Calculating Angular Separation of Stars

Ursa Major - a common sight in the northern skies

In this article I'll give you the tools to calculate the angular separation between two stars. If you've arrived at this page by random chance you might be wondering why you'd want to do this and the answer is that you need this information when measuring the focal length of a lens by a method I've described here - Measuring Focal Length. Using stars for this measurement is probably the easiest and most accurate method of measuring the focal length of a lens focused at infinity, at least for amateurs without access to an advanced optics lab!

Below you'll find a calculator and a list of all the stars that are brighter than 3rd magnitude. These are stars that should be visible from pretty much anywhere, even under light polluted city skies. The star names are abbreviated and consist of three parts:

1. The Flamsteed designation number. Not used much and not used for all stars
2. The Bayer designation which is a greek letter assigned to the star. e.g. alp = Alpha, bet = Beta, del = Delta
3. The Constellation. e.g. Ori = Orion, Air = Aires, CMin = Canis Minor

So for example the brightest star is 9Alp CMa and that name corresponds to the star Alpha Canis Major (also known as Sirius). It's also 9 Canis Major, but that's a designation rarely used.

To identify the names of the stars you photograph to determine focal length you'll need a star chart. You'll also need one that gives you the catalog names of the stars, so the brightest star in the sky is 9 Alpha Canis Majoris (or 9Alp CMa). If the map just labels it as "Sirius" you'll not be able to identify it in the list below.

I'd start with the free downloadable .PDF star charts from SFA. You can zoom in on the .pdf files and the catalog names (and "proper names") of the stars are given as shown below:

If you don't know your greek alphabet, you may also need this Wikipedia: Greek Alphabet or the chart above.

If you don't know your constellations and their three letter abbreviations, here they are:

OK, so once you've identified your stars you can enter their data in the form below and calculate their angular separation. Note the coordinates in the table are in the correct format, so you can just copy and paste them into the form to avoid transcription errors. Once you've done that you can go back to calculating the focal length of your lens!

Angular Separation Calculation

RA first star	hours
Dec first star	degrees
RA second star	hours
Dec second star	degrees

Remove all data from above fields:

You can enter coordinates either as decimal values (e.g. 5.67534 degrees or 12.7654 hours) or as degrees/hours, minutes and seconds (e.g. 5° 24' 45" or 6hrs 45min 32s).

If you use degrees/hours, minutes and seconds the format is HH MM SS or DDD MM SS with ONE space between the numbers. This is the format given in the table of star coordinates. If you use more than one space between the numbers, the calculation will be incorrect. The seconds field can contain a decimal number (e.g. 32.67). In this format hours, degrees and minutes must be 1 or 2 digit integers (e.g. 10, 3, 07). Note the first "D" in "DDD" can be a sign for negative declinations. A "+" sign is optional (declinations are assumed to be positive), but a "-" sign is required for negative declinations, so that -10, -1, -02, 12, +08, 6, and 06 are all acceptable values.

Examples of correct formatting for non-decimal entries are 06 45 08.90 for RA (Right Ascension) and -16 42 58.0 for a (negative) declination

If you use HH MM SS or DDD MM SS, click the convert button which will convert those values into the decimal equivalents that the calculation requires.

Angular Distance between stars =	degrees

If you want to check you're doing things right, the angular distance between Alpha Canis Major and Beta Canis Major should be 5.4984 degrees. "NaN" means "Not a Number" and indicates some error in your input data.

NOTE: This calculation does not take into account any shift in a stars apparent position due to refraction by the earth's atmosphere. For the purposes of this calculation such effects are negligible, especially if the stars are high in the sky and reasonably close together. Also, star coordinates are for the year 2000 and do not take into account proper motion. Again for the purposes here, the effect of this is negligible.

