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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).
The Rata Die method works by adding up the number of days d that has passed since a date of known day of the week D. The day of-the-week is then given by (D + d) mod 7, conforming to whatever convention was used to encode D. For example, the date of 13 August 2009 is 733632 days from 1 January AD 1. Taking the number mod 7 yields 4, hence a ...
The conventions of this class calculate the number of days between two dates (e.g., between Date1 and Date2) as the Julian day difference. This is the function Days(StartDate, EndDate). The conventions are distinguished primarily by the amount of the CouponRate they assign to each day of the accrual period.
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 ...
Rata Die is somewhat similar to Julian Dates (JD), in that the values are plain real numbers that increase by 1 each day. The systems differ principally in that JD takes on a particular value at a particular absolute time, and is the same in all contexts, whereas R.D. values may be relative to time zone , depending on the implementation.
February's 28 or 29 days is a problem, so the formula rolls January and February around to the end so February's short count will not cause a problem. The formula is interested in days of the week, so the numbers in the sequence can be taken modulo 7.
For example, the Gregorian date Tuesday, 10 December 2024 corresponds to day number 2 in the week number 50 of 2024, and is written as 2024-W50-2 (in extended form) or 2024W502 (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 ...
All examples use example date 2021-03-31 / 2021 March 31 / 31 March 2021 / March 31, 2021 – except where a single-digit day is illustrated. Basic components of a calendar date for the most common calendar systems: D – day; M – month; Y – year; Specific formats for the basic components: yy – two-digit year, e.g. 24; yyyy – four-digit ...