Chord Lengths when Dividing a Circle in Equal Segments

Calculate chord lengths when dividing the circumference of a circle into equal number of segments

Circle - dividing circumference and chord lengths

The length - L - of a chord when dividing a circumference of a circle into equal number of segments can be calculated from the table below. The chord length - L - in the table is for a "unit circle" with radius = 1.

To calculate the actual length of a chord - multiply the "unit circle" length - L - with the radius for the the actual circle. 

Example - Chord Length

A circle with radius 3 m is divided in 24 segments. From the table below: the length - L - of a single chord in a "unit circle" with 24 segments is 0.2611 units.

The length of the chord for a circle with radius 3 m can be calculated as

0.2611 (3 m) = 0.7833 m

The summarized length of all chords in the circle can be calculated as

(0.7833 m) 24

= 6.2653 (3m)

= 18.7959 m

The circumference of the circle can be calculated as

C = 2 π r

   = 2 π (3 m)

= 18.8496 m

Number of Segments
- n -
Center Angle - θ -Length of Single Chord
- L -
Summarized Lengths of Chords
degrees radians
2 180.0000 3.1416 2.0000 4.0000
4 90.0000 1.5708 1.4142 5.6569
6 60.0000 1.0472 1.0000 6.0000
8 45.0000 0.7854 0.7654 6.1229
10 36.0000 0.6283 0.6180 6.1803
12 30.0000 0.5236 0.5176 6.2117
14 25.7143 0.4488 0.4450 6.2306
16 22.5000 0.3927 0.3902 6.2429
18 20.0000 0.3491 0.3473 6.2513
20 18.0000 0.3142 0.3129 6.2574
22 16.3636 0.2856 0.2846 6.2619
24 15.0000 0.2618 0.2611 6.2653
26 13.8462 0.2417 0.2411 6.2679
28 12.8571 0.2244 0.2239 6.2700
30 12.0000 0.2094 0.2091 6.2717
32 11.2500 0.1963 0.1960 6.2731
34 10.5882 0.1848 0.1845 6.2742
36 10.0000 0.1745 0.1743 6.2752
38 9.4737 0.1653 0.1652 6.2760
40 9.0000 0.1571 0.1569 6.2767
42 8.5714 0.1496 0.1495 6.2773
44 8.1818 0.1428 0.1427 6.2778
46 7.8261 0.1366 0.1365 6.2783
48 7.5000 0.1309 0.1308 6.2787
50 7.2000 0.1257 0.1256 6.2791
52 6.9231 0.1208 0.1208 6.2794
54 6.6667 0.1164 0.1163 6.2796
56 6.4286 0.1122 0.1121 6.2799
58 6.2069 0.1083 0.1083 6.2801
60 6.0000 0.1047 0.1047 6.2803
62 5.8065 0.1013 0.1013 6.2805
64 5.6250 0.0982 0.0981 6.2807
66 5.4545 0.0952 0.0952 6.2808
68 5.2941 0.0924 0.0924 6.2810
70 5.1429 0.0898 0.0897 6.2811
72 5.0000 0.0873 0.0872 6.2812
74 4.8649 0.0849 0.0849 6.2813
76 4.7368 0.0827 0.0826 6.2814
78 4.6154 0.0806 0.0805 6.2815
80 4.5000 0.0785 0.0785 6.2816
82 4.3902 0.0766 0.0766 6.2816
84 4.2857 0.0748 0.0748 6.2817
86 4.1860 0.0731 0.0730 6.2818
88 4.0909 0.0714 0.0714 6.2819
90 4.0000 0.0698 0.0698 6.2819
92 3.9130 0.0683 0.0683 6.2820
94 3.8298 0.0668 0.0668 6.2820
96 3.7500 0.0654 0.0654 6.2821
98 3.6735 0.0641 0.0641 6.2821
100 3.6000 0.0628 0.0628 6.2822
102 3.5294 0.0616 0.0616 6.2822
104 3.4615 0.0604 0.0604 6.2822
106 3.3962 0.0593 0.0593 6.2823
108 3.3333 0.0582 0.0582 6.2823
110 3.2727 0.0571 0.0571 6.2823
112 3.2143 0.0561 0.0561 6.2824
114 3.1579 0.0551 0.0551 6.2824
116 3.1034 0.0542 0.0542 6.2824
118 3.0508 0.0532 0.0532 6.2824
120 3.0000 0.0524 0.0524 6.2825
122 2.9508 0.0515 0.0515 6.2825
124 2.9032 0.0507 0.0507 6.2825
126 2.8571 0.0499 0.0499 6.2825
128 2.8125 0.0491 0.0491 6.2826
130 2.7692 0.0483 0.0483 6.2826
132 2.7273 0.0476 0.0476 6.2826
134 2.6866 0.0469 0.0469 6.2826
136 2.6471 0.0462 0.0462 6.2826
138 2.6087 0.0455 0.0455 6.2826
140 2.5714 0.0449 0.0449 6.2827
142 2.5352 0.0442 0.0442 6.2827
144 2.5000 0.0436 0.0436 6.2827
146 2.4658 0.0430 0.0430 6.2827
