Formulas and Tables

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