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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 ...
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:
A precise date is specified by the ISO week-numbering year in the format YYYY, a week number in the format ww prefixed by the letter 'W', and the weekday number, a digit d from 1 through 7, beginning with Monday and ending with Sunday. For example, the Gregorian date Friday, 31 January 2025 corresponds to day number 5 in the week number 05 of ...
The first Sunday after December 21, 2024 is given by "{{Weekday after date|2024|December|21|Sunday}}" as "December 22, 2024". In the following table, 24 October 2010 is a Sunday. Syntax
Thus, for any date except February 29, the intervals between common years falling on a particular weekday are 6, 11, 11. See e.g. at the bottom of the page Common year starting on Monday the years in the range 1906–2091. For February 29 falling on a particular weekday, there is just one in every 28 years, and it is of course a leap year.
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 31 January 2025 is 2460707.
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