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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.
The doomsday's anchor day calculation is effectively calculating the number of days between any given date in the base year and the same date in the current year, then taking the remainder modulo 7. When both dates come after the leap day (if any), the difference is just 365y + y / 4 (rounded down). But 365 equals 52 × 7 + 1, so after ...
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).
The authors design individual calendrical calculation algorithms for converting each of these calendars to and from a common format, the Rata Die system of days numbered from January 1 of the (fictional) Gregorian year 1. Combining these methods allows the conversion between any two of the calendars.
Rata Die (R.D.) is a system for assigning numbers to calendar days (optionally with time of day), independent of any calendar, for the purposes of calendrical calculations. It was named (after the Latin ablative feminine singular for "from a fixed date") by Howard Jacobson. [1] [2]
Up to 28 February in the calendar being converted 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 into. When subtracting days to calculate the Gregorian equivalent of 29 February (Julian), 29 February is discounted.
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 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.