For astronomical calculations you need the astronomical way to count the years. But there exists also a historical way to count the years. Both methods give the same results starting with the year 1 CE. But before that year, the differ.
In the historical count the year 1 BCE precedes the year 1 CE. The year 0 does not exist.
In the astronomical count there is a year 0. The year 0 precedes the year 1, and the year -1 precedes the year 0.
If you translate the historical count of 1 CE to +1 en 1 BCE to -1, you will miss one year.
So you cannot use the historical count for calculations. You need to translate historical years
The formula is straightforward:
Calculate AY (Astronomical Year) from HY (Historical Year):
- if HY has a prefix ‘CE’ : AY = HY
- if HY has a prefix ‘BCE’ : AY = -HY – 1
In stead of ‘CE’ (Common Era) you might also find ‘AD’ (Anno Domini).
In stead of ‘BCE’ (Before Common Era) some people also use ‘BC’ (Before Christ)
HY = 3 CE → AY = HY = 3
HY = 8 CE → AY = -HY – 1 = -9
– Doggett, L. E: Calendars. In Explanatory Supplement to the Astronomical Almanac, ed. P. Kennet Seidelmann. Sausalito, California, 1992/2006.