Ptolemy's Table of Chords
Arc ( ° ) Chord 60 Chord 10 Sixtieths 60 Sixtieths 10
0.5 0 31 25 0.523611 0 1 2 50 0.017226
1.0 1 2 50 1.047222 0 1 2 50 0.017226
1.5 1 34 15 1.570833 0 1 2 50 0.017226
2.0 2 5 40 2.094444 0 1 2 50 0.017226
2.5 2 37 4 2.617778 0 1 2 48 0.017226
3.0 3 8 28 3.141111 0 1 2 48 0.017226
3.5 3 39 52 3.664444 0 1 2 48 0.017226
4.0 4 11 16 4.187778 0 1 2 47 0.017226
4.5 4 42 40 4.711111 0 1 2 47 0.017226
5.0 5 14 4 5.234444 0 1 2 46 0.017226
5.5 5 45 27 5.757500 0 1 2 45 0.017226
6.0 6 16 49 6.280278 0 1 2 44 0.017226
6.5 6 48 11 6.803056 0 1 2 43 0.017226
7.0 7 19 33 7.325833 0 1 2 42 0.017225
7.5 7 50 54 7.848333 0 1 2 41 0.017225
8.0 8 22 15 8.370833 0 1 2 40 0.017225
8.5 8 53 35 8.893056 0 1 2 39 0.017225
9.0 9 24 54 9.415000 0 1 2 38 0.017225
9.5 9 56 13 9.936944 0 1 2 37 0.017225
10.0 10 27 32 10.458889 0 1 2 35 0.017225
10.5 10 58 49 10.980278 0 1 2 33 0.017225
11.0 11 30 5 11.501389 0 1 2 32 0.017225
11.5 12 1 21 12.022500 0 1 2 30 0.017225
12.0 12 32 36 12.543333 0 1 2 28 0.017224
12.5 13 3 50 13.063889 0 1 2 27 0.017224
13.0 13 35 4 13.584444 0 1 2 25 0.017224
13.5 14 6 16 14.104444 0 1 2 23 0.017224
14.0 14 37 27 14.624167 0 1 2 21 0.017224
14.5 15 8 38 15.143889 0 1 2 19 0.017224
15.0 15 39 47 15.663056 0 1 2 17 0.017224
15.5 16 10 56 16.182222 0 1 2 15 0.017223
16.0 16 42 3 16.700833 0 1 2 13 0.017223
16.5 17 13 9 17.219167 0 1 2 10 0.017223
17.0 17 44 14 17.737222 0 1 2 7 0.017223
17.5 18 15 17 18.254722 0 1 2 5 0.017223
18.0 18 46 19 18.771944 0 1 2 2 0.017222
18.5 19 17 21 19.289167 0 1 2 0 0.017222
19.0 19 48 21 19.805833 0 1 1 57 0.016949
19.5 20 19 19 20.321944 0 1 1 54 0.016949
20.0 20 50 16 20.837778 0 1 1 51 0.016948
20.5 21 21 11 21.353056 0 1 1 48 0.016948
21.0 21 52 6 21.868333 0 1 1 45 0.016948
21.5 22 22 58 22.382778 0 1 1 42 0.016948
22.0 22 53 49 22.896944 0 1 1 39 0.016947
22.5 23 24 39 23.410833 0 1 1 36 0.016947
23.0 23 55 27 23.924167 0 1 1 33 0.016947
23.5 24 26 13 24.436944 0 1 1 30 0.016947
24.0 24 56 58 24.949444 0 1 1 26 0.016946
24.5 25 27 41 25.461389 0 1 1 22 0.016946
25.0 25 58 22 25.972778 0 1 1 19 0.016946
25.5 26 29 1 26.483611 0 1 1 15 0.016946
26.0 26 59 38 26.993889 0 1 1 11 0.016945
26.5 27 30 14 27.503889 0 1 1 8 0.016945
27.0 28 0 48 28.013333 0 1 1 4 0.016945
27.5 28 31 20 28.522222 0 1 1 0 0.016944
28.0 29 1 50 29.030556 0 1 0 56 0.016671
28.5 29 32 18 29.538333 0 1 0 52 0.016671
29.0 30 2 44 30.045556 0 1 0 48 0.016670
29.5 30 33 8 30.552222 0 1 0 44 0.016670
30.0 31 3 30 31.058333 0 1 0 40 0.016670
30.5 31 33 50 31.563889 0 1 0 35 0.016669
31.0 32 4 7 32.068611 0 1 0 31 0.016669
