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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.
Leap years have two letters, so for January and February calculate the day of the week for January 1 and for March to December calculate the day of the week for October 1. Leap years are all years that divide exactly by four, with the following exceptions: Gregorian calendar – all years divisible by 100, except those that divide exactly by 400.
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).
Since in the Gregorian calendar there are 146,097 days, or exactly 20,871 seven-day weeks, in 400 years, the anchor day repeats every four centuries. For example, the anchor day of 1700–1799 is the same as the anchor day of 2100–2199, i.e. Sunday.
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:
To reinstate the association, the reform advanced the date by 10 days: [c] Thursday 4 October 1582 was followed by Friday 15 October 1582. [3] In addition, the reform also altered the lunar cycle used by the Church to calculate the date for Easter, because astronomical new moons were occurring four days before the calculated dates.
The day of the week can be easily calculated given a date's Julian day number (JD, i.e. the integer value at noon UT): Adding one to the remainder after dividing the Julian day number by seven (JD modulo 7 + 1) yields that date's ISO 8601 day of the week. For example, the Julian day number of 4 February 2025 is 2460711.
For example, the Gregorian date Tuesday, 4 February 2025 corresponds to day number 2 in the week number 06 of 2025, and is written as 2025-W06-2 (in extended form) or 2025W062 (in compact form). The ISO year is slightly offset to the Gregorian year; for example, Monday 30 December 2019 in the Gregorian calendar is the first day of week 1 of ...