148 2.4324 0.0425 0.0425 6.2827
150 2.4000 0.0419 0.0419 6.2827
152 2.3684 0.0413 0.0413 6.2827
154 2.3377 0.0408 0.0408 6.2827
156 2.3077 0.0403 0.0403 6.2828
158 2.2785 0.0398 0.0398 6.2828
160 2.2500 0.0393 0.0393 6.2828
162 2.2222 0.0388 0.0388 6.2828
164 2.1951 0.0383 0.0383 6.2828
166 2.1687 0.0379 0.0378 6.2828
168 2.1429 0.0374 0.0374 6.2828
170 2.1176 0.0370 0.0370 6.2828
172 2.0930 0.0365 0.0365 6.2828
174 2.0690 0.0361 0.0361 6.2828
176 2.0455 0.0357 0.0357 6.2829
178 2.0225 0.0353 0.0353 6.2829
180 2.0000 0.0349 0.0349 6.2829
182 1.9780 0.0345 0.0345 6.2829
184 1.9565 0.0341 0.0341 6.2829
186 1.9355 0.0338 0.0338 6.2829
188 1.9149 0.0334 0.0334 6.2829
190 1.8947 0.0331 0.0331 6.2829
192 1.8750 0.0327 0.0327 6.2829
194 1.8557 0.0324 0.0324 6.2829
196 1.8367 0.0321 0.0321 6.2829
198 1.8182 0.0317 0.0317 6.2829
200 1.8000 0.0314 0.0314 6.2829
202 1.7822 0.0311 0.0311 6.2829
204 1.7647 0.0308 0.0308 6.2829
206 1.7476 0.0305 0.0305 6.2829
208 1.7308 0.0302 0.0302 6.2829
210 1.7143 0.0299 0.0299 6.2830
212 1.6981 0.0296 0.0296 6.2830
214 1.6822 0.0294 0.0294 6.2830
216 1.6667 0.0291 0.0291 6.2830
218 1.6514 0.0288 0.0288 6.2830
220 1.6364 0.0286 0.0286 6.2830
222 1.6216 0.0283 0.0283 6.2830
224 1.6071 0.0280 0.0280 6.2830
226 1.5929 0.0278 0.0278 6.2830
228 1.5789 0.0276 0.0276 6.2830
230 1.5652 0.0273 0.0273 6.2830
232 1.5517 0.0271 0.0271 6.2830
234 1.5385 0.0269 0.0269 6.2830
236 1.5254 0.0266 0.0266 6.2830
238 1.5126 0.0264 0.0264 6.2830
240 1.5000 0.0262 0.0262 6.2830
242 1.4876 0.0260 0.0260 6.2830
244 1.4754 0.0258 0.0258 6.2830
246 1.4634 0.0255 0.0255 6.2830
248 1.4516 0.0253 0.0253 6.2830
250 1.4400 0.0251 0.0251 6.2830
252 1.4286 0.0249 0.0249 6.2830
254 1.4173 0.0247 0.0247 6.2830
256 1.4063 0.0245 0.0245 6.2830
258 1.3953 0.0244 0.0244 6.2830
260 1.3846 0.0242 0.0242 6.2830
262 1.3740 0.0240 0.0240 6.2830
264 1.3636 0.0238 0.0238 6.2830
266 1.3534 0.0236 0.0236 6.2830
268 1.3433 0.0234 0.0234 6.2830
270 1.3333 0.0233 0.0233 6.2830
272 1.3235 0.0231 0.0231 6.2830
274 1.3139 0.0229 0.0229 6.2830
276 1.3043 0.0228 0.0228 6.2830
278 1.2950 0.0226 0.0226 6.2831
280 1.2857 0.0224 0.0224 6.2831
282 1.2766 0.0223 0.0223 6.2831
284 1.2676 0.0221 0.0221 6.2831
286 1.2587 0.0220 0.0220 6.2831
288 1.2500 0.0218 0.0218 6.2831
290 1.2414 0.0217 0.0217 6.2831
292 1.2329 0.0215 0.0215 6.2831
294 1.2245 0.0214 0.0214 6.2831
296 1.2162 0.0212 0.0212 6.2831
298 1.2081 0.0211 0.0211 6.2831
300 1.2000 0.0209 0.0209 6.2831
302 1.1921 0.0208 0.0208 6.2831
304 1.1842 0.0207 0.0207 6.2831
306 1.1765 0.0205 0.0205 6.2831
308 1.1688 0.0204 0.0204 6.2831
310 1.1613 0.0203 0.0203 6.2831
312 1.1538 0.0201 0.0201 6.2831
314 1.1465 0.0200 0.0200 6.2831
316 1.1392 0.0199 0.0199 6.2831
318 1.1321 0.0198 0.0198 6.2831
320 1.1250 0.0196 0.0196 6.2831
322 1.1180 0.0195 0.0195 6.2831
324 1.1111 0.0194 0.0194 6.2831
326 1.1043 0.0193 0.0193 6.2831
328 1.0976 0.0192 0.0192 6.2831
330 1.0909 0.0190 0.0190 6.2831
332 1.0843 0.0189 0.0189 6.2831
334 1.0778 0.0188 0.0188 6.2831
336 1.0714 0.0187 0.0187 6.2831
338 1.0651 0.0186 0.0186 6.2831
340 1.0588 0.0185 0.0185 6.2831
342 1.0526 0.0184 0.0184 6.2831
344 1.0465 0.0183 0.0183 6.2831
346 1.0405 0.0182 0.0182 6.2831
348 1.0345 0.0181 0.0181 6.2831
350 1.0286 0.0180 0.0180 6.2831
352 1.0227 0.0178 0.0178 6.2831
354 1.0169 0.0177 0.0177 6.2831
356 1.0112 0.0176 0.0176 6.2831
358 1.0056 0.0176 0.0176 6.2831
360 1.0000 0.0175 0.0175 6.2831

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