# Gaussian Formulae

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). The formulae: 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*