# Golden number (calendar)

Cod. Pal. germ. 15 , sheet 13v: Table for determining the golden number and the signs of the zodiac , Salzburg diocese around 1496

The golden number ( Latin : Numerus aureus ) marks the position of a calendar year of the Christian era within the 19-year lunar circle . The golden numbers 1 to 19 are consecutively assigned to this position, on which the Easter date depends.

## Calculation of the golden number

The most commonly given formula for determining the golden number for the year with the year is: ${\ displaystyle GZ}$${\ displaystyle j}$

${\ displaystyle GZ = (j + 1) \; mod \; 19}$

With

• the calculation type for modulo${\ displaystyle mod}$
• the possible results GZ =    0 , 1,…, 17 or 18.

The result 0 is to be converted to 19 , after which the result series is:

• GZ = 19 , 1, ..., 17 or 18.

The year 2009 has the golden number (2009 + 1) mod 19 = 15.
In 2013, the conversion rule (0 → 19) must be applied:
The year 2013 has the golden number (2013 + 1) mod 19 = 0, i.e. 19.

The following formula leads to the same result (except for the year 1 BC, for which the first formula does not provide a correct result either), without having to apply the conversion rule in exceptional years:

${\ displaystyle GZ = j \; mod \; 19 + 1}$

Because of its importance in the calculation of Easter ( Computus (Osterrechnung) ) - the most important festival in Christianity - this auxiliary variable was often written in golden color in late medieval annual calendars, which is said to have resulted in the designation golden number. It is also possible that it got this name because of its outstanding meaning.

### table

year Golden number
1 BC 1
( Year 0 ) ( not available in traditional Christian calendar )
... ...
19 AD 1 (counting starts again from the beginning)
... ...