Formulas and Tables (From the “Pocket Companion,” Published by the Carnegie Steel Co.)
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 |