31.5 32 34 22 32.572778 0 1 0 27 0.016669
32.0 33 4 35 33.076389 0 1 0 22 0.016668
32.5 33 34 46 33.579444 0 1 0 17 0.016668
33.0 34 4 55 34.081944 0 1 0 12 0.016668
33.5 34 35 1 34.583611 0 1 0 8 0.016667
34.0 35 5 5 35.084722 0 1 0 3 0.016667
34.5 35 35 6 35.585000 0 0 59 57 0.016393
35.0 36 5 5 36.084722 0 0 59 52 0.016393
35.5 36 35 1 36.583611 0 0 59 48 0.016393
36.0 37 4 55 37.081944 0 0 59 43 0.016392
36.5 37 34 47 37.579722 0 0 59 38 0.016392
37.0 38 4 36 38.076667 0 0 59 32 0.016391
37.5 38 34 22 38.572778 0 0 59 27 0.016391
38.0 39 4 5 39.068056 0 0 59 22 0.016391
38.5 39 33 46 39.562778 0 0 59 16 0.016390
39.0 40 3 25 40.056944 0 0 59 11 0.016390
39.5 40 33 0 40.550000 0 0 59 5 0.016389
40.0 41 2 33 41.042500 0 0 59 0 0.016389
40.5 41 32 3 41.534167 0 0 58 54 0.016115
41.0 42 1 30 42.025000 0 0 58 48 0.016115
41.5 42 30 54 42.515000 0 0 58 42 0.016114
42.0 43 0 15 43.004167 0 0 58 36 0.016114
42.5 43 29 33 43.492500 0 0 58 31 0.016114
43.0 43 58 49 43.980278 0 0 58 25 0.016113
43.5 44 28 1 44.466944 0 0 58 18 0.016113
44.0 44 57 10 44.952778 0 0 58 12 0.016112
44.5 45 26 16 45.437778 0 0 58 6 0.016112
45.0 45 55 19 45.921944 0 0 58 0 0.016111
45.5 46 24 19 46.405278 0 0 57 54 0.015838
46.0 46 53 16 46.887778 0 0 57 47 0.015837
46.5 47 22 9 47.369167 0 0 57 41 0.015836
47.0 47 51 0 47.850000 0 0 57 34 0.015836
47.5 48 19 47 48.329722 0 0 57 27 0.015835
48.0 48 48 30 48.808333 0 0 57 21 0.015835
48.5 49 17 11 49.286389 0 0 57 14 0.015834
49.0 49 45 48 49.763333 0 0 57 7 0.015834
49.5 50 14 21 50.239167 0 0 57 0 0.015833
50.0 50 42 51 50.714167 0 0 56 53 0.015560
50.5 51 11 18 51.188333 0 0 56 46 0.015559
51.0 51 39 41 51.661389 0 0 56 39 0.015559
51.5 52 8 0 52.133333 0 0 56 32 0.015558
52.0 52 36 16 52.604444 0 0 56 25 0.015557
52.5 53 4 29 53.074722 0 0 56 18 0.015557
53.0 53 32 38 53.543889 0 0 56 10 0.015556
53.5 54 0 43 54.011944 0 0 56 3 0.015556
54.0 54 28 44 54.478889 0 0 55 55 0.015282
54.5 54 56 42 54.945000 0 0 55 48 0.015281
55.0 55 24 36 55.410000 0 0 55 40 0.015281
55.5 55 52 26 55.873889 0 0 55 33 0.015280
56.0 56 50 12 56.836667 0 0 55 25 0.015280
56.5 56 47 54 56.798333 0 0 55 17 0.015279
57.0 57 15 33 57.259167 0 0 55 9 0.015278
57.5 57 43 7 57.718611 0 0 55 1 0.015278
58.0 58 10 38 58.177222 0 0 54 53 0.015004
58.5 58 38 5 58.634722 0 0 54 45 0.015003
59.0 59 5 27 59.090833 0 0 54 37 0.015003
59.5 59 32 45 59.545833 0 0 54 29 0.015002
60.0 60 0 0 60.000000 0 0 54 31 0.015002
60.5 60 27 11 60.453056 0 0 54 12 0.015001
61.0 60 54 17 60.904722 0 0 54 4 0.015000
61.5 61 21 19 61.355278 0 0 53 56 0.014727
62.0 61 48 17 61.804722 0 0 53 47 0.014726
