Zeller's Congruence - Formula

Formula

For the Gregorian calendar, Zeller's congruence is

for the Julian calendar it is

where

  • h is the day of the week (0 = Saturday, 1 = Sunday, 2 = Monday, ...)
  • q is the day of the month
  • m is the month (3 = March, 4 = April, 5 = May, ..., 14 = February)
  • K the year of the century .
  • J is the century (actually ) (For example, in 1995 the century would be 19, even though it was the 20th century.)

NOTE: In this algorithm January and February are counted as months 13 and 14 of the previous year. E.g. if it is February 2, 2010, the algorithm counts the date as the second day of the fourteenth month of 2009 (02/14/2009 in DD/MM/YYYY format)

For an ISO week date Day-of-Week d (1 = Monday to 7 = Sunday), use

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