Determination of Julian Day Numbers

The Julian day number of a given day can be determined from Tables 27-29. The date must be expressed in terms of the Gregorian calendar.

The procedure is as follows:

1. Enter the table of century years (Table 27) with the century year immediately preceding the date in question, and take out the tabular value. If the century year is marked with a $\dag$, note this fact for use in step 2.
2. Enter the table of years of the century (Table 28) with the last two digits of the year in question, and take out the tabular value. If the century year used in step 1 was marked with a $\dag$, diminish the tabular value by one day, unless the tabular value is zero. If the year in question is a leap year, marked with a $\ast$, note this fact for use in step 3.

3. Enter the table of the days of the year (Table 29) with the day in question, and take out the tabular value. If the year in question is a leap year and the table entry falls after February 28, add one day to the tabular value. The sum of the values obtained in steps 1, 2, and 3 then gives the Julian day number of the date in question.

 
Example 1: June 10, 1992 CE:
 

1. Century year	$^\dag$1900		2415020
2. Year of the century	$^\ast$92	33603 - 1 =	33602
3. Day of the year	June 10	161+1 =	162
Julian day number			2448784

Observe that in step 2 the tabular value has been diminished by 1 because 1900 is a common year (marked with a $\dag$ in Table 27). In step 3, the tabular value has been increased by 1 because 1992 is a leap year (marked with a $\ast$ in Table 28), and the date falls after February 28.

 
Example 2: January 18, 1824 CE:
 

1. Century year	$^\dag$1800		2378496
2. Year of the century	$^\ast$24	8766 - 1 =	8765
3. Day of the year	January 18	18 =	18
Julian day number			2387279

Observe that in step 2 the tabular value has been diminished by 1 because 1800 is a common year (marked with a $\dag$ in Table 27). In step 3, the tabular value has not been increased by 1, despite the fact that 1824 is a leap year (marked with an $\ast$ in Table 28), because the date falls before February 28.

We can specify the time of day (in universal time), as well as the date, by means of fractional Julian day numbers. For instance, $t=2\,448\,784.0$ JD corresponds to 12:00 UT on June 10, 1992 CE, whereas $t=2\,448\,784.5$ JD corresponds to 24:00 UT later the same day.

Table 27: Julian Day Number: Century Years. $\dag$Common years. All years are CE. From ``The History and Practice of Ancient Astronomy", J. Evans (Oxford University Press, Oxford UK, 1998).

$^\dag$1800	2378496
$^\dag$1900	2415020
2000	2451544

Table 28: Julian Day Number: Years of the Century. $\ast$Leap year. $S$Leap year unless century is marked $\dag$. In centuries marked $\dag$, subtract one day from the tabulated values for the years 1 through 99. From ``The History and Practice of Ancient Astronomy", J. Evans (Oxford University Press, Oxford UK, 1998).

$^\S$0	0	$^\ast$20	7305	$^\ast$40	14610	$^\ast$60	21915	$^\ast$80	29220
1	336	21	7671	41	14976	61	22281	81	29586
2	731	22	8036	42	15341	62	22646	82	29951
3	1096	23	8401	43	15706	63	22011	83	30316
$^\ast$4	1461	$^\ast$24	8766	$^\ast$44	16071	$^\ast$64	23376	$^\ast$84	30681
5	1827	25	9132	45	16437	65	23742	85	31047
6	2192	26	9497	46	16802	66	24107	86	31412
7	2557	27	9862	47	17167	67	24472	87	31777
$^\ast$8	2922	$^\ast$28	10227	$^\ast 48$	17532	$^\ast 68$	24837	$^\ast$88	32142
9	3288	29	10593	49	17898	69	25203	89	32508
10	3653	30	10958	50	18263	70	25568	90	32873
11	4018	31	11323	51	18628	71	25933	91	33238
$^\ast$12	4383	$^\ast$32	11688	$^\ast$52	18993	$^\ast$72	26298	$^\ast$92	33603
13	4749	33	12054	53	19359	73	26664	93	33969
14	5114	34	12419	54	19724	74	27029	94	34334
15	5479	35	12784	55	20089	75	27394	95	34699
$^\ast$16	5844	$^\ast$36	13149	$^\ast$56	20454	$^\ast$76	27759	$^\ast$96	35064
17	6210	37	13515	57	20820	77	28125	97	35430
18	6575	38	13880	58	21185	78	28490	98	35795
19	6940	39	14245	59	21550	79	28855	99	36160

Table 29: Julian Day Number: Days of the Year. $\ast$In leap year, after February 28, add 1 to the tabulated value. From ``The History and Practice of Ancient Astronomy", J. Evans (Oxford University Press, Oxford UK, 1998).

Day	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
1	1	32	60	91	121	152	182	213	244	274	305	335
2	2	33	61	92	122	153	183	214	245	275	306	336
3	3	34	62	93	123	154	184	215	246	276	307	337
4	4	35	63	94	124	155	185	216	247	277	308	338
5	5	36	64	95	125	156	186	217	248	278	309	339
6	6	37	65	96	126	157	187	218	249	279	310	340
7	7	38	66	97	127	158	188	219	250	280	311	341
8	8	39	67	98	128	159	189	220	251	281	312	342
9	9	40	68	99	129	160	190	221	252	282	313	343
10	10	41	69	100	130	161	191	222	253	283	314	344
11	11	42	70	101	131	162	192	223	254	284	315	345
12	12	43	71	102	132	163	193	224	255	285	316	346
13	13	44	72	103	133	164	194	225	256	286	317	347
14	14	45	73	104	134	165	195	226	257	285	318	348
15	15	46	74	105	135	166	196	227	258	288	319	349
16	16	47	75	106	136	167	197	228	259	289	320	350
17	17	48	76	107	137	168	198	229	260	290	321	351
18	18	49	77	108	138	169	199	230	261	291	322	352
19	19	50	78	109	139	170	200	231	262	292	323	353
20	20	51	79	110	140	171	201	232	263	293	324	354
21	21	52	80	111	141	172	202	233	264	294	325	355
22	22	53	81	112	142	173	203	234	265	295	326	356
23	23	54	82	113	143	174	204	235	266	296	327	357
24	24	55	83	114	144	175	205	236	267	297	328	358
25	25	56	84	115	145	176	206	237	268	298	329	359
26	26	57	85	116	146	177	207	238	269	299	330	360
27	27	58	86	117	147	178	208	239	270	300	331	361
28	28	59	87	118	148	179	209	240	271	301	332	362
29	29	$\ast$	88	119	149	180	210	241	272	302	333	363
30	30		89	120	150	181	211	242	273	303	334	364
31	31		90		151		212	243		304		365