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For determination of the day of the week (1 January 2000, Saturday) the day of the month: 1 ~ 31 (1) the month: (6) the year: (0) the century mod 4 for the Gregorian calendar and mod 7 for the Julian calendar (0). adding 1+6+0+0=7. Dividing by 7 leaves a remainder of 0, so the day of the week is Saturday. The formula is w = (d + m + y + c) mod 7.
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:
Extending this to get the anchor day, the procedure is often described as accumulating a running total T in six steps, as follows: Let T be the year's last two digits. If T is odd, add 11. Now let T = T / 2 . If T is odd, add 11. Now let T = 7 − (T mod 7). Count forward T days from the century's anchor day to get the year's anchor day.
Retrieved from "https://en.wikipedia.org/w/index.php?title=Calculating_the_day_of_the_week&oldid=473328703"
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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 January 2025 is 2460690.
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