 1⁄2
33 .515625
17 34 .53125
35 .546875
18 36 .5625 9⁄16
37 .578125
19 38 .59375
39 .609375
20 40 .625 5⁄8
41 .640625
21 42 .65625
43 .671875
22 44 .6875 11⁄16
45 .703125
23 46 .71875
47 .734375
24 48 .75 3⁄4
49 .765625
25 50 .78125
51 .796875
26 52 .8125 13⁄16
53 .828125
27 54 .84375
55 .859375
28 56 .875 7⁄8
57 .890625
29 58 .90625
59 .921875
30 60 .9375 15⁄16
61 .953125
31 62 .96875
63 .984375
32 64 1. 1
6. Weights of Flat Rolled Steel per Linear Foot
One cubic foot weighing 489.6 pounds
Thick- ness in inches 1″ 11⁄4″ 11⁄2″ 13⁄4″ 2″ 21⁄4″ 21⁄2″ 23⁄4″
3⁄16 .638 .797 .957 1.11 1.28 1.44 1.59 1.75
1⁄4 .850 1.06 1.28 1.49 1.70 1.91 2.12 2.34
5⁄16 1.06 1.33 1.59 1.86 2.12 2.39 2.65 2.92
3⁄8 1.28 1.59 1.92 2.23 2.55 2.87 3.19 3.51
7⁄16 1.49 1.86 2.23 2.60 2.98 3.35 3.72 4.09
1⁄2 1.70 2.12 2.55 2.98 3.40 3.83 4.25 4.67
9⁄16 1.92 2.39 2.87 3.35 3.83 4.30 4.78 5.26
5⁄8 2.12 2.65 3.19 3.72 4.25 4.78 5.31 5.84
11⁄16 2.34 2.92 3.51 4.09 4.67 5.26 5.84 6.43
3⁄4 2.55 3.19 3.83 4.47 5.10 5.75 6.38 7.02
13⁄16 2.76 3.45 4.14 4.84 5.53 6.21 6.90 7.60
7⁄8 2.98 3.72 4.47 5.20 5.95 6.69 7.44 8.18
15⁄16 3.19 3.99 4.78 5.58 6.38 7.18 7.97 8.77
1 3.40 4.25 5.10 5.95 6.80 7.65 8.50 9.35
11⁄16 3.61 4.52 5.42 6.32 7.22 8.13 9.03 9.93
11⁄8 3.83 4.78 5.74 6.70 7.65 8.61 9.57 10.52
13⁄16 4.04 5.05 6.06 7.07 8.08 9.09 10.10 11.11
11⁄4 4.25 5.31 6.38 7.44 8.50 9.57 10.63 11.69
15⁄16 4.46 5.58 6.69 7.81 8.93 10.04 11.16 12.27
13⁄8 4.67 5.84 7.02 8.18 9.35 10.52 11.69 12.85
17⁄16 4.89 6.11 7.34 8.56 9.78 11.00 12.22 13.44
11⁄2 5.10 6.38 7.65 8.93 10.20 11.48 12.75 14.03
19⁄16 5.32 6.64 7.97 9.30 10.63 11.95 13.28 14.61
15⁄8 5.52 6.90 8.29 9.67 11.05 12.43 13.81 15.19
111⁄16 5.74 7.17 8.61 10.04 11.47 12.91 14.34 15.78
13⁄4 5.95 7.44 8.93 10.42 11.90 13.40 14.88 16.37
113⁄16 6.16 7.70 9.24 10.79 12.33 13.86 15.40 16.95
17⁄8 6.38 7.97 9.57 11.15 12.75 14.34 15.94 17.53
115⁄16 6.59 8.24 9.88 11.53 13.18 14.83 16.47 18.12
2 6.80 8.50 10.20 11.90 13.60 15.30 17.00 18.70
Thick- ness in inches 3″ 31⁄4″ 31⁄2″ 33⁄4″ 4″ 41⁄4″ 41⁄2″ 43⁄4″
3⁄16 1.91 2.07 2.23 2.39 2.55 2.71 2.87 3.03
1⁄4 2.55 2.76 2.98 3.19 3.40 3.61 3.83 4.04
5⁄16 3.19 3.45 3.72 3.99 4.25 4.52 4.78 5.05
3⁄8 3.83 4.15 4.47 4.78 5.10 5.42 5.74 6.06
7⁄16 4.46 4.83 5.20 5.58 5.95 6.32 6.70 7.07
1⁄2 5.10 5.53 5.95 6.38 6.80 7.22 7.65 8.08
9⁄16 5.74 6.22 6.70 7.17 7.65 8.13 8.61 9.09
5⁄8 6.38 6.91 7.44 7.97 8.50 9.03 9.57 10.10
11⁄16 7.02 7.60 8.18 8.76 9.35 9.93 10.52 11.11
3⁄4 7.65 8.29 8.93 9.57 10.20 10.84 11.48 12.12
13⁄16 8.29 8.98 9.67 10.36 11.05 11.74 12.43 13.12
7⁄8 8.93 9.67 10.41 11.16 11.90 12.65 13.39 14.13
15⁄16 9.57 10.36 11.16 11.95 12.75 13.55 14.34 15.14
