Template:JULIANDAY.YEAR

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This template takes a julian day number and returns the associated year number within the Gregorian calendar.

1 Computing formula (partially indented)
2 Examples with a non-leap secular year (of rank 3)
3 Examples with a leap secular year (of rank 4)
4 Examples with a non-leap non-secular year (of rank 1)
5 Examples with a non-leap non-secular year (of rank 2)
6 Examples with a non-leap non-secular year (of rank 3)
7 Examples with a leap non-secular year (of rank 4)
8 See also

Computing formula (partially indented) change

For more information about how this formula works, see Julian day.

{{#expr:
   (   (({{{1}}})+32044 round 0)     / 146097         + 0.5 round 0)                      * 400
+
  ((   (({{{1}}})+32044 round 0)   mod 146097 / 36524 + 0.5 round 0) * 3/4 + 0.5 round 0) * 100
+
  ((   (({{{1}}})+32044 round 0)   mod 146097 + 36524 -
  ((   (({{{1}}})+32044 round 0)   mod 146097 / 36524 + 0.5 round 0) * 3/4 + 0.5 round 0) * 36524
   )  /  1461       + 0.5 round 0) * 4
+
 (((   (({{{1}}})+32044 round 0)   mod 146097 + 36524 -
  ((   (({{{1}}})+32044 round 0)   mod 146097 / 36524 + 0.5 round 0) * 3/4 + 0.5 round 0) * 36524
   ) mod 1461 / 365 + 0.5 round 0) * 3 / 4 + 0.5 round 0)
+
((((   (({{{1}}})+32044 round 0)   mod 146097 + 36524 -
  ((   (({{{1}}})+32044 round 0)   mod 146097 / 36524 + 0.5 round 0) * 3/4 + 0.5 round 0) * 36524
   ) mod 1461
-
 (((   (({{{1}}})+32044 round 0)   mod 146097 + 36524 -
  ((   (({{{1}}})+32044 round 0)   mod 146097 / 36524 + 0.5 round 0) * 3/4 + 0.5 round 0) * 36524
   ) mod 1461 / 365 + 0.5 round 0) * 3 / 4 + 0.5 round 0) * 365 + 365) * 5 + 308) / 153 - 0.5 round 0)
 / 12
- 5305.5
round 0}}

The actual formula in the template drops all whitespaces shown here, as well as the "0" in "0.5".
The constant 146097 is the number of days in 400 years (Gregorian calendar)
The constant 36524 is the number of days in 100 years (Gregorian calendar)
The constant 1461 is the number of days in 4 years (Gregorian calendar)
The constant 308 adjusts the number of days in a year since last March 1 (possibly from the previous year)
The constant 153 is the number of days every 5 months (in the same year starting on March 1) excepting the addition of 1 day on July 31 and December 31.

Examples with a non-leap secular year (of rank 3) change

{{JULIANDAY.YEAR|{{JULIANDAY|1900| 1| 1}}}} = "1900".
{{JULIANDAY.YEAR|{{JULIANDAY|1900| 1|31}}}} = "1900".
{{JULIANDAY.YEAR|{{JULIANDAY|1900| 2| 1}}}} = "1900".
{{JULIANDAY.YEAR|{{JULIANDAY|1900| 2|28}}}} = "1900".
{{JULIANDAY.YEAR|{{JULIANDAY|1900| 3| 1}}}} = "1900".
{{JULIANDAY.YEAR|{{JULIANDAY|1900| 3|31}}}} = "1900".
{{JULIANDAY.YEAR|{{JULIANDAY|1900| 4| 1}}}} = "1900".
{{JULIANDAY.YEAR|{{JULIANDAY|1900| 4|30}}}} = "1900".
{{JULIANDAY.YEAR|{{JULIANDAY|1900| 5| 1}}}} = "1900".
{{JULIANDAY.YEAR|{{JULIANDAY|1900| 5|31}}}} = "1900".
{{JULIANDAY.YEAR|{{JULIANDAY|1900| 6| 1}}}} = "1900".
{{JULIANDAY.YEAR|{{JULIANDAY|1900| 6|30}}}} = "1900".
{{JULIANDAY.YEAR|{{JULIANDAY|1900| 7| 1}}}} = "1900".
{{JULIANDAY.YEAR|{{JULIANDAY|1900| 7|31}}}} = "1900".
{{JULIANDAY.YEAR|{{JULIANDAY|1900| 8| 1}}}} = "1900".
{{JULIANDAY.YEAR|{{JULIANDAY|1900| 8|31}}}} = "1900".
{{JULIANDAY.YEAR|{{JULIANDAY|1900| 9| 1}}}} = "1900".
{{JULIANDAY.YEAR|{{JULIANDAY|1900| 9|30}}}} = "1900".
{{JULIANDAY.YEAR|{{JULIANDAY|1900|10| 1}}}} = "1900".
{{JULIANDAY.YEAR|{{JULIANDAY|1900|10|31}}}} = "1900".
{{JULIANDAY.YEAR|{{JULIANDAY|1900|11| 1}}}} = "1900".
{{JULIANDAY.YEAR|{{JULIANDAY|1900|11|30}}}} = "1900".
{{JULIANDAY.YEAR|{{JULIANDAY|1900|12| 1}}}} = "1900".
{{JULIANDAY.YEAR|{{JULIANDAY|1900|12|31}}}} = "1900".

