# Proleptic Gregorian calendar

The proleptic Gregorian calendar is produced by extending the Gregorian calendar backward to dates preceding its official introduction in 1582.

## Usage

The proleptic Gregorian calendar is explicitly required for all dates before 1582 by ISO 8601:2004 (clause 4.3.2.1 The Gregorian calendar) if the partners to information exchange agree. It is also used by most Maya scholars,1 especially when converting Long Count dates (1st century BC – 10th century). However, neither astronomers nor non-Maya historians generally use it.

For these calendars we can distinguish two systems of numbering years BC. Bede and later historians did not use the Latin zero, nulla, as a year (see Year zero), so the year preceding AD 1 is 1 BC. In this system the year 1 BC is a leap year (likewise in the proleptic Julian calendar). Mathematically, it is more convenient to include a year zero and represent earlier years as negative, for the specific purpose of facilitating the calculation of the number of years between a negative (BC) year and a positive (AD) year. This is the convention used in astronomical year numbering and in the international standard date system, ISO 8601. In these systems, the year 0 is a leap year.2

Although the nominal Julian calendar began in 45 BC, leap years between 45 BC and 1 BC were irregular (see Leap year error). Thus the Julian calendar with quadrennial leap years was only used from AD 1 until 1582 or later, so historians and astronomers prefer to use the actual Julian calendar during that period (see From Julian to Gregorian). But when seasonal dates are important, the proleptic Gregorian calendar is sometimes used, especially when discussing cultures that did not use the Julian calendar.

The proleptic Gregorian calendar is sometimes used in computer software to simplify the handling of older dates. For example, it is the calendar used by MySQL,3 SQLite,4 PHP, CIM, Delphi, Python5 and COBOL.

## Difference between Julian and proleptic Gregorian calendar dates

Before the introduction of the Gregorian calendar, the difference between Julian and proleptic Gregorian calendar dates were as follows: Whenever the calendars do not have corresponding days — such as the Julian leap day missing from the proleptic Gregorian calendar, or the ten days dropped when the Julian became the Gregorian calendar — the number of days that the calendars differ by is undefined around those dates.

The table below assumes a Julian leap day of 29 February, but the Julian leap day (the bissextile day) was ante diem bis sextum Kalendas Martias in Latin or 24 February (see Julian reform), so dates between 24 and 29 February in all leap years were irregular.

Julian range Proleptic Gregorian range Gregorian ahead by:
From 3 March 1 BC
to 28 February 100
From 1 March 1 BC
to 26 February 100
−2 days
From 2 March 100
to 28 February 200
From 1 March 100
to 27 February 200
−1 days
From 1 March 200
to 28 February 300
From 1 March 200
to 28 February 300
0 days
From 1 March 300
to 27 February 500
From 2 March 300
to 28 February 500
1 day
From 1 March 500
to 26 February 600
From 3 March 500
to 28 February 600
2 days
From 1 March 600
to 25 February 700
From 4 March 600
to 28 February 700
3 days
From 1 March 700
to 24 February 900
From 5 March 700
to 28 February 900
4 days
From 1 March 900
to 23 February 1000
From 6 March 900
to 28 February 1000
5 days
From 1 March 1000
to 22 February 1100
From 7 March 1000
to 28 February 1100
6 days
From 1 March 1100
to 21 February 1300
From 8 March 1100
to 28 February 1300
7 days
From 1 March 1300
to 20 February 1400
From 9 March 1300
to 28 February 1400
8 days
From 1 March 1400
to 19 February 1500
From 10 March 1400
to 28 February 1500
9 days
From 1 March 1500
to 24 September 1582
From 11 March 1500
to 4 October 1582
10 days

## References

1. ^ The proceedings of the Maya hieroglyphic workshop. University of Texas. 1992. p. 173.
2. ^ Doggett, L. E. (1992). "Calendars". In P. Kennneth Seidelmann. Explanatory Supplement to the Astronomical Almanac. Sausalito, CA: University Science Books. ISBN 0-935702-68-7.
3. ^ "11.8. What Calendar Is Used By MySQL?". MySQL 5.0 Reference Manual. Retrieved 21 July 2010.
4. ^ "Date And Time Functions". SQL As Understood By SQLite. Retrieved 16 September 2010.
5. ^ "8.1.3. date Objects". Python v2.7.2 documentation.