4 SEGMENTS OF CIRCLES
Segments of Circles for Radius = 1 (English or metric units)
Formulas for segments of circles are given on page 1. When the central
angle α and radius r are known, the tables on these pages can be used to find
the length of arc l, height of segment h, chord length c, and segment area A.
When angle α and radius r are not known, but segment height h and chord
length c are known or can be measured, the ratio h/c can be used to enter the
table and find α, l, and A by linear interpolation. Radius r is found by the
formula on page 1. The value of l is then multiplied by the radius r and the
area A by r
2
, the square of the radius.
Angle α can be found thus with an accuracy of about 0.001 degree; arc
length l with an error of about 0.02 per cent; and area A with an error rang-
ing from about 0.02 per cent for the highest entry value of h/c to about 1 per
cent for values of h/c of about 0.050. For lower values of h/c, and where
greater accuracy is required, area A should be found by the formula on
page 1.
θ,
Deg. lhcArea Ah/c
θ,
Deg. lhcArea Ah/c
1 0.01745 0.00004 0.01745 0.0000 0.00218 41 0.71558 0.06333 0.70041 0.0298 0.09041
2 0.03491 0.00015 0.03490 0.0000 0.00436 42 0.73304 0.06642 0.71674 0.0320 0.09267
3 0.05236 0.00034 0.05235 0.0000 0.00655 43 0.75049 0.06958 0.73300 0.0342 0.09493
4 0.06981 0.00061 0.06980 0.0000 0.00873 44 0.76794 0.07282 0.74921 0.0366 0.09719
5 0.08727 0.00095 0.08724 0.0001 0.01091 45 0.78540 0.07612 0.76537 0.0391 0.09946
6 0.10472 0.00137 0.10467 0.0001 0.01309 46 0.80285 0.07950 0.78146 0.0418 0.10173
7 0.12217 0.00187 0.12210 0.0002 0.01528 47 0.82030 0.08294 0.79750 0.0445 0.10400
8 0.13963 0.00244 0.13951 0.0002 0.01746 48 0.83776 0.08645 0.81347 0.0473 0.10628
9 0.15708 0.00308 0.15692 0.0003 0.01965 49 0.85521 0.09004 0.82939 0.0503 0.10856
10 0.17453 0.00381 0.17431 0.0004 0.02183 50 0.87266 0.09369 0.84524 0.0533 0.11085
11 0.19199 0.00460 0.19169 0.0006 0.02402 51 0.89012 0.09741 0.86102 0.0565 0.11314
12 0.20944 0.00548 0.20906 0.0008 0.02620 52 0.90757 0.10121 0.87674 0.0598 0.11543
13 0.22689 0.00643 0.22641 0.0010 0.02839 53 0.92502 0.10507 0.89240 0.0632 0.11773
14 0.24435 0.00745 0.24374 0.0012 0.03058 54 0.94248 0.10899 0.90798 0.0667 0.12004
15 0.26180 0.00856 0.26105 0.0015 0.03277 55 0.95993 0.11299 0.92350 0.0704 0.12235
16 0.27925 0.00973 0.27835 0.0018 0.03496 56 0.97738 0.11705 0.93894 0.0742 0.12466
17 0.29671 0.01098 0.29562 0.0022 0.03716 57 0.99484 0.12118 0.95432 0.0781 0.12698
18 0.31416 0.01231 0.31287 0.0026 0.03935 58 1.01229 0.12538 0.96962 0.0821 0.12931
19 0.33161 0.01371 0.33010 0.0030 0.04155 59 1.02974 0.12964 0.98485 0.0863 0.13164
20 0.34907 0.01519 0.34730 0.0035 0.04374 60 1.04720 0.13397 1.00000 0.0906 0.13397
21 0.36652 0.01675 0.36447 0.0041 0.04594 61 1.06465 0.13837 1.01508 0.0950 0.13632
22 0.38397 0.01837 0.38162 0.0047 0.04814 62 1.08210 0.14283 1.03008 0.0996 0.13866
23 0.40143 0.02008 0.39874 0.0053 0.05035 63 1.09956 0.14736 1.04500 0.1043 0.14101
24 0.41888 0.02185 0.41582 0.0061 0.05255 64 1.11701 0.15195 1.05984 0.1091 0.14337
25 0.43633 0.02370 0.43288 0.0069 0.05476 65 1.13446 0.15661 1.07460 0.1141 0.14574
26 0.45379 0.02563 0.44990 0.0077 0.05697 66 1.15192 0.16133 1.08928 0.1192 0.14811
27 0.47124 0.02763 0.46689 0.0086 0.05918 67 1.16937 0.16611 1.10387 0.1244 0.15048
28 0.48869 0.02970 0.48384 0.0096 0.06139 68 1.18682 0.17096 1.11839 0.1298 0.15287
29 0.50615 0.03185 0.50076 0.0107 0.06361 69 1.20428 0.17587 1.13281 0.1353 0.15525
30 0.52360 0.03407 0.51764 0.0118 0.06583 70 1.22173 0.18085 1.14715 0.1410 0.15765
31 0.54105 0.03637 0.53448 0.0130 0.06805 71 1.23918 0.18588 1.16141 0.1468 0.16005
32 0.55851 0.03874 0.55127 0.0143 0.07027 72 1.25664 0.19098 1.17557 0.1528 0.16246
33 0.57596 0.04118 0.56803 0.0157 0.07250 73 1.27409 0.19614 1.18965 0.1589 0.16488
34 0.59341 0.04370 0.58474 0.0171 0.07473 74 1.29154 0.20136 1.20363 0.1651 0.16730
35 0.61087 0.04628 0.60141 0.0186 0.07696 75 1.30900 0.20665 1.21752 0.1715 0.16973
36 0.62832 0.04894 0.61803 0.0203 0.07919 76 1.32645 0.21199 1.23132 0.1781 0.17216
37 0.64577 0.05168 0.63461 0.0220 0.08143 77 1.34390 0.21739 1.24503 0.1848 0.17461
38 0.66323 0.05448 0.65114 0.0238 0.08367 78 1.36136 0.22285 1.25864 0.1916 0.17706
39 0.68068 0.05736 0.66761 0.0257 0.08592 79 1.37881 0.22838 1.27216 0.1986 0.17952
40 0.69813 0.06031 0.68404 0.0277 0.08816 80 1.39626 0.23396 1.28558 0.2057 0.18199