EQUAL AREA CIRCLES AND SQUARES Diameters of Circles and Sides of Squares of Equal Area (US Customary or Metric Units) Machinery's Handbook, 31st Edition
86
The table below will be found useful for determining the diameter of a circle of an area equal to that of a square, the side of which is known, or for determining the side of a square which has an area equal to that of a circle, the area or diameter of which is known. For example, if the diameter of a circle is 17 1 ⁄ 2 inches, it is found from the table by reading across from the first column that the side of a square of the same area is 15.51 inches. And both have area 240.53 in 2 .
D
S
Dia. of Circle, D
Side of Square, S
Area of Circle or Square
Dia. of Circle, D
Side of Square, S
Area of Circle or Square
Dia. of Circle, D
Side of Square, S
Area of Circle or Square
0.44 0.89 1.33 1.77 2.22 2.66 3.10 3.54 3.99 4.43 4.87 5.32 5.76 6.20 6.65 7.09 7.53 7.98 8.42 8.86 9.31 9.75
0.196 0.785 1.767 3.142 4.909 7.069 9.621
18.17 18.61 19.05 19.50 19.94 20.38 20.83 21.27 21.71 22.16 22.60 23.04 23.49 23.93 24.37 24.81 25.26 25.70 26.14 26.59 27.03 27.47 27.92 28.36 28.80 29.25 29.69 30.13 30.57 31.02 31.46 31.90 32.35 32.79 33.23 33.68 34.12 34.56 35.01 35.45
330.06 346.36 363.05 380.13 397.61 415.48 433.74 452.39 471.44 490.87 510.71 530.93 551.55 572.56 593.96 615.75 637.94 660.52 683.49 706.86 730.62 754.77 779.31 804.25 829.58 855.30 881.41 907.92 934.82 962.11 989.80 1017.88 1046.35 1075.21 1104.47 1134.11 1164.16 1194.59 1225.42 1256.64
35.89 36.34 36.78 37.22 37.66 38.11 38.55 38.99 39.44 39.88 40.32 40.77 41.21 41.65 42.10 42.54 42.98 43.43 43.87 44.31 44.75 45.20 45.64 46.08 46.53 46.97 47.41 47.86 48.30 48.74 49.19 49.63 50.07 50.51 50.96 51.40 51.84 52.29 52.73 53.17
1288.25 1320.25 1352.65 1385.44 1418.63 1452.20 1486.17 1520.53 1555.28 1590.43 1625.97 1661.90 1698.23 1734.94 1772.05 1809.56 1847.45 1885.74 1924.42 1963.50 2002.96 2042.82 2083.07 2123.72 2164.75 2206.18 2248.01 2290.22 2332.83 2375.83 2419.22 2463.01 2507.19 2551.76 2596.72 2642.08 2687.83 2733.97 2780.51 2827.43
20 21 21 22 22 23 23 24 24 25 25 26 26 27 27 28 28 29 29 30 30 31 31 32 32 33 33 34 34 35 35 36 36 37 37 38 38 39 39 40
40 41 41 42 42 43 43 44 44 45 45 46 46 47 47 48 48 49 49 50 50 51 51 52 52 53 53 54 54 55 55 56 56 57
1 ⁄
1 ⁄
1 ⁄
2
2
2
1
1 1 ⁄
1 ⁄
1 ⁄
2
2
2
2
2 1 ⁄
1 ⁄
1 ⁄
2
2
2
3
3 1 ⁄
1 ⁄
1 ⁄
2
2
2
4
12.566 15.904 19.635 23.758 28.274 33.183 38.485 44.179 50.265 56.745 63.617 70.882 78.540 86.590 95.033 103.87 113.10 122.72 132.73 143.14 153.94 165.13 176.71 188.69 201.06 213.82 226.98 240.53 254.47 268.80 283.53 298.65 314.16
4 1 ⁄
1 ⁄
1 ⁄
2
2
2
5
5 1 ⁄
1 ⁄
1 ⁄
2
2
2
6
6 1 ⁄
1 ⁄
1 ⁄
2
2
2
7
7 1 ⁄
1 ⁄
1 ⁄
2
2
2
8
8 1 ⁄
1 ⁄
1 ⁄
2
2
2
9
9 1 ⁄
1 ⁄
1 ⁄
2
2
2
10
10 1 ⁄
1 ⁄
1 ⁄
2
2
2
11
10.19 10.63 11.08 11.52 11.96 12.41 12.85 13.29 13.74 14.18 14.62 15.07 15.51 15.95 16.40 16.84 17.28 17.72
11 1 ⁄
1 ⁄
1 ⁄
2
2
2
12
12 1 ⁄
1 ⁄
1 ⁄
2
2
2
13
13 1 ⁄
1 ⁄
1 ⁄
2
2
2
14
14 1 ⁄
1 ⁄
1 ⁄
2
2
2
15
15 1 ⁄
1 ⁄
1 ⁄
2
2
2
16
16 1 ⁄
1 ⁄
1 ⁄
2
2
2
17
17 1 ⁄
57 58 58
1 ⁄
1 ⁄
2
2
2
18
18 1 ⁄
1 ⁄
1 ⁄
2
2
2
19
59 59 60
19 1 ⁄
1 ⁄
1 ⁄
2
2
2
20
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