 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 YYYYDDD to comply with the ISO 8601 ordinal date format.
Contents
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 modulo7 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.
This is the weekday relative to "Doomsday."
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 41, 1988 JANUARY 27, National Institute of Standards and Technology
 Perpetual Julian/ordinal date chart (browser needs to be able to read PDF files).
See also
Categories: Calendars
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