Dominical Letter - Calculation

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 example:

• 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, there is a choice of several shortcuts, e.g.:
    • go back one letter for every 12 years
    • ignore multiples of 28 years (note that when jumping from e.g. 1900 to 1928 the last letter of 1928 is the same as the letter of 1900)
    • apply steps between multiples of 10, writing from right to left:

• Note the dummy step (we skip A between 1900 and 1910) because 1900 is not a leap year.

For example, to find the Dominical Letter of the year 1913:

• 1900 is G
• 1910 is B
• count B A GF E, 1913 is E

Similarly, for 2007:

• 2000 is BA
• count BA G F E DC B A G, 2007 is G

For 2065:

• 2000 is BA
• 2012 is AG, 2024 is GF, 2036 is FE, 2048 is ED, 2060 is DC, then B A G FE D, 2065 is D
• or from 2000 to 2060 in steps of 10, written backward: DC B AG F ED C BA, starting from 2000 is BA we get 2060 is DC, then again B A G FE D, 2065 is D (or, writing the last part backward too: D FE G A B B AG F ED C BA)
• or ignore 56 years, 2056 is BA, count G F E DC B A G FE D, 2065 is D