62.5 62 15 10 62.252778 0 0 53 39 0.014725
63.0 62 42 0 62.700000 0 0 53 30 0.014725
63.5 63 8 45 63.145833 0 0 53 22 0.014724
64.0 63 35 26 63.590556 0 0 53 13 0.014723
64.5 64 2 2 64.033889 0 0 53 4 0.014723
65.0 64 28 34 64.476111 0 0 52 55 0.014449
65.5 64 55 1 64.916944 0 0 52 46 0.014448
66.0 65 21 24 65.356667 0 0 52 37 0.014447
66.5 65 47 43 65.795278 0 0 52 28 0.014447
67.0 66 13 57 66.232500 0 0 52 19 0.014446
67.5 66 40 7 66.668611 0 0 52 10 0.014445
68.0 67 6 12 67.103333 0 0 52 1 0.014445
68.5 67 32 12 67.536667 0 0 51 52 0.014171
69.0 67 58 8 67.968889 0 0 51 43 0.014170
69.5 68 23 59 68.399722 0 0 51 33 0.014169
70.0 68 49 45 68.829167 0 0 51 21 0.014168
70.5 69 15 27 69.257500 0 0 51 14 0.014168
71.0 69 41 4 69.684444 0 0 51 4 0.014167
71.5 70 6 36 70.110000 0 0 50 55 0.013893
72.0 70 32 4 70.534444 0 0 50 45 0.013892
72.5 70 57 26 70.957222 0 0 50 35 0.013892
73.0 71 22 44 71.378889 0 0 50 26 0.013891
73.5 71 47 56 71.798889 0 0 50 16 0.013890
74.0 72 13 4 72.217778 0 0 50 6 0.013889
74.5 72 38 7 72.635278 0 0 49 56 0.013615
75.0 73 3 5 73.051389 0 0 49 46 0.013615
75.5 73 27 58 73.466111 0 0 49 36 0.013614
76.0 73 52 46 73.879444 0 0 49 26 0.013613
76.5 74 17 29 74.291389 0 0 49 16 0.013612
77.0 74 42 7 74.701944 0 0 49 6 0.013612
77.5 75 6 39 75.110833 0 0 48 55 0.013338
78.0 75 31 7 75.518611 0 0 48 45 0.013337
78.5 75 55 29 75.924722 0 0 48 34 0.013336
79.0 76 19 46 76.329444 0 0 48 24 0.013335
79.5 76 43 58 76.732778 0 0 48 13 0.013334
80.0 77 8 5 77.134722 0 0 48 3 0.013334
80.5 77 32 6 77.535000 0 0 47 52 0.013060
81.0 77 56 2 77.933889 0 0 47 41 0.013059
81.5 78 19 52 78.331111 0 0 47 31 0.013058
82.0 78 43 38 78.727222 0 0 47 20 0.013057
82.5 79 7 18 79.121667 0 0 47 9 0.013056
83.0 79 30 52 79.514444 0 0 46 58 0.012782
83.5 79 54 21 79.905833 0 0 46 47 0.012781
84.0 80 17 45 80.295833 0 0 46 36 0.012781
84.5 80 41 3 80.684167 0 0 46 25 0.012780
85.0 81 4 15 81.070833 0 0 46 14 0.012779
85.5 81 27 22 81.456111 0 0 46 3 0.012778
86.0 81 50 24 81.840000 0 0 45 52 0.012504
86.5 82 13 19 82.221944 0 0 45 40 0.012503
87.0 82 36 9 82.602500 0 0 45 29 0.012502
87.5 82 58 54 82.981667 0 0 45 18 0.012501
88.0 83 21 33 83.359167 0 0 45 6 0.012500
88.5 83 44 6 83.735000 0 0 44 55 0.012226
89.0 84 6 33 84.109167 0 0 44 43 0.012226
89.5 84 28 54 84.481667 0 0 44 31 0.012225
90.0 84 51 10 84.852778 0 0 44 20 0.012224
90.5 85 13 20 85.222222 0 0 44 8 0.012223
91.0 85 35 24 85.590000 0 0 43 57 0.011949
91.5 85 57 23 85.956389 0 0 43 45 0.011948
92.0 86 19 15 86.320833 0 0 43 33 0.011947
92.5 86 41 2 86.683889 0 0 43 21 0.011946
93.0 87 2 42 87.045000 0 0 43 9 0.011945