1 10.20 11.05 11.90 12.75 13.60 14.45 15.30 16.15
11⁄16 10.84 11.74 12.65 13.55 14.45 15.35 16.26 17.16
11⁄8 11.48 12.43 13.39 14.34 15.30 16.26 17.22 18.17
13⁄16 12.12 13.12 14.13 15.14 16.15 17.16 18.17 19.18
11⁄4 12.75 13.81 14.87 15.94 17.00 18.06 19.13 20.19
15⁄16 13.39 14.50 15.62 16.74 17.85 18.96 20.08 21.20
133⁄8 14.03 15.20 16.36 17.53 18.70 19.87 21.04 22.21
17⁄16 14.66 15.88 17.10 18.33 19.55 20.77 21.99 23.22
11⁄2 15.30 16.58 17.85 19.13 20.40 21.68 22.95 24.23
19⁄16 15.94 17.27 18.60 19.92 21.25 22.58 23.91 25.24
15⁄8 16.58 17.96 19.34 20.72 22.10 23.48 24.87 26.25
111⁄16 17.22 18.65 20.08 21.51 22.95 24.38 25.82 27.26
13⁄4 17.85 19.34 20.83 22.32 23.80 25.29 26.78 28.27
113⁄16 18.49 20.03 21.57 23.11 24.65 26.19 27.73 29.27
17⁄8 19.13 20.72 22.31 23.91 25.50 27.10 28.69 30.28
115⁄16 19.77 21.41 23.06 24.70 26.35 28.00 29.64 31.29
2 20.40 22.10 23.80 25.50 27.20 28.90 30.60 32.30
Thick- ness in inches 5″ 51⁄4″ 51⁄2″ 53⁄4″ 6″ 12″
3⁄16 3.19 3.35 3.51 3.67 3.83 7.65
1⁄4 4.25 4.46 4.67 4.89 5.10 10.20
5⁄16 5.31 5.58 5.84 6.11 6.38 12.75
3⁄8 6.38 6.69 7.02 7.34 7.65 15.30
7⁄16 7.44 7.81 8.18 8.56 8.93 17.85
1⁄2 8.50 8.93 9.35 9.77 10.20 20.40
9⁄16 9.57 10.04 10.52 11.00 11.48 22.95
5⁄8 10.63 11.16 11.69 12.22 12.75 25.50
11⁄16 11.69 12.27 12.85 13.44 14.03 28.05
3⁄4 12.75 13.39 14.03 14.67 15.30 30.60
13⁄16 13.81 14.50 15.19 15.88 16.58 33.15
7⁄8 14.87 15.62 16.36 17.10 17.85 35.70
15⁄16 15.94 16.74 17.53 18.33 19.13 38.25
1 17.00 17.85 18.70 19.55 20.40 40.80
11⁄16 18.06 18.96 19.87 20.77 21.68 43.35
11⁄8 19.13 20.08 21.04 21.99 22.95 45.90
13⁄16 20.19 21.20 22.21 23.22 24.23 48.45
11⁄4 21.25 22.32 23.38 24.44 25.50 51.00
15⁄16 22.32 23.43 24.54 25.66 26.78 53.55
13⁄8 23.38 24.54 25.71 26.88 28.05 56.10
17⁄16 24.44 25.66 26.88 28.10 29.33 58.65
11⁄2 25.50 26.78 28.05 29.33 30.60 61.20
19⁄16 26.57 27.89 29.22 30.55 31.88 63.75
15⁄8 27.63 29.01 30.39 31.77 33.15 66.30
111⁄16 28.69 30.12 31.55 32.99 34.43 68.85
13⁄4 29.75 31.24 32.73 34.22 35.70 71.40
113⁄16 30.81 32.35 33.89 35.43 36.98 73.95
17⁄8 31.87 33.47 35.06 36.65 38.25 76.50
115⁄16 32.94 34.59 36.23 37.88 39.53 79.05
2 34.00 35.70 37.40 39.10 40.80 81.60
7. Weights and Areas of Square and Round Bars and Circumferences of Round Bars
Thickness or Diameter in inches Weight of □ Bar one foot long Weight of ○ Bar one foot long Area of □ Bar in sq. inches Area of ○ Bar in sq. inches Circumference of ○ Bar in inches
1⁄16 .013 .010 .0039 .0031 .1963
1⁄8 .053 .042 .0156 .0123 .3927
3⁄16 .119 .094 .0352 .0276 .5890
1⁄4 .212 .167 .0625 .0491 .7854
5⁄16 .333 .261 .0977 .0767 .9817
