Ordinal date
An ordinal date is a calendar date typically consisting of a year and a day of year ranging between 1 and 366 (starting on January 1), though year may sometimes be omitted. The two numbers can be formatted as YYYY-DDD to comply with the ISO 8601 ordinal date format.
Calculation
Computation of the ordinal date within a year is part of calculating the ordinal date throughout the years from a reference date, such as the Julian date. It is also part of calculating the day of the week, though for this purpose modulo-7 simplifications can be made.
For these purposes it is convenient to count January and February as month 13 and 14 of the previous year, for two reasons: the shortness of February and its variable length. In that case the date counted from 1 March is given by
- floor ( 30.6 ( m + 1 ) ) + d − 122
which can also be written
- floor (30.6 m − 91.4 ) + d
with m the month number and d the date.
The formula reflects the fact that any five consecutive months in the range March–January have a total length of 153 days, due to a fixed pattern 31–30–31–30–31 repeating itself some more than twice.
"Doomsday" properties:
For m = 2n and d=m we get
- floor (63.2 n − 91.4 )
giving consecutive differences of 63 (9 weeks) for n = 2, 3, 4, 5, and 6, i.e., between 4/4, 6/6, 8/8, 10/10, and 12/12.
For m = 2n + 1 and d=m + 4 we get
- floor (63.2 n − 56.8 )
and with m and d interchanged
- floor (63.2 n − 56.8 + 118.4 )
giving a difference of 119 (17 weeks) for n = 2 (difference between 5/9 and 9/5), and also for n = 3 (difference between 7/11 and 11/7).
The ordinal date from 1 January is:
- for January: d
- for February: d + 31
- for the other months: the ordinal date from 1 March plus 59, or 60 in a leap year
or equivalently, the ordinal date from 1 March of the previous year (for which the formula above can be used) minus 306.
Modulo 7
Again counting January and February as month 13 and 14 of the previous year, the date counted from 1 March is modulo 7 equal to
- floor (2.6 m − 0.4 ) + d
with m the month number and d the date.
Table
| To the day of | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Add | 0 | 31 | 59 | 90 | 120 | 151 | 181 | 212 | 243 | 273 | 304 | 334 |
| Leap years | 0 | 31 | 60 | 91 | 121 | 152 | 182 | 213 | 244 | 274 | 305 | 335 |
For example, the ordinal date of April 15 is 90 + 15 = 105 in a common year, and 91 + 15 = 106 in a leap year.
References and external links
- Abstract for article on standard "Representation for Calendar Date and Ordinal Date for Information Interchange", Federal Information Processing Standards Publication 4-1, 1988 January 27, National Institute of Standards and Technology
- Perpetual Julian/ordinal date chart (browser needs to be able to read PDF files).