Ordinal date

Ordinal date is the preferred name for what was formerly called the "Julian date" or JD, or JDATE, which still seen in old programming languages and spreadsheet software. 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.

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

To the day of	13 Jan	14 Feb	3 Mar	4 Apr	5 May	6 Jun	7 Jul	8 Aug	9 Sep	10 Oct	11 Nov	12 Dec	i
Add	0	31	59	90	120	151	181	212	243	273	304	334	3
Leap years	0	31	60	91	121	152	182	213	244	274	305	335	2
Algorithm	${\displaystyle 30(m-1)+\left\lfloor 0.6(m+1)\right\rfloor -i}$

For example, the ordinal date of April 15 is 90 + 15 = 105 in a common year, and 91 + 15 = 106 in a leap year.

The number of the month and date is given by

${\displaystyle m=\left\lfloor od/30\right\rfloor +1}$

${\displaystyle d={\bmod {\!}}\!(od,30)+i-\left\lfloor 0.6(m+1)\right\rfloor }$

the term ${\displaystyle {\bmod {\!}}\!(od,30)}$ can also be replaced by ${\displaystyle od-30(m-1)}$ with ${\displaystyle od}$ the ordinal date.

• Day 100 of a common year:

${\displaystyle m=\left\lfloor 100/30\right\rfloor +1=4}$

${\displaystyle d={\bmod {\!}}\!(100,30)+3-\left\lfloor 0.6(4+1)\right\rfloor =10+3-3=10}$

April 10.

• Day 200 of a common year:

${\displaystyle m=\left\lfloor 200/30\right\rfloor +1=7}$

${\displaystyle d={\bmod {\!}}\!(200,30)+3-\left\lfloor 0.6(7+1)\right\rfloor =20+3-4=19}$

July 19.

• Day 300 of a leap year:

${\displaystyle m=\left\lfloor 300/30\right\rfloor +1=11}$

${\displaystyle d={\bmod {\!}}\!(300,30)+2-\left\lfloor 0.6(11+1)\right\rfloor =0+2-7=-5}$

November - 5 = October 26 (31 - 5).

• Julian day
• Zeller's congruence
• ISO week date