# Proleptic Gregorian calendar

The proleptic Gregorian calendar is produced by extending the Gregorian calendar backward to the dates preceding its official introduction in 1582. In nations that adopted the Gregorian calendar after its official and first introduction, dates occurring in the interim period of 15 October 1582 (the first date of use of Gregorian calendrical dates, being dated 5 October 1582 in the preceding Julian calendar) to the date on which the pertinent nation adopted the Gregorian calendar and abandoned the Julian calendar are sometimes 'Gregorianized' also. For example, the birthday of U.S. President George Washington was originally dated 11 February 1731 (Old Style) because Great Britain, of which he was born a subject, used (until September 1752) the Julian calendar and dated the beginning of English years as 25 March instead of 1 January (e.g. 31 December 1700 was followed by 1 January 1700, and 24 March 1700 was followed by 25 March 1701). After Great Britain switched to the Gregorian calendar, Washington's birthday was dated 22 February 1732 proleptically, according to the Gregorian calendar applied backward. This remains the modern dating of his birthday.

## Usage

ISO 8601:2004 (clause 3.2.1 The Gregorian calendar) allows use of the proleptic Gregorian calendar for dates before its introduction only if the parties to the communication agree. Most scholars of the Maya civilization also use it, especially when converting Long Count dates (1st century BC – 10th century AD).
The best practice for citation of historically contemporary documents is to cite the date as expressed in the original text and to notate any contextual implications and conclusions regarding the calendar used and equivalents in other calendars. This practice permits others to re-evaluate the original evidence.
For these calendars one can distinguish two systems of numbering years BC. Bede and later historians did not enumerate any year as zero (nulla in Latin; see Year zero); therefore 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 0 and represent earlier years as negative numbers 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 in astronomical year numbering and the international standard date system, ISO 8601. In these systems, the year 0 is a leap year.
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 the end of AD 4 until 1582 or later (contingent on the specific nation in question).
The proleptic Gregorian calendar is sometimes used in computer software to simplify identifying pre-Gregorian dates, e. g. in PostgreSQL, MySQL, SQLite, PHP, CIM, Delphi and Python.

## Julian calendar differences

Before the official and first introduction of the Gregorian calendar, the differences between Julian and proleptic Gregorian calendar dates are as follows:
The table below assumes a Julian leap day of 29 February, but the Julian leap day, that is, the bissextile day (ante diem bis sextum Kalendas Martias in Latin) was accomplished by repeating 24 February (see Julian reform). Therefore, the dates between 24 and 29 February in all leap years were irregular.
Note: When converting a date in a year which is leap in the Julian calendar but not in the Gregorian, 29 February is included in the calculation when the conversion crosses the border of February and March.
| Julian range | Proleptic Gregorian range | Gregorian ahead by |
| From 3 March AD 4 (beginning of quadrennial leap years) to 1 March 100 | From 1 March AD 4 to 28 February 100 | −2 days |
| From 2 March 100 to 29 February 200 | From 1 March 100 to 28 February 200 | −1 day |
| From 1 March 200 to 28 February 300 | From 1 March 200 to 28 February 300 | 0 days |
| From 29 February 300 to 27 February 500 | From 1 March 300 to 28 February 500 | 1 day |
| From 28 February 500 to 26 February 600 | From 1 March 500 to 28 February 600 | 2 days |
| From 27 February 600 to 25 February 700 | From 1 March 600 to 28 February 700 | 3 days |
| From 26 February 700 to 24 February 900 | From 1 March 700 to 28 February 900 | 4 days |
| From 25 February 900 to 23 February 1000 | From 1 March 900 to 28 February 1000 | 5 days |
| From 24 February 1000 to 22 February 1100 | From 1 March 1000 to 28 February 1100 | 6 days |
| From 23 February 1100 to 21 February 1300 | From 1 March 1100 to 28 February 1300 | 7 days |
| From 22 February 1300 to 20 February 1400 | From 1 March 1300 to 28 February 1400 | 8 days |
| From 21 February 1400 to 19 February 1500 | From 1 March 1400 to 28 February 1500 | 9 days |
| From 20 February 1500 to 4 October 1582 | From 1 March 1500 to 14 October 1582 | 10 days |
| Julian range | Gregorian range | Difference |
| From 5 October 1582 to 18 February 1700 | From 15 October 1582 to 28 February 1700 | 10 days |
| From 19 February 1700 to 17 February 1800 | From 1 March 1700 to 28 February 1800 | 11 days |
| From 18 February 1800 to 16 February 1900 | From 1 March 1800 to 28 February 1900 | 12 days |
| From 17 February 1900 to 15 February 1923 | From 1 March 1900 to 28 February 1923 | 13 days |
| Orthodox Julian range | Gregorian range | Julian behind by |
| From 16 February 1923 to 14 February 2100 | From 1 March 1923 to 28 February 2100 | 13 days |