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Computation of the ordinal day within a year is part of calculating the ordinal day 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. In the following text, several algorithms for calculating the ordinal day O are ...
This template generates an ordinal date. Used alone as {{Ordinal date}} it will generate the ordinal date for the current year-month-day. Check the result at tycho.usno.navy.mil after this page. This template may also be used to generate the ordinal date for any Gregorian calendar dates by passing the proper syntax to the following variables:
This template returns the date (month name and day of month) from a day number in a year. Syntax: {{Date from ordinal|day of year}} {{Date from ordinal|day of year|year}} {{Date from ordinal|day of year|leapyear=isleap}} The year parameter is optional. If specified the date serial is handled for that specific year (leapyear is then ignored).
No guidance is provided about conversion of dates before March 5, -500, or after February 29, 2100 (both being Julian dates). For unlisted dates, find the date in the table closest to, but earlier than, the date to be converted. Be sure to use the correct column. If converting from Julian to Gregorian, add the number from the "Difference" column.
The result is the ordinal date, which can be converted into a calendar date. If the ordinal date thus obtained is zero or negative, the date belongs to the previous calendar year; if it is greater than the number of days in the year, it belongs to the following year. Formula
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Or, like a Julian day, does an ordinal date begin at noon, so: At midnight when January 1 begins, the ordinal date is -0.5; At noon on January 1, the ordinal date is 1.0; At midnight when January 2 begins, the ordinal date is 1.5; This question relates to the formulas in declination#Sun, where the value of 'N' is
And the function θ γ is defined to be the function enumerating the ordinals δ with δ∉C(γ,δ). The problem with this system is that ordinal notations and collapsing functions are not identical, and therefore this function does not qualify as an ordinal notation. An associated ordinal notation is not known.