Examples with a leap secular year (of rank 4) change

{{JULIANDAY.YEAR|{{JULIANDAY|2000| 1| 1}}}} = "2000".
{{JULIANDAY.YEAR|{{JULIANDAY|2000| 1|31}}}} = "2000".
{{JULIANDAY.YEAR|{{JULIANDAY|2000| 2| 1}}}} = "2000".
{{JULIANDAY.YEAR|{{JULIANDAY|2000| 2|29}}}} = "2000".
{{JULIANDAY.YEAR|{{JULIANDAY|2000| 3| 1}}}} = "2000".
{{JULIANDAY.YEAR|{{JULIANDAY|2000| 3|31}}}} = "2000".
{{JULIANDAY.YEAR|{{JULIANDAY|2000| 4| 1}}}} = "2000".
{{JULIANDAY.YEAR|{{JULIANDAY|2000| 4|30}}}} = "2000".
{{JULIANDAY.YEAR|{{JULIANDAY|2000| 5| 1}}}} = "2000".
{{JULIANDAY.YEAR|{{JULIANDAY|2000| 5|31}}}} = "2000".
{{JULIANDAY.YEAR|{{JULIANDAY|2000| 6| 1}}}} = "2000".
{{JULIANDAY.YEAR|{{JULIANDAY|2000| 6|30}}}} = "2000".
{{JULIANDAY.YEAR|{{JULIANDAY|2000| 7| 1}}}} = "2000".
{{JULIANDAY.YEAR|{{JULIANDAY|2000| 7|31}}}} = "2000".
{{JULIANDAY.YEAR|{{JULIANDAY|2000| 8| 1}}}} = "2000".
{{JULIANDAY.YEAR|{{JULIANDAY|2000| 8|31}}}} = "2000".
{{JULIANDAY.YEAR|{{JULIANDAY|2000| 9| 1}}}} = "2000".
{{JULIANDAY.YEAR|{{JULIANDAY|2000| 9|30}}}} = "2000".
{{JULIANDAY.YEAR|{{JULIANDAY|2000|10| 1}}}} = "2000".
{{JULIANDAY.YEAR|{{JULIANDAY|2000|10|31}}}} = "2000".
{{JULIANDAY.YEAR|{{JULIANDAY|2000|11| 1}}}} = "2000".
{{JULIANDAY.YEAR|{{JULIANDAY|2000|11|30}}}} = "2000".
{{JULIANDAY.YEAR|{{JULIANDAY|2000|12| 1}}}} = "2000".
{{JULIANDAY.YEAR|{{JULIANDAY|2000|12|31}}}} = "2000".