93.5 87 24 17 87.404722 0 0 42 57 0.011671
94.0 87 45 45 87.762500 0 0 42 45 0.011670
94.5 88 7 7 88.118611 0 0 42 33 0.011669
95.0 88 28 24 88.473333 0 0 42 21 0.011668
95.5 88 49 34 88.826111 0 0 42 9 0.011667
96.0 89 10 39 89.177500 0 0 41 57 0.011393
96.5 89 31 37 89.526944 0 0 41 45 0.011392
97.0 89 52 29 89.874722 0 0 41 33 0.011391
97.5 90 13 15 90.220833 0 0 41 21 0.011391
98.0 90 33 55 90.565278 0 0 41 8 0.011390
98.5 90 54 29 90.908056 0 0 40 55 0.011115
99.0 91 14 56 91.248889 0 0 40 42 0.011114
99.5 91 35 17 91.588056 0 0 40 30 0.011113
100.0 91 55 32 91.925556 0 0 40 17 0.011112
100.5 92 15 40 92.261111 0 0 40 4 0.011111
101.0 92 35 42 92.595000 0 0 39 52 0.010837
101.5 92 55 38 92.927222 0 0 39 39 0.010836
102.0 93 15 27 93.257500 0 0 39 26 0.010835
102.5 93 35 11 93.586389 0 0 39 13 0.010834
103.0 93 54 47 93.913056 0 0 39 0 0.010833
103.5 94 15 17 94.254722 0 0 38 47 0.010559
104.0 94 33 41 94.561389 0 0 38 34 0.010558
104.5 94 52 58 94.882778 0 0 38 21 0.010557
105.0 95 12 9 95.202500 0 0 38 8 0.010556
105.5 95 31 13 95.520278 0 0 37 55 0.010282
106.0 95 50 11 95.836389 0 0 37 42 0.010281
106.5 96 9 2 96.150556 0 0 37 29 0.010280
107.0 96 27 47 96.463056 0 0 37 16 0.010279
107.5 96 46 24 96.773333 0 0 37 3 0.010278
108.0 97 4 56 97.082222 0 0 36 50 0.010004
108.5 97 23 20 97.388889 0 0 36 36 0.010003
109.0 97 41 38 97.693889 0 0 36 23 0.010002
109.5 97 59 49 97.996944 0 0 36 9 0.010001
110.0 98 19 54 98.331667 0 0 35 56 0.009727
110.5 98 35 52 98.597778 0 0 35 42 0.009725
111.0 98 53 43 98.895278 0 0 35 29 0.009724
111.5 99 11 27 99.190833 0 0 35 15 0.009723
112.0 99 29 5 99.484722 0 0 34 48 0.009448
112.5 99 46 35 99.776389 0 0 34 34 0.009447
113.0 100 3 59 100.066389 0 0 34 34 0.009447
113.5 100 21 16 100.354444 0 0 34 20 0.009446
114.0 100 38 26 100.640556 0 0 34 6 0.009445
114.5 100 55 38 100.927222 0 0 33 53 0.009171
115.0 101 12 25 101.206944 0 0 33 39 0.009170
115.5 101 29 15 101.487500 0 0 33 25 0.009169
116.0 101 45 57 101.765833 0 0 33 11 0.009168
116.5 102 2 33 102.042500 0 0 32 57 0.008893
117.0 102 19 1 102.316944 0 0 32 43 0.008892
117.5 102 35 22 102.589444 0 0 32 29 0.008891
118.0 102 51 37 102.860278 0 0 32 15 0.008890
118.5 103 7 44 103.128889 0 0 32 0 0.008889
119.0 103 23 44 103.395556 0 0 31 46 0.008615
119.5 103 39 37 103.660278 0 0 31 32 0.008614
120.0 103 55 23 103.923056 0 0 31 18 0.008613
120.5 104 11 2 104.183889 0 0 31 4 0.008611
121.0 104 26 34 104.442778 0 0 30 49 0.008337
121.5 104 41 59 104.699722 0 0 30 35 0.008336
122.0 104 57 16 104.954444 0 0 30 21 0.008335
122.5 105 12 26 105.207222 0 0 30 7 0.008334
