Ordinal date

The older names are deprecated because they are easily confused with the earlier dating system called 'Julian day number' or JDN, which was in prior use and which remains ubiquitous in astronomical and some historical calculations.

It is also part of calculating the day of the week, though for this purpose modulo 7 simplifications can be made.

The inputs taken are integers y, m and d, for the year, month, and day numbers of the Gregorian or Julian calendar date.

The most trivial method of calculating the ordinal day involves counting up all days that have elapsed per the definition: Similarly trivial is the use of a lookup table, such as the one referenced.

[3] The table of month lengths can be replaced following the method of encoding the month-length variation in Zeller's congruence.

It can be shown (see below) that for a month-number m, the total days of the preceding months is equal to ⌊(153 * (m − 3) + 2) / 5⌋.

As a result, the March 1-based ordinal day number is OMar = ⌊(153 × (m − 3) + 2) / 5⌋ + d. 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 twice.

This is similar to encoding of the month offset (which would be the same sequence modulo 7) in Zeller's congruence.