Examples with a non-leap non-secular year (of rank 1) change

{{JULIANDAY.YEAR|{{JULIANDAY|2001| 1| 1}}}} = "2001".
{{JULIANDAY.YEAR|{{JULIANDAY|2001| 1|31}}}} = "2001".
{{JULIANDAY.YEAR|{{JULIANDAY|2001| 2| 1}}}} = "2001".
{{JULIANDAY.YEAR|{{JULIANDAY|2001| 2|28}}}} = "2001".
{{JULIANDAY.YEAR|{{JULIANDAY|2001| 3| 1}}}} = "2001".
{{JULIANDAY.YEAR|{{JULIANDAY|2001| 3|31}}}} = "2001".
{{JULIANDAY.YEAR|{{JULIANDAY|2001| 4| 1}}}} = "2001".
{{JULIANDAY.YEAR|{{JULIANDAY|2001| 4|30}}}} = "2001".
{{JULIANDAY.YEAR|{{JULIANDAY|2001| 5| 1}}}} = "2001".
{{JULIANDAY.YEAR|{{JULIANDAY|2001| 5|31}}}} = "2001".
{{JULIANDAY.YEAR|{{JULIANDAY|2001| 6| 1}}}} = "2001".
{{JULIANDAY.YEAR|{{JULIANDAY|2001| 6|30}}}} = "2001".
{{JULIANDAY.YEAR|{{JULIANDAY|2001| 7| 1}}}} = "2001".
{{JULIANDAY.YEAR|{{JULIANDAY|2001| 7|31}}}} = "2001".
{{JULIANDAY.YEAR|{{JULIANDAY|2001| 8| 1}}}} = "2001".
{{JULIANDAY.YEAR|{{JULIANDAY|2001| 8|31}}}} = "2001".
{{JULIANDAY.YEAR|{{JULIANDAY|2001| 9| 1}}}} = "2001".
{{JULIANDAY.YEAR|{{JULIANDAY|2001| 9|30}}}} = "2001".
{{JULIANDAY.YEAR|{{JULIANDAY|2001|10| 1}}}} = "2001".
{{JULIANDAY.YEAR|{{JULIANDAY|2001|10|31}}}} = "2001".
{{JULIANDAY.YEAR|{{JULIANDAY|2001|11| 1}}}} = "2001".
{{JULIANDAY.YEAR|{{JULIANDAY|2001|11|30}}}} = "2001".
{{JULIANDAY.YEAR|{{JULIANDAY|2001|12| 1}}}} = "2001".
{{JULIANDAY.YEAR|{{JULIANDAY|2001|12|31}}}} = "2001".

Examples with a non-leap non-secular year (of rank 2) change

{{JULIANDAY.YEAR|{{JULIANDAY|2002| 1| 1}}}} = "2002".
{{JULIANDAY.YEAR|{{JULIANDAY|2002| 1|31}}}} = "2002".
{{JULIANDAY.YEAR|{{JULIANDAY|2002| 2| 1}}}} = "2002".
{{JULIANDAY.YEAR|{{JULIANDAY|2002| 2|28}}}} = "2002".
{{JULIANDAY.YEAR|{{JULIANDAY|2002| 3| 1}}}} = "2002".
{{JULIANDAY.YEAR|{{JULIANDAY|2002| 3|31}}}} = "2002".
{{JULIANDAY.YEAR|{{JULIANDAY|2002| 4| 1}}}} = "2002".
{{JULIANDAY.YEAR|{{JULIANDAY|2002| 4|30}}}} = "2002".
{{JULIANDAY.YEAR|{{JULIANDAY|2002| 5| 1}}}} = "2002".
{{JULIANDAY.YEAR|{{JULIANDAY|2002| 5|31}}}} = "2002".
{{JULIANDAY.YEAR|{{JULIANDAY|2002| 6| 1}}}} = "2002".
{{JULIANDAY.YEAR|{{JULIANDAY|2002| 6|30}}}} = "2002".
{{JULIANDAY.YEAR|{{JULIANDAY|2002| 7| 1}}}} = "2002".
{{JULIANDAY.YEAR|{{JULIANDAY|2002| 7|31}}}} = "2002".
{{JULIANDAY.YEAR|{{JULIANDAY|2002| 8| 1}}}} = "2002".
{{JULIANDAY.YEAR|{{JULIANDAY|2002| 8|31}}}} = "2002".
{{JULIANDAY.YEAR|{{JULIANDAY|2002| 9| 1}}}} = "2002".
{{JULIANDAY.YEAR|{{JULIANDAY|2002| 9|30}}}} = "2002".
{{JULIANDAY.YEAR|{{JULIANDAY|2002|10| 1}}}} = "2002".
{{JULIANDAY.YEAR|{{JULIANDAY|2002|10|31}}}} = "2002".
{{JULIANDAY.YEAR|{{JULIANDAY|2002|11| 1}}}} = "2002".
{{JULIANDAY.YEAR|{{JULIANDAY|2002|11|30}}}} = "2002".
{{JULIANDAY.YEAR|{{JULIANDAY|2002|12| 1}}}} = "2002".
{{JULIANDAY.YEAR|{{JULIANDAY|2002|12|31}}}} = "2002".