123.0 105 27 30 105.458333 0 0 29 52 0.008060
123.5 105 42 26 105.707222 0 0 29 37 0.008058
124.0 105 57 14 105.953889 0 0 29 23 0.008057
124.5 106 11 55 106.198611 0 0 29 8 0.008056
125.0 106 26 29 106.441389 0 0 28 54 0.007782
125.5 106 40 56 106.682222 0 0 28 39 0.007781
126.0 106 55 15 106.920833 0 0 28 24 0.007780
126.5 107 9 27 107.157500 0 0 28 10 0.007779
127.0 107 23 32 107.392222 0 0 27 56 0.007504
127.5 107 37 30 107.625000 0 0 27 40 0.007503
128.0 107 51 20 107.855556 0 0 27 25 0.007502
128.5 108 5 2 108.083889 0 0 27 10 0.007501
129.0 108 18 37 108.310278 0 0 26 56 0.007227
129.5 108 32 5 108.534722 0 0 26 41 0.007225
130.0 108 45 25 108.756944 0 0 26 26 0.007224
130.5 108 58 38 108.977222 0 0 26 11 0.007223
131.0 109 11 44 109.195556 0 0 25 56 0.006949
131.5 109 24 42 109.411667 0 0 25 41 0.006948
132.0 109 37 32 109.625556 0 0 25 26 0.006946
132.5 109 50 15 109.837500 0 0 25 11 0.006945
133.0 110 2 50 110.047222 0 0 24 56 0.006671
133.5 110 15 18 110.255000 0 0 24 41 0.006670
134.0 110 27 39 110.460833 0 0 24 26 0.006669
134.5 110 39 52 110.664444 0 0 24 10 0.006667
135.0 110 51 57 110.865833 0 0 23 55 0.006393
135.5 111 3 54 111.065000 0 0 23 40 0.006392
136.0 111 15 44 111.262222 0 0 23 25 0.006391
136.5 111 27 26 111.457222 0 0 23 9 0.006390
137.0 111 39 1 111.650278 0 0 22 54 0.006115
137.5 111 50 28 111.841111 0 0 22 39 0.006114
138.0 112 1 47 112.029722 0 0 22 24 0.006113
138.5 112 12 59 112.216389 0 0 22 8 0.006112
139.0 112 24 3 112.400833 0 0 21 53 0.005837
139.5 112 35 0 112.583333 0 0 21 37 0.005836
140.0 112 45 48 112.763333 0 0 21 22 0.005835
140.5 112 56 29 112.941389 0 0 21 7 0.005834
141.0 113 7 2 113.117222 0 0 20 51 0.005559
141.5 113 17 26 113.290556 0 0 20 36 0.005558
142.0 113 27 44 113.462222 0 0 20 20 0.005557
142.5 113 37 54 113.631667 0 0 20 4 0.005556
143.0 113 47 56 113.798889 0 0 19 49 0.005282
143.5 113 57 50 113.963889 0 0 19 33 0.005280
144.0 114 7 37 114.126944 0 0 19 17 0.005279
144.5 114 17 15 114.287500 0 0 19 2 0.005278
145.0 114 26 46 114.446111 0 0 18 46 0.005004
145.5 114 36 9 114.602500 0 0 18 30 0.005002
146.0 114 45 24 114.756667 0 0 18 14 0.005001
146.5 114 54 31 114.908611 0 0 17 59 0.004727
147.0 115 3 30 115.058333 0 0 17 43 0.004726
147.5 115 12 22 115.206111 0 0 17 27 0.004724
148.0 115 21 6 115.351667 0 0 17 11 0.004723
148.5 115 29 41 115.494722 0 0 16 55 0.004449
149.0 115 38 9 115.635833 0 0 16 40 0.004448
149.5 115 46 29 115.774722 0 0 16 24 0.004446
150.0 115 54 40 115.911111 0 0 16 8 0.004445
150.5 116 2 44 116.045556 0 0 15 52 0.004171
151.0 116 10 40 116.177778 0 0 15 36 0.004169
