Dominical letters or Sunday letters are a method used to determine the day of the week for particular dates. When using this method, each year is assigned a letter (or pair of letters for leap years) depending on which day of the week the year starts with. The Dominical letter for the current year 2026 is D.
Dominical letters are derived from the Roman practice of marking the repeating sequence of eight letters A–H (commencing with A on January 1) on stone calendars to indicate each day's position in the eight-day market week (). The word is derived from the number nine due to their practice of inclusive counting. After the introduction of Christianity a similar sequence of seven letters A–G was added alongside, again commencing with January 1. The dominical letter marks the Sundays. Nowadays they are used primarily as part of the computus, which is the method of calculating the date of Easter.
A common year is assigned a single dominical letter, indicating which lettered days are Sundays in that particular year (hence the name, from Latin dominica for Sunday). Thus, 2026 is D, indicating that all D days will be Sunday, and by inference, January 4, 2026, is a Sunday. Leap years are given two letters, the first valid for January 1 – February 28 (or February 24, see below), the second for the remainder of the year.
In leap years, the leap day may or may not have a letter. In the Catholic version it does, but in the 1662 and subsequent Anglican versions it does not. The Catholic version causes February to have 29 days by doubling the sixth day before March 1, inclusive, thus both halves of the doubled day have a dominical letter of F.Calendarium (Calendar attached to the papal bull "Inter gravissimas"). The Anglican version adds a day to February that did not exist in common years, February 29, thus it does not have a dominical letter of its own."Anno vicesimo quarto Georgii II. c. 23" (1751), The Statutes at Large, from Magna Charta to the end of the Eleventh Parliament of Great Britain, Anno 1761, ed. Danby Pickering, p. 194. After the 1662 reform there was correspondence between the Archbishop of Canterbury and the printer of the Book of Common Prayer, in which it was explained that the feast day of St Matthias now fell on February 24 every year.
In either case, all other dates have the same dominical letter every year, but the days of the dominical letters change within a leap year before and after the intercalary day, February 24 or February 29.
History and arrangement According to dominical letters are:
Another one is "Add G, beg C, fad F," and yet another is "At Dover dwell George Brown, Esquire; Good Christopher Finch; and David Fryer."
Dominical letter cycle
continues:
Of course, "24 February" is not "counted twice". The 23rd is ante diem vii kalendas Martias, the next day in a leap year is a.d. bis sextum kal. Mart., the next day is the regular a.d.vi kal. Mart., and so to the end of the month. For example, in 2024 (=GF), all days preceding the leap day corresponded to a common-year G calendar, and all days afterward corresponded to a common-year F calendar. The same thing will happen in 2028 (=BA), for example all days preceding the leap day will correspond to a common-year B calendar, and all days afterward will correspond to a common-year A calendar. The relevant line of the Februarius page in the Kalendarium of a 1913 Breviarium Romanum reads:
The first column is the epact, a replacement for the golden number, from which the age of the moon was computed and announced in some English cathedrals prior to the Reformation. The second column is the letter, the third the Roman date and the fourth the modern date. A note at the foot of the page reads:
Dominical letters of the years The dominical letter of a year provides the link between the date and the day of the week on which it falls. The following are the correspondences between dominical letters and the day of the week on which their corresponding years is day and date:
Common years: A: common year starting on Sunday B: common year starting on Saturday C: common year starting on Friday D: common year starting on Thursday E: common year starting on Wednesday F: common year starting on Tuesday G: common year starting on Monday
Leap years: AG: leap year starting on Sunday BA: leap year starting on Saturday CB: leap year starting on Friday DC: leap year starting on Thursday ED: leap year starting on Wednesday FE: leap year starting on Tuesday GF: leap year starting on Monday
The Gregorian calendar repeats every 400 years (i. e., every four centuries). Of the 400 years in one Gregorian cycle, there are: 44 common years for each single Dominical letter D and F; 43 common years for each single Dominical letter A, B, C, E, and G; 15 leap years for each double Dominical letter AG and CB; 14 leap years for each double Dominical letter ED and FE; 13 leap years for each double Dominical letter BA, DC, and GF. Thus 58 out of 400 years begin as A, C, or F, while 57 begin as D or E and 56 begin as B or G. The end of a year preceding a given year has the next letter (meaning A years are preceded by years ending as B), so 58 of 400 years end as B, D or G, whereas 57 end as E or F and 56 end as C or A. This means, for example, that Christmas falls on a Saturday or Monday (C and A years, respectively) 56 times, Wednesday or Thursday (F and E years, respectively) 57 times, and Friday, Sunday or Tuesday (D, B and G years, resp.) 58 times in the span of four centuries.
The Julian calendar repeats every 28 years. Of the 28 years in one Julian cycle, there are: 3 common years for each single Dominical letter A, B, C, D, E, F, and G; 1 leap year for each double Dominical letter BA, CB, DC, ED, FE, GF, and AG.
