Astronomical Year Numbering
and the Common Era Calendar
In the Julian and Gregorian Calendars years prior to the year 1 are numbered by counting backwards from that year and adding a suffix to distinguish years prior to the year 1 from years following the year 1, e.g., 1 B.C., 2 B.C., and so on.
This method of numbering years, although still in widespread use, makes it difficult to perform simple arithmetic operations on years. (E.g., how many years elapsed from January 1st, 6 B.C., to January 1st, 6 A.D.? 11? 12? 13?) Thus many astronomers and calendrical scientists prefer to use a system of numbering years prior to the year 1 using zero and negative numbers: ... -2, -1, 0, 1, ... Hence we have the following correspondences:
4 B.C. 4 v.Chr. 4 BCE -3 CE 3 B.C. 3 v.Chr. 3 BCE -2 CE 2 B.C. 2 v.Chr. 2 BCE -1 CE 1 B.C. 1 v.Chr. 1 BCE 0 CE 1 A.D. 1 n.Chr. 1 CE 1 CE 2 A.D. 2 n.Chr. 2 CE 2 CE
"CE" is an abbreviation for "Common Era". The suffixes "CE" and "BCE" ("Before Common Era") in the "religiously neutral" system simply replace the traditional Christian suffixes "A.D." ("Anno Domini"), "n.Chr." ("nach Christus"), "B.C." ("Before Christ") and "v.Chr." ("vor Christus"), so the "religiously neutral" system of year numbering is no different — except for the cosmetic suffix changes — from the proleptic Gregorian Calendar (the Gregorian Calendar projected back prior to its start on October 15, 1582).
A calendar using the astronomical system numbers years in a fundamentally different way from the traditional Gregorian Calendar. Dates with years so numbered should have a suffix to distinguish them from dates with years numbered in some other way. In practice, however, "CE" is used both (a) for years from the year 1 onwards in the proleptic Gregorian Calendar in its "religiously neutral" form and (b) for all years (both positive and negative) in the proleptic Gregorian Calendar in the form which uses the astronomical system of year numbering.
The astronomical year numbering system may also be used with calendars other than the proleptic Gregorian Calendar, provided some suffix is used to identify the calendar. Thus, e.g., we have "0 JC" for the year in the Julian Calendar (with astronomical year numbering) which preceded the year "1 JC".
For years prior to the year 1 in the traditional Gregorian and Julian Calendars the following conversion formulas may be used:
n B.C. = -(n-1) CE
-n CE = n+1 B.C.
- To convert a year B.C. to CE subtract 1 and prepend a minus sign (e.g., 201 B.C. = -200 CE).
- To convert a negative year CE to B.C. drop the minus sign and add 1 (e.g., -533 CE = 534 B.C.).
The astronomical year numbering system is used in all dates (both as input and as displayed) in all Hermetic Systems calendrical software (though the Julian-Gregorian-Dee Date Calculator program handles dates with both systems of year numbering).
The term "Common Era Calendar" is used in all articles on this website, and in all calendrical software user manuals, to mean that calendar which has the same structure (days, months, years) as the proleptic Gregorian Calendar and in which years are numbered according to the astronomical system. Dates in this calendar are always designated "CE".
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