3⁄8 .478 .375 .1406 .1104 1.1781
7⁄16 .651 .511 .1914 .1503 1.3744
1⁄2 .850 .667 .2500 .1963 1.5708
9⁄16 1.076 .845 .3164 .2485 1.7671
5⁄8 1.328 1.043 .3906 .3068 1.9635
11⁄16 1.608 1.262 .4727 .3712 2.1598
3⁄4 1.913 1.502 .5625 .4418 2.3562
13⁄16 2.245 1.763 .6602 .5185 2.5525
7⁄8 2.603 2.044 .7656 .6013 2.7489
15⁄16 2.989 2.347 .8789 .6903 2.9452
1 3.400 2.670 1.0000 .7854 3.1416
1⁄16 3.838 3.014 1.1289 .8866 3.3379
1⁄8 4.303 3.379 1.2656 .9940 3.5343
3⁄16 4.795 3.766 1.4102 1.1075 3.7306
1⁄4 5.312 4.173 1.5625 1.2272 3.9270
5⁄16 5.857 4.600 1.7227 1.3530 4.1233
3⁄8 6.428 5.049 1.8906 1.4849 4.3197
7⁄16 7.026 5.518 2.0664 1.6230 4.5160
1⁄2 7.650 6.008 2.2500 1.7671 4.7124
9⁄16 8.301 6.520 2.4414 1.9175 4.9087
5⁄8 8.978 7.051 2.6406 2.0739 5.1051
11⁄16 9.682 7.604 2.8477 2.2365 5.3014
3⁄4 10.41 8.178 3.0625 2.4053 5.4978
13⁄16 11.17 8.773 3.2852 2.5802 5.6941
7⁄8 11.95 9.388 3.5156 2.7612 5.8905
15⁄16 12.76 10.02 3.7539 2.9483 6.0868
2 13.60 10.68 4.0000 3.1416 6.2832
1⁄16 14.46 11.36 4.2539 3.3410 6.4795
1⁄8 15.35 12.06 4.5156 3.5466 6.6759
3⁄16 16.27 12.78 4.7852 3.7583 6.8722
1⁄4 17.22 13.52 5.0625 3.9761 7.0686
5⁄16 18.19 14.28 5.3477 4.2000 7.2649
3⁄8 19.18 15.07 5.6406 4.4301 7.4613
7⁄16 20.20 15.86 5.9414 4.6664 7.6576
1⁄2 21.25 16.69 6.2500 4.9087 7.8540
9⁄16 22.33 17.53 6.5664 5.1572 8.0503
5⁄8 23.43 18.40 6.8906 5.4119 8.2467
11⁄16 24.56 19.29 7.2227 5.6727 8.4430
3⁄4 25. 20.20 7.5625 5.9396 8.6394
13⁄16 26.90 21.12 7.9102 6.2126 8.8357
7⁄8 28.10 22.07 8.2656 6.4918 9.0321
15⁄16 29.34 23.04 8.6289 6.7771 9.2284
3 30.60 24.03 9.0000 7.0686 9.4248
1⁄16 31.89 25.04 9.3789 7.3662 9.6211
1⁄8 33.20 26.08 9.7656 7.6699 9.8175
3⁄16 34.55 27.13 10.160 7.9798 10.014
1⁄4 35.92 28.20 10.563 8.2958 10.210
5⁄16 37.31 29.30 10.973 8.6179 10.407
3⁄8 38.73 30.42 11.391 8.9462 10.603
7⁄16 40.18 31.56 11.816 9.2806 10.799
1⁄2 41.65 32.71 12.250 9.6211 10.996
9⁄16 43.14 33.90 12.691 9.9678 11.192
5⁄8 44.68 35.09 13.141 10.321 11.388
11⁄16 46.24 36.31 13.598 10.680 11.585
3⁄4 47.82 37.56 14.063 11.045 11.781
13⁄16 49.42 38.81 14.535 11.416 11.977
7⁄8 51.05 40.10 15.016 11.793 12.174
15⁄16 52.71 41.40 15.504 12.177 12.370
4 54.40 42.73 16.000 12.566 12.566
1⁄16 56.11 44.07 16.504 12.962 12.763
1⁄8 57.85 45.44 17.016 13.364 12.959
3⁄16 59.62 46.83 17.535 13.772 13.155
1⁄4 61.41 48.24 18.063 14.186 13.352
5⁄16 63.23 49.66 18.598 14.607 13.548
3⁄8 65.08 51.11 19.141 15.033 13.744
7⁄16 66.95 52.58 19.691 15.466 13.941
1⁄2 68.85 54.07 20.250 15.904 14.137
9⁄16 70.78 55.59 20.816 16.349 14.334
5⁄8 72.73 57.12 21.391 16.800 14.530
11⁄16 74.70 58.67 21.973 17.257 14.726
3⁄4 76.71 60.25 22.563 17.721 14.923