List of stars brighter than magnitude 3

Star Name	Right Ascension H M S	Declination D M S	Magnitude
9Alp CMa	06 45 08.90	-16 42 58.0	-1.46
Alp Car	06 23 57.10	-52 41 44.9	-0.72
16Alp Boo	14 15 39.70	+19 10 57.0	-0.04
Alp1Cen	14 39 35.90	-60 50 07.1	-0.01
3Alp Lyr	18 36 56.30	+38 47 01.0	0.03
13Alp Aur	05 16 41.40	+45 59 53.2	0.08
19Bet Ori	05 14 32.30	-08 12 06.1	0.12
10Alp CMi	07 39 18.10	+05 13 30.0	0.38
Alp Eri	01 37 42.89	-57 14 12.1	0.46
58Alp Ori	05 55 10.30	+07 24 24.8	0.50
Bet Cen	14 03 49.39	-60 22 23.2	0.61
53Alp Aql	19 50 46.99	+08 52 05.9	0.77
87Alp Tau	04 35 55.20	+16 30 33.1	0.85
21Alp Sco	16 29 24.41	-26 25 54.8	0.96
67Alp Vir	13 25 11.59	-11 09 41.0	0.98
78Bet Gem	07 45 18.91	+28 01 34.0	1.14
24Alp PsA	22 57 39.10	-29 37 19.9	1.16
Bet Cru	12 47 43.20	-59 41 19.0	1.25
50Alp Cyg	20 41 25.90	+45 16 49.1	1.25
Alp2Cen	14 39 36.10	-60 50 08.2	1.33
Alp1Cru	12 26 35.90	-63 05 57.1	1.33
32Alp Leo	10 08 22.30	+11 58 01.9	1.35
21Eps CMa	06 58 37.49	-28 58 19.9	1.50
Gam Cru	12 31 09.89	-57 06 47.9	1.63
35Lam Sco	17 33 36.50	-37 06 14.0	1.63
24Gam Ori	05 25 07.90	+06 20 58.9	1.64
112Bet Tau	05 26 17.50	+28 36 27.0	1.65
Bet Car	09 13 12.00	-69 43 01.9	1.68
46Eps Ori	05 36 12.79	-01 12 06.8	1.70
Alp2Cru	12 26 36.50	-63 05 57.8	1.73
Alp Gru	22 08 13.99	-46 57 40.0	1.74
77Eps UMa	12 54 01.70	+55 57 34.9	1.77
Gam2Vel	08 09 31.99	-47 20 12.1	1.78
50Alp UMa	11 03 43.70	+61 45 02.9	1.79
33Alp Per	03 24 19.39	+49 51 40.0	1.79
25Del CMa	07 08 23.50	-26 23 35.9	1.84
20Eps Sgr	18 24 10.30	-34 23 04.9	1.85
Eps Car	08 22 30.79	-59 30 34.9	1.86
85Eta UMa	13 47 32.40	+49 18 47.9	1.86
The Sco	17 37 19.20	-42 59 52.1	1.87
34Bet Aur	05 59 31.70	+44 56 51.0	1.90
Alp TrA	16 48 39.89	-69 01 40.1	1.92
24Gam Gem	06 37 42.70	+16 23 57.1	1.93
Alp Pav	20 25 38.90	-56 44 06.0	1.94
Del Vel	08 44 42.19	-54 42 29.9	1.96
30Alp Hya	09 27 35.21	-08 39 31.0	1.98
66Alp Gem	07 34 36.00	+31 53 17.9	1.98
2Bet CMa	06 22 42.00	-17 57 20.9	1.98
13Alp Ari	02 07 10.39	+23 27 45.0	2.00
1Alp UMi	02 31 48.70	+89 15 51.1	2.02
34Sig Sgr	18 55 15.91	-26 17 48.1	2.02
16Bet Cet	00 43 35.40	-17 59 12.1	2.04
50Zet Ori	05 40 45.50	-01 56 34.1	2.05
5The Cen	14 06 40.99	-36 22 12.0	2.06
