An ordinal date is a calendar date

Calendar date

A date in a calendar is a reference to a particular day represented within a calendar system. The calendar date allows the specific day to be identified. The number of days between two dates may be calculated. For example, "24 " is ten days after "14 " in the Gregorian calendar. The date of a...

 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

Epoch (reference date)

In the fields of chronology and periodization, an epoch is an instance in time chosen as the origin of a particular era. The "epoch" then serves as a reference point from which time is measured...

, such as the Julian date. It is also part of calculating the day of the week

Calculating the day of the week

This article details various mathematical algorithms to calculate the day of the week for any particular date in the past or future.A typical application is to calculate the day of the week on which someone was born or some other special event occurred....

, 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

Floor function

In mathematics and computer science, the floor and ceiling functions map a real number to the largest previous or the smallest following integer, respectively...

 ( 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

Doomsday (weekday)

The Doomsday rule or Doomsday algorithm is a way of calculating the day of the week of a given date. It provides a perpetual calendar since the Gregorian calendar moves in cycles of 400 years....

" 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
  Leap year
  A leap year is a year containing one extra day in order to keep the calendar year synchronized with the astronomical or seasonal 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.

See also

• Julian day - Calculation
• Zeller's congruence
  Zeller's congruence
  Zeller's congruence is an algorithm devised by Christian Zeller to calculate the day of the week for any Julian or Gregorian calendar date.- Formula :For the Gregorian calendar, Zeller's congruence is...