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A calendrical calculation is a calculation concerning calendar dates. Calendrical calculations can be considered an area of applied mathematics. Some examples of calendrical calculations: Converting a Julian or Gregorian calendar date to its Julian day number and vice versa (see § Julian day number calculation within that article for details).
For January, January 3 is a doomsday during common years and January 4 a doomsday during leap years, which can be remembered as "the 3rd during 3 years in 4, and the 4th in the 4th year". For March, one can remember either Pi Day or "March 0", the latter referring to the day before March 1, i.e. the last day of February.
With 97 leap years every 400 years, the year has an average length of 365.2425 days. Other formula-based calendars can have lengths which are further out of step with the solar cycle: for example, the Julian calendar has an average length of 365.25 days, and the Hebrew calendar has an average length of 365.2468 days. The Lunar Hijri calendar is ...
The basic approach of nearly all of the methods to calculate the day of the week begins by starting from an "anchor date": a known pair (such as 1 January 1800 as a Wednesday), determining the number of days between the known day and the day that you are trying to determine, and using arithmetic modulo 7 to find a new numerical day of the week.
A calendar date is a reference to a particular day represented within a calendar system. The calendar date allows the specific day to be identified. The number of days between two dates may be calculated. For example, "25 December 2024" is ten days after "15 December 2024". The date of a particular event depends on the observed time zone.
In a paper calendar, one or two sheets can show a single day, a week, a month, or a year. If a sheet is for a single day, it easily shows the date and the weekday. If a sheet is for multiple days it shows a conversion table to convert from weekday to date and back.
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The most common way to reconcile the two is to vary the number of days in the calendar year. In solar calendars, this is done by adding an extra day ("leap day" or "intercalary day") to a common year of 365 days, about once every four years, creating a leap year that has 366 days (Julian, Gregorian and Indian national calendars).