21Alp And	00 08 23.30	+29 05 26.2	2.06
43Bet And	01 09 43.90	+35 37 14.2	2.06
53Kap Ori	05 47 45.41	-09 40 10.9	2.06
7Bet UMi	14 50 42.31	+74 09 20.2	2.08
55Alp Oph	17 34 56.11	+12 33 36.0	2.08
Bet Gru	22 42 40.10	-46 53 04.9	2.10
26Bet Per	03 08 10.10	+40 57 20.2	2.12
94Bet Leo	11 49 03.60	+14 34 18.8	2.14
Gam Cen	12 41 31.01	-48 57 34.9	2.17
37Gam Cyg	20 22 13.70	+40 15 24.1	2.20
Lam Vel	09 07 59.81	-43 25 57.0	2.21
18Alp Cas	00 40 30.50	+56 32 13.9	2.23
34Del Ori	05 32 00.41	-00 17 57.1	2.23
5Alp CrB	15 34 41.30	+26 42 52.9	2.23
33Gam Dra	17 56 36.41	+51 29 20.0	2.23
Iot Car	09 17 05.40	-59 16 31.1	2.25
Zet Pup	08 03 35.09	-40 00 11.9	2.25
57Gam1And	02 03 54.00	+42 19 46.9	2.26
79Zet UMa	13 23 55.49	+54 55 31.1	2.27
11Bet Cas	00 09 10.70	+59 08 58.9	2.27
26Eps Sco	16 50 09.79	-34 17 35.9	2.29
Eps Cen	13 39 53.21	-53 27 59.0	2.30
Alp Lup	14 41 55.80	-47 23 17.9	2.30
Eta Cen	14 35 30.41	-42 09 28.1	2.31
7Del Sco	16 00 19.99	-22 37 18.1	2.32
48Bet UMa	11 01 50.50	+56 22 57.0	2.37
8Eps Peg	21 44 11.21	+09 52 30.0	2.39
Alp Phe	00 26 16.99	-42 18 22.0	2.39
Kap Sco	17 42 29.30	-39 01 48.0	2.41
53Bet Peg	23 03 46.51	+28 04 58.1	2.42
35Eta Oph	17 10 22.70	-15 43 28.9	2.43
64Gam UMa	11 53 49.80	+53 41 40.9	2.44
5Alp Cep	21 18 34.80	+62 35 08.2	2.44
31Eta CMa	07 24 05.71	-29 18 11.2	2.45
53Eps Cyg	20 46 12.70	+33 58 13.1	2.46
27Gam Cas	00 56 42.50	+60 43 00.1	2.47
54Alp Peg	23 04 45.70	+15 12 19.1	2.49
Kap Vel	09 22 06.79	-55 00 38.9	2.50
92Alp Cet	03 02 16.80	+04 05 22.9	2.53
Zet Cen	13 55 32.40	-47 17 17.9	2.55
68Del Leo	11 14 06.50	+20 31 25.0	2.56
13Zet Oph	16 37 09.50	-10 34 01.9	2.56
11Alp Lep	05 32 43.80	-17 49 19.9	2.58
4Gam Crv	12 15 48.41	-17 32 30.8	2.59
Del Cen	12 08 21.50	-50 43 21.0	2.60
38Zet Sgr	19 02 36.70	-29 52 49.1	2.60
41Gam1Leo	10 19 58.30	+19 50 30.1	2.61
27Bet Lib	15 17 00.41	-09 22 59.2	2.61
37The Aur	05 59 43.30	+37 12 45.0	2.62
8Bet1Sco	16 05 26.21	-19 48 20.2	2.62
6Bet Ari	01 54 38.40	+20 48 29.2	2.64
Alp Col	05 39 38.90	-34 04 27.1	2.64
24Alp Ser	15 44 16.10	+06 25 32.2	2.65
9Bet Crv	12 34 23.21	-23 23 48.1	2.65
37Del Cas	01 25 49.01	+60 14 07.1	2.68
Bet Lup	14 58 31.90	-43 08 02.0	2.68
8Eta Boo	13 54 41.09	+18 23 52.1	2.68
Alp Mus	12 37 10.99	-69 08 08.2	2.69
