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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).
These formulas are based on the observation that the day of the week progresses in a predictable manner based upon each subpart of that date. Each term within the formula is used to calculate the offset needed to obtain the correct day of the week. For the Gregorian calendar, the various parts of this formula can therefore be understood as follows:
Month-to-date (MTD) is a period starting at the beginning of the current calendar month and ending on either the current date or the last business day before the current date. Month-to-date is used in many contexts, mainly for recording results of an activity in the time between a date (exclusive, since this day may not yet be "complete") and ...
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 January 2025" is ten days after "15 January 2025". The date of a particular event depends on the observed time zone.
A 50-year "pocket calendar" that is adjusted by turning the dial to place the name of the month under the current year. One can then deduce the day of the week or the date. A perpetual calendar is a calendar valid for many years, usually designed to look up the day of the week for a given date in the past or future.
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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.