The Gaussian Formulae for Pascha were created by the prolific German mathematician Karl Friedrich Gauss (1777-1855).
In these formulae, mod indicates the Modulus, a mathematical operator that returns the remainder from division. For example, <math>8 mod 3 = 2</math> because <math>8 / 3 = 2 remainder 2</math>.
In addition, int indicates the Integer Part of a number. For positive numbers, it returns the greatest integer less than the number. For example, <math>Int(8.25) = 8</math>.
Year indicates the year of interest (AD).
a = Year mod 4
b = Year mod 7
c = Year mod 19
d = (19c + 15) mod 30
e = (2a + 4b - d + 34) mod 7
f = Int((d + e + 114) / 31)
g = ((d + e + 114) mod 31) + 1
f is the month of Pascha.
g is the day of Pascha. For example, if f is 3 and g is 27, then Pascha occurs on March 27.
Important, this returns the date of Pascha ONLY on the Old Calendar. To get the Gregorian date, add 13 days.
- Source: Hieromonk Cassian, A Scientific Examination of the Orthodox Church Calendar
- Programs using these formulae: Menologion