Gregorian calendar

==Difference between Gregorian and Julian calendar dates==
{| class="wikitable floatright"
|+Conversion from Julian to Gregorian dates.<ref>A more extensive list is available at [[Conversion between Julian and Gregorian calendars]]</ref>
! Gregorian range || Julian range || Difference
|- align=right
|From 15 October 1582<br />to 28 February 1700
|From 5 October 1582<br />to 18 February 1700
| align=center |10 days
|- align=right
|From 1 March 1700<br />to 28 February 1800
|From 19 February 1700<br />to 17 February 1800
| align=center |11 days
|- align=right
|From 1 March 1800<br />to 28 February 1900
|From 18 February 1800<br />to 16 February 1900
| align=center |12 days
|- align=right
|From 1 March 1900<br />to 28 February 2100
|From 17 February 1900<br />to 15 February 2100
| align=center |13 days
|- align=right
|From 1 March 2100<br />to 28 February 2200
|From 16 February 2100<br />to 14 February 2200
| align=center |14 days<!--
|When converting a date in a year which is leap in one calendar but not the other include 29 February in the calculation when the conversion crosses the border between February and March.-->
|}

This section always places the intercalary day on {{nowrap|29 February}} even though it was always obtained by doubling {{nowrap|24 February}} (the {{lang|la|bissextum}} (twice sixth) or bissextile day) until the late [[Middle Ages]]. The Gregorian calendar is [[Proleptic Gregorian calendar|proleptic]] before 1582 (calculated backwards on the same basis, for years before 1582), and the difference between Gregorian and Julian calendar dates increases by three days every four centuries (all date ranges are inclusive).

The following equation gives the number of days that the Gregorian calendar is ahead of the Julian calendar, called the "secular difference" between the two calendars. A negative difference means the Julian calendar is ahead of the Gregorian calendar.{{sfnp|Blackburn|Holford-Strevens|1999|page=788}}
<math display=block>D = \left\lfloor{Y/100}\right\rfloor - \left\lfloor{Y/400}\right\rfloor - 2,</math>
where <math>D</math> is the secular difference and <math>Y</math> is the year using [[astronomical year numbering]], that is, use {{nowrap|1 − (year BC)}} for BC years. <math>\left\lfloor{x}\right\rfloor</math> means that if the result of the division is not an integer it is rounded down to the nearest integer.

The general rule, in years which are leap years in the Julian calendar but not the Gregorian, is:

Up to 28 February in the calendar being converted {{em|from}}, add one day less or subtract one day more than the calculated value. Give February the appropriate number of days for the calendar being converted {{em|into}}. When subtracting days to calculate the Gregorian equivalent of 29 February (Julian), 29 February is discounted. Thus if the calculated value is −4 the Gregorian equivalent of this date is 24 February.<ref>{{cite book |first1=James | last1=Evans | url=https://books.google.com/books?id=nS51_7qbEWsC&pg=PA169 |title= The history and practice of ancient astronomy |location= Oxford |publisher= Oxford University Press | year=1998 |page=169|isbn=0-19-509539-1}}</ref><ref>{{cite book| title= Explanatory Supplement to The Astronomical Ephemeris and The American Ephemeris and Nautical Almanac |location=London |publisher= Her Majesty's Stationery Office| year=1961| page=417 |url=https://archive.org/details/calendar-ephemeris/page/n7/mode/1up}}</ref>
{{clear}}
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