On the first of these pages, a perpetual calendar was shown by means of which one could obtain the last digit of the Julian Day for any date. However, obtaining the whole Julian Day Number is useful for relating specific dates, and is also a different kind of problem.
As with the perpetual calendars on the first of these pages, for simplicity one treats January and February as though they belong to the end of the preceding year.
Start from this number, giving the Julian Day number for noon GMT on March 1st on the first year of a century:
Julian:
400 1867218 800 2013318 1200 2159418 1600 2305518
500 1903743 900 2049843 1300 2195943 1700 2342043
600 1940268 1000 2086368 1400 2232468
700 1976793 1100 2122893 1500 2268993
Gregorian:
1600 2305508 2000 2451605 2400 2597702
1700 2342032 2100 2488129 2500 2634226
1800 2378556 2200 2524653 2600 2670750
1500 2268983 1900 2415080 2300 2561177 2700 2707274
2800 2743799
2900 2780323
3000 2816847
3100 2853371
add this number for the year of the century:
0 1 2 3 4 5 6 7 8 9
00 0 365 730 1095 1461 1826 2191 2556 2922 3287
10 3652 4017 4383 4748 5113 5478 5844 6209 6574 6939
20 7305 7670 8035 8400 8766 9131 9496 9861 10227 10592
30 10957 11322 11688 12053 12418 12783 13149 13514 13879 14244
40 14610 14975 15340 15705 16071 16436 16801 17166 17532 17897
50 18262 18627 18993 19358 19723 20088 20454 20819 21184 21549
60 21915 22280 22645 23010 23376 23741 24106 24471 24837 25202
70 25567 25932 26298 26663 27028 27393 27759 28124 28489 28854
80 29220 29585 29950 30315 30681 31046 31411 31776 32142 32507
90 32872 33237 33603 33968 34333 34698 35064 35429 35794 36159
add this number for the day of the year:
Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb
1 0 31 61 92 122 153 184 214 245 275 306 337
2 1 32 62 93 123 154 185 215 246 276 307 338
3 2 33 63 94 124 155 186 216 247 277 308 339
4 3 34 64 95 125 156 187 217 248 278 309 340
5 4 35 65 96 126 157 188 218 249 279 310 341
6 5 36 66 97 127 158 189 219 250 280 311 342
7 6 37 67 98 128 159 190 220 251 281 312 343
8 7 38 68 99 129 160 191 221 252 282 313 344
9 8 39 69 100 130 161 192 222 253 283 314 345
10 9 40 70 101 131 162 193 223 254 284 315 346
11 10 41 71 102 132 163 194 224 255 285 316 347
12 11 42 72 103 133 164 195 225 256 286 317 348
13 12 43 73 104 134 165 196 226 257 287 318 349
14 13 44 74 105 135 166 197 227 258 288 319 350
15 14 45 75 106 136 167 198 228 259 289 320 351
16 15 46 76 107 137 168 199 229 260 290 321 352
17 16 47 77 108 138 169 200 230 261 291 322 353
18 17 48 78 109 139 170 201 231 262 292 323 354
19 18 49 79 110 140 171 202 232 263 293 324 355
20 19 50 80 111 141 172 203 233 264 294 325 356
21 20 51 81 112 142 173 204 234 265 295 326 357
22 21 52 82 113 143 174 205 235 266 296 327 358
23 22 53 83 114 144 175 206 236 267 297 328 359
24 23 54 84 115 145 176 207 237 268 298 329 360
25 24 55 85 116 146 177 208 238 269 299 330 361
26 25 56 86 117 147 178 209 239 270 300 331 362
27 26 57 87 118 148 179 210 240 271 301 332 363
28 27 58 88 119 149 180 211 241 272 302 333 364
29 28 59 89 120 150 181 212 242 273 303 334 365
30 29 60 90 121 151 182 213 243 274 304 335
31 30 91 152 183 244 305 336
and the total is the Julian Day number for noon GMT on the day for which one has consulted the table.
These three tables make it simple to calculate a Julian Day Number by adding only three numbers together.
Essentially, these tables are constructed by adding the number of days in the major cycles of the Gregorian calendar.
A year is normally 365 days long. But four years, including one leap year, is normally 1,461 days long. A hundred years, in the Gregorian calendar, normally includes one span of four years without a leap year, so it is 36,524 days long. But four hundred years in the Gregorian calendar includes one century where every span of four years has its leap year, so they are 146,097 days long.
Thus, one might construct smaller tables, each involving only one of these rules, starting from Julian Day 2305507, one day before March 1st, 1600 AD.
Thus, the first table, adding 146,097 each time, would be:
1600 2305507 2000 2451604 2400 2597701 2800 2743798
Then, for intermediate centuries, we use the preceding rule to construct this table:
0 0 100 36524 200 73048 300 109572
and combining these two tables for convenience produces the first compound table above.
Similarly, for years within the century, we can start with a table that shows the number of days for every fourth year:
0 0 20 7305 40 14610 60 21915 80 29220 4 1461 24 8766 44 16071 64 23376 84 30681 8 2922 28 10227 48 17532 68 24837 88 32142 12 4383 32 11688 52 18993 72 26298 92 33603 16 5844 36 13149 56 20454 76 27759 96 35064
combined with a short table allowing us to handle individual years:
0 0 1 365 2 730 3 1095
Combining these two tables to save another addition gives us the second combined table above.
And the final table can be replaced by just one of its rows,
Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb 0 31 61 92 122 153 184 214 245 275 306 337
since one can always add the day of the month to the month number. And since the first day of the month is numbered "1", not zero, that's why the starting century numbers were one smaller in the first of these tables than in the combined tables.
A JavaScript program to convert to and from Julian Day Numbers is available on this page.