The proleptic Gregorian calendar is produced by extending the Gregorian calendar

Gregorian calendar

The Gregorian calendar, also known as the Western calendar, or Christian calendar, is the internationally accepted civil calendar. It was introduced by Pope Gregory XIII, after whom the calendar was named, by a decree signed on 24 February 1582, a papal bull known by its opening words Inter...

 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

ISO 8601

ISO 8601 Data elements and interchange formats – Information interchange – Representation of dates and times is an international standard covering the exchange of date and time-related data. It was issued by the International Organization for Standardization and was first published in 1988...

:2004 (clause 3.2.1) if the partners to information exchange agree. It is also used by most Maya

Maya civilization

The Maya is a Mesoamerican civilization, noted for the only known fully developed written language of the pre-Columbian Americas, as well as for its art, architecture, and mathematical and astronomical systems. Initially established during the Pre-Classic period The Maya is a Mesoamerican...

 scholars, especially when