13⁄16 78.74 61.84 23.160 18.190 15.119
7⁄8 80.81 63.46 23.766 18.665 15.315
15⁄16 82.89 65.10 24.379 19.147 15.512
5 85.00 66.76 25.000 19.635 15.708
1⁄16 87.14 68.44 25.629 20.129 15.904
1⁄8 89.30 70.14 26.266 20.629 16.101
3⁄16 91.49 71.86 26.910 21.135 16.297
1⁄4 93.72 73.60 27.563 21.648 16.493
5⁄16 95.96 75.37 28.223 22.166 16.690
3⁄8 98.23 77.15 28.891 22.691 16.886
7⁄16 100.5 78.95 29.566 23.221 17.082
1⁄2 102.8 80.77 30.250 23.758 17.279
9⁄16 105.2 82.62 30.941 24.301 17.475
5⁄8 107.6 84.49 31.641 24.850 17.671
11⁄16 110.0 86.38 32.348 25.406 17.868
3⁄4 112.4 88.29 33.063 25.967 18.064
13⁄16 114.9 90.22 33.785 26.535 18.261
7⁄8 117.4 92.17 34.516 27.109 18.457
15⁄16 119.9 94.14 35.254 27.688 18.653
8. Circumferences and Circular Areas of Numbers from 1 to 100
No. Number = Diameter
Circumference Area
1 3.142 0.7854
2 6.283 3.1416
3 9.425 7.0686
4 12.566 12.5664
5 15.708 19.6350
6 18.850 28.2743
7 21.991 38.4845
8 25.133 50.2655
9 28.274 63.6173
10 31.416 78.5398
11 34.558 95.0332
12 37.699 113.097
13 40.841 132.732
14 43.982 153.938
15 47.124 176.715
16 50.265 201.062
17 53.407 226.980
18 56.549 254.469
19 59.690 283.529
20 62.832 314.159
21 65.973 346.361
22 69.115 380.133
23 72.257 415.476
24 75.398 452.389
25 78.540 490.874
26 81.681 530.929
27 84.823 572.555
28 87.965 615.752
29 91.106 660.520
30 94.248 706.858
31 97.389 754.768
32 100.531 804.248
33 103.673 855.299
34 106.814 907.920
35 109.956 962.113
36 113.097 1017.88
37 116.239 1075.21
38 119.381 1134.11
39 122.522 1194.59
40 125.66 1256.64
41 128.81 1320.25
42 131.95 1385.44
43 135.09 1452.20
44 138.23 1520.53
45 141.37 1590.43
46 144.51 1661.90
47 147.65 1734.94
48 150.80 1809.56
49 153.94 1885.74
50 157.08 1963.50
51 160.22 2042.82
52 163.36 2123.72
53 166.50 2206.18
54 169.65 2290.22
55 172.79 2375.83
56 175.93 2463.01
57 179.07 2551.76
58 182.21 2642.08
59 185.35 2733.97
60 188.50 2827.43
61 191.64 2922.47
62 194.78 3019.07
63 197.92 3117.25
64 201.06 3216.99
65 204.20 3318.31
66 207.35 3421.19
67 210.49 3525.65
68 213.63 3631.68
69 216.77 3739.28
70 219.91 3848.45
71 223.05 3959.19
72 226.19 4071.50
73 229.34 4185.39
74 232.48 4300.84
75 235.62 4417.86
76 238.76 4536.46
77 241.90 4656.63
78 245.04 4778.36
79 248.19 4901.67
80 251.33 5026.55
81 254.47 5153.00
82 257.61 5281.02
83 260.75 5410.61
84 263.89 5541.77
85 267.04 5674.50
86 270.18 5808.80
87 273.32 5944.68
88 276.46 6082.12
89 279.60 6221.14
90 282.74 6361.73
91 285.88 6503.88
92 289.03 6647.61
93 292.17 6792.91
94 295.31 6939.78
95 298.45 7088.22
96 301.59 7238.23
97 304.73 7389.81
98 307.88 7542.96
99 311.02 7697.69
100 314.16 7853.98