Examples with a non-leap non-secular year (of rank 3) change

{{JULIANDAY.YEAR|{{JULIANDAY|2003| 1| 1}}}} = "2003".
{{JULIANDAY.YEAR|{{JULIANDAY|2003| 1|31}}}} = "2003".
{{JULIANDAY.YEAR|{{JULIANDAY|2003| 2| 1}}}} = "2003".
{{JULIANDAY.YEAR|{{JULIANDAY|2003| 2|28}}}} = "2003".
{{JULIANDAY.YEAR|{{JULIANDAY|2003| 3| 1}}}} = "2003".
{{JULIANDAY.YEAR|{{JULIANDAY|2003| 3|31}}}} = "2003".
{{JULIANDAY.YEAR|{{JULIANDAY|2003| 4| 1}}}} = "2003".
{{JULIANDAY.YEAR|{{JULIANDAY|2003| 4|30}}}} = "2003".
{{JULIANDAY.YEAR|{{JULIANDAY|2003| 5| 1}}}} = "2003".
{{JULIANDAY.YEAR|{{JULIANDAY|2003| 5|31}}}} = "2003".
{{JULIANDAY.YEAR|{{JULIANDAY|2003| 6| 1}}}} = "2003".
{{JULIANDAY.YEAR|{{JULIANDAY|2003| 6|30}}}} = "2003".
{{JULIANDAY.YEAR|{{JULIANDAY|2003| 7| 1}}}} = "2003".
{{JULIANDAY.YEAR|{{JULIANDAY|2003| 7|31}}}} = "2003".
{{JULIANDAY.YEAR|{{JULIANDAY|2003| 8| 1}}}} = "2003".
{{JULIANDAY.YEAR|{{JULIANDAY|2003| 8|31}}}} = "2003".
{{JULIANDAY.YEAR|{{JULIANDAY|2003| 9| 1}}}} = "2003".
{{JULIANDAY.YEAR|{{JULIANDAY|2003| 9|30}}}} = "2003".
{{JULIANDAY.YEAR|{{JULIANDAY|2003|10| 1}}}} = "2003".
{{JULIANDAY.YEAR|{{JULIANDAY|2003|10|31}}}} = "2003".
{{JULIANDAY.YEAR|{{JULIANDAY|2003|11| 1}}}} = "2003".
{{JULIANDAY.YEAR|{{JULIANDAY|2003|11|30}}}} = "2003".
{{JULIANDAY.YEAR|{{JULIANDAY|2003|12| 1}}}} = "2003".
{{JULIANDAY.YEAR|{{JULIANDAY|2003|12|31}}}} = "2003".

Examples with a leap non-secular year (of rank 4) change

{{JULIANDAY.YEAR|{{JULIANDAY|2004| 1| 1}}}} = "2004".
{{JULIANDAY.YEAR|{{JULIANDAY|2004| 1|31}}}} = "2004".
{{JULIANDAY.YEAR|{{JULIANDAY|2004| 2| 1}}}} = "2004".
{{JULIANDAY.YEAR|{{JULIANDAY|2004| 2|29}}}} = "2004".
{{JULIANDAY.YEAR|{{JULIANDAY|2004| 3| 1}}}} = "2004".
{{JULIANDAY.YEAR|{{JULIANDAY|2004| 3|31}}}} = "2004".
{{JULIANDAY.YEAR|{{JULIANDAY|2004| 4| 1}}}} = "2004".
{{JULIANDAY.YEAR|{{JULIANDAY|2004| 4|30}}}} = "2004".
{{JULIANDAY.YEAR|{{JULIANDAY|2004| 5| 1}}}} = "2004".
{{JULIANDAY.YEAR|{{JULIANDAY|2004| 5|31}}}} = "2004".
{{JULIANDAY.YEAR|{{JULIANDAY|2004| 6| 1}}}} = "2004".
{{JULIANDAY.YEAR|{{JULIANDAY|2004| 6|30}}}} = "2004".
{{JULIANDAY.YEAR|{{JULIANDAY|2004| 7| 1}}}} = "2004".
{{JULIANDAY.YEAR|{{JULIANDAY|2004| 7|31}}}} = "2004".
{{JULIANDAY.YEAR|{{JULIANDAY|2004| 8| 1}}}} = "2004".
{{JULIANDAY.YEAR|{{JULIANDAY|2004| 8|31}}}} = "2004".
{{JULIANDAY.YEAR|{{JULIANDAY|2004| 9| 1}}}} = "2004".
{{JULIANDAY.YEAR|{{JULIANDAY|2004| 9|30}}}} = "2004".
{{JULIANDAY.YEAR|{{JULIANDAY|2004|10| 1}}}} = "2004".
{{JULIANDAY.YEAR|{{JULIANDAY|2004|10|31}}}} = "2004".
{{JULIANDAY.YEAR|{{JULIANDAY|2004|11| 1}}}} = "2004".
{{JULIANDAY.YEAR|{{JULIANDAY|2004|11|30}}}} = "2004".
{{JULIANDAY.YEAR|{{JULIANDAY|2004|12| 1}}}} = "2004".
{{JULIANDAY.YEAR|{{JULIANDAY|2004|12|31}}}} = "2004".

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