151.5 116 18 28 116.307778 0 0 15 20 0.004168
152.0 116 26 8 116.435556 0 0 15 4 0.004167
152.5 116 33 40 116.561111 0 0 14 48 0.003893
153.0 116 41 4 116.684444 0 0 14 32 0.003891
153.5 116 48 20 116.805556 0 0 14 16 0.003890
154.0 116 55 28 116.924444 0 0 14 0 0.003889
154.5 117 2 28 117.041111 0 0 13 44 0.003615
155.0 117 9 20 117.155556 0 0 13 28 0.003613
155.5 117 16 4 117.267778 0 0 13 12 0.003612
156.0 117 22 40 117.377778 0 0 12 56 0.003338
156.5 117 29 8 117.485556 0 0 12 40 0.003336
157.0 117 35 28 117.591111 0 0 12 24 0.003335
157.5 117 41 40 117.694444 0 0 12 7 0.003334
158.0 117 47 43 117.795278 0 0 11 51 0.003059
158.5 117 53 39 117.894167 0 0 11 35 0.003058
159.0 117 59 27 117.990833 0 0 11 19 0.003057
159.5 118 5 7 118.085278 0 0 10 53 0.002782
160.0 118 10 37 118.176944 0 0 10 47 0.002781
160.5 118 16 1 118.266944 0 0 10 31 0.002780
161.0 118 21 16 118.354444 0 0 10 14 0.002779
161.5 118 26 23 118.439722 0 0 9 58 0.002504
162.0 118 31 22 118.522778 0 0 9 42 0.002503
162.5 118 36 13 118.603611 0 0 9 25 0.002502
163.0 118 40 55 118.681944 0 0 9 9 0.002501
163.5 118 45 30 118.758333 0 0 8 53 0.002226
164.0 118 49 56 118.832222 0 0 8 37 0.002225
164.5 118 54 15 118.904167 0 0 8 20 0.002224
165.0 118 58 25 118.973611 0 0 8 4 0.002223
165.5 119 2 26 119.040556 0 0 7 48 0.001948
166.0 119 6 20 119.105556 0 0 7 31 0.001947
166.5 119 10 6 119.168333 0 0 7 15 0.001946
167.0 119 13 44 119.228889 0 0 6 59 0.001671
167.5 119 17 13 119.286944 0 0 6 42 0.001670
168.0 119 20 34 119.342778 0 0 6 26 0.001669
168.5 119 23 47 119.396389 0 0 6 10 0.001667
169.0 119 26 52 119.447778 0 0 5 53 0.001393
169.5 119 29 49 119.496944 0 0 5 37 0.001392
170.0 119 32 37 119.543611 0 0 5 20 0.001390
170.5 119 35 17 119.588056 0 0 5 4 0.001389
171.0 119 37 49 119.630278 0 0 4 48 0.001115
171.5 119 40 13 119.670278 0 0 4 31 0.001114
172.0 119 42 28 119.707778 0 0 4 14 0.001112
172.5 119 44 35 119.743056 0 0 3 58 0.000838
173.0 119 46 35 119.776389 0 0 3 42 0.000837
173.5 119 48 26 119.807222 0 0 3 26 0.000835
174.0 119 50 8 119.835556 0 0 3 9 0.000834
174.5 119 51 43 119.861944 0 0 2 53 0.000560
175.0 119 53 10 119.886111 0 0 2 36 0.000558
175.5 119 54 27 119.907500 0 0 2 20 0.000557
176.0 119 55 38 119.927222 0 0 2 3 0.000556
176.5 119 56 39 119.944167 0 0 1 47 0.000281
177.0 119 57 32 119.958889 0 0 1 30 0.000280
177.5 119 58 18 119.971667 0 0 1 14 0.000279
178.0 119 58 55 119.981944 0 0 0 57 0.000004
178.5 119 59 24 119.990000 0 0 0 41 0.000003
179.0 119 59 44 119.995556 0 0 0 25 0.000002
179.5 119 59 56 119.998889 0 0 0 9 0.000001
180.0 120 0 0 120.000000 0 0 0 0 0.000000