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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 ...
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.
Converting a date between different calendars. For instance, dates in the Gregorian calendar can be converted to dates in the Islamic calendar with the Kuwaiti algorithm. Calculating the day of the week. Calendrical calculation is one of the five major Savant syndrome characteristics. [1]
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 14 February 2025 is 2460721.
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, 14 February 2025 corresponds to day number 5 in the week number 07 of ...
A perennial calendar differs also from a perpetual calendar, which is a tool or reference to compute the weekdays of dates for any given year, or for representing a wide range of annual calendars. For example, most representations of the Gregorian calendar year include weekdays and are therefore annual calendars, because the weekdays of its ...
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 ...