Within the 28-year cycle, the single Dominical letters have gaps of 6 years or 11 years. For example, for Dominical letter G, there is a 6-year gap between 2001 and 2007, then an 11-year gap between 2007 and 2018.
Calculation
The dominical letter of a year can be calculated based on any method for calculating the day of the week, with letters in reverse order compared to numbers indicating the day of the week.
For Gregorian calendar: ignore periods of 400 years considering the second letter in the case of a leap year: for one century within two multiples of 400, go forward two letters from BA for 2000, hence C, E, G. for remaining years, go back one letter every year, two for leap years (this corresponds to writing two letters, no letter is skipped). to avoid up to 99 steps within a century, the table below can be used. Year mod 28 00 06 12 17 23 0 01 07 12 18 24 6 02 08 13 19 24 5 03 08 14 20 25 4 04 09 15 20 26 3 04 10 16 21 27 2 05 11 16 22 00 1 Red for the first two months of leap years.
For example, to find the Dominical Letter of the year 1913:
1900 is G and 13 corresponds to 5 G + 5 = G − 2 = E, so 1913 is E Sundays of 1913 were on E days (e.g. January 5)
Similarly, for 2007: 2000 is BA and 7 corresponds to 6 A + 6 = A − 1 = G, so 2007 is G Sundays of 2007 were on G days (e.g. January 7)
For leap year 2040: 2000 is BA and 40 mod 28 = 12 For the first two months of 2040, red 12 corresponds to 0: A + 0 = A, so 2040 starts with A Sundays of January and February 2040 are on A days (e.g. January 1) For the remaining months of 2040, plain 12 corresponds to 6: A + 6 = A - 1 = G, so 2040 ends with G Sundays of March to December 2040 are on G days (e.g. October 7) Overall, 2040 is AG
For 2065: 2000 is BA and 65 mod 28 = 9 corresponds to 3 A + 3 = A − 4 = D, so 2065 is D Sundays of 2065 are on D days (e.g. January 4)
The odd plus 11 method A simpler method suitable for finding the year's dominical letter was discovered in 2010. It is called the "odd plus 11" method.
The procedure accumulates a running total as follows: Let be the year's last two digits. If is odd, add 11. Let . If is odd, add 11. Let . Count forward letters from the century's dominical letter (A, C, E or G see above) to get the year's dominical letter.
The formula is
De Morgan's rule This rule was stated by Augustus De Morgan:
So the formulae (using the floor function) for the Gregorian calendar is
It is equivalent to
and (where = last two digits of the year, = century part of the year).
For example, to find the Dominical Letter of the year 1913:
Hence, the Dominical Letter is E in the Gregorian calendar.
De Morgan's rules no. 1 and 2 for the Julian calendar:
To find the Dominical Letter of the year 1913 in the Julian calendar:
Hence, the Dominical Letter is F in the Julian calendar.
In leap years the formulae above give the Dominical Letter for the last ten months of the year. To find the Dominical Letter for the first two months of the year to the leap day (inclusive) subtract 1 from the calculated number representing the original Dominical Letter; if the new number is less than 0, it must be changed to 6.
Dominical letter in relation to the Doomsday Rule
The "doomsday" concept in the doomsday algorithm is mathematically related to the Dominical letter. Because the letter of a date equals the dominical letter of a year (DL) plus the day of the week (DW), and the letter for the doomsday is C except for the portion of leap years before February 29 in which it is D, we have:
Note: in our context, letters and days of the week are assigned indices:
# Letter of a date Dominical letter of year (DL) Day of the week (DW) 0 G Sunday 1 A Monday 2 B Tuesday 3 C Wednesday 4 D Thursday 5 E Friday 6 F Saturday i.e. in our context, C is mathematically identical to 3.
Hence, for instance, the doomsday of the year 2013 is Thursday, so . The dominical letter of the year 1913 is E, so the doomsday that year has .
Doomsday Dominical letterCommon yearLeap year Sunday C DC Monday B CB Tuesday A BA Wednesday G AG Thursday F GF Friday E FE Saturday D ED
All in one table If the year of interest is not within the table, use a tabular year which gives the same remainder when divided by 400 (Gregorian calendar) or 700 (Julian calendar). In the case of the Revised Julian calendar, find the date of Easter Sunday (see the section "Calculating Easter Sunday", subsection "Revised Julian calendar" below) and enter it into the "Table of letters for the days of the year" below. If the year is a leap year, the dominical letter for January and February is found by inputting the date of Easter Monday. Note the different rules for leap years: Gregorian calendar: every year which divides exactly by 4, but of century years only those which divide exactly by 400; therefore ignore the left-hand letter given for a century year which is not a leap year. Julian calendar: every year which divides exactly by 4. Revised Julian calendar: every year which divides exactly by 4, but of century years only those which give the remainder 200 or 600 when divided by 900.