Mu Vel	10 46 46.20	-49 25 12.0	2.69
34Ups Sco	17 30 45.79	-37 17 44.9	2.69
3Iot Aur	04 56 59.59	+33 09 58.0	2.69
Pi Pup	07 17 08.59	-37 05 51.0	2.70
36Eps Boo	14 44 59.21	+27 04 27.1	2.70
19Del Sgr	18 20 59.69	-29 49 41.2	2.70
50Gam Aql	19 46 15.60	+10 36 47.9	2.72
14Eta Dra	16 23 59.50	+61 30 51.1	2.74
1Del Oph	16 14 20.69	-03 41 39.8	2.74
Iot Cen	13 20 35.81	-36 42 43.9	2.75
9Alp2Lib	14 50 52.70	-16 02 30.1	2.75
The Car	10 42 57.41	-64 23 39.8	2.76
44Iot Ori	05 35 25.99	-05 54 36.0	2.77
60Bet Oph	17 43 28.39	+04 34 01.9	2.77
27Bet Her	16 30 13.20	+21 29 22.9	2.77
Gam Lup	15 35 08.50	-41 10 00.8	2.78
67Bet Eri	05 07 51.00	-05 05 11.0	2.79
23Bet Dra	17 30 25.99	+52 18 05.0	2.79
Bet Hyi	00 25 45.10	-77 15 15.1	2.80
Del Cru	12 15 08.71	-58 44 56.0	2.80
40Zet Her	16 41 17.21	+31 36 11.2	2.81
22Lam Sgr	18 27 58.20	-25 25 18.1	2.81
15Rho Pup	08 07 32.59	-24 18 15.1	2.81
23Tau Sco	16 35 52.99	-28 12 58.0	2.82
47Eps Vir	13 02 10.61	+10 57 33.1	2.83
88Gam Peg	00 13 14.21	+15 11 01.0	2.83
9Bet Lep	05 28 14.69	-20 45 33.8	2.84
Bet TrA	15 55 08.50	-63 25 50.2	2.85
Bet Ara	17 25 18.00	-55 31 48.0	2.85
44Zet Per	03 54 07.90	+31 53 01.0	2.85
Alp Hyi	01 58 46.20	-61 34 10.9	2.86
Alp Tuc	22 18 30.10	-60 15 34.9	2.86
25Eta Tau	03 47 29.11	+24 06 18.0	2.87
18Del Cyg	19 44 58.49	+45 07 50.9	2.87
49Del Cap	21 47 02.40	-16 07 37.9	2.87
13Mu Gem	06 22 57.60	+22 30 49.0	2.88
66Alp Gem	07 34 36.00	+31 53 19.0	2.88
Gam TrA	15 18 54.60	-68 40 45.8	2.89
6Pi Sco	15 58 51.10	-26 06 51.1	2.89
20Sig Sco	16 21 11.30	-25 35 34.1	2.89
45Eps Per	03 57 51.19	+40 00 37.1	2.89
41Pi Sgr	19 09 45.79	-21 01 25.0	2.89
3Bet CMi	07 27 09.00	+08 17 21.8	2.90
12Alp2CVn	12 56 01.70	+38 19 05.9	2.90
22Bet Aqr	21 31 33.50	-05 34 16.0	2.91
Tau Pup	06 49 56.21	-50 36 52.9	2.93
23Gam Per	03 04 47.81	+53 30 23.0	2.93
44Eta Peg	22 43 00.10	+30 13 17.0	2.94
Alp Ara	17 31 50.50	-49 52 34.0	2.95
34Gam Eri	03 58 01.80	-13 30 31.0	2.95
7Del Crv	12 29 51.89	-16 30 56.2	2.95
34Alp Aqr	22 05 46.99	-00 19 10.9	2.96
17Eps Leo	09 45 51.10	+23 46 27.1	2.98
27Eps Gem	06 43 55.90	+25 07 52.0	2.98
17Zet Aql	19 05 24.60	+13 51 47.9	2.99
10Gam2Sgr	18 05 48.50	-30 25 27.1	2.99
7Eps Aur	05 01 58.10	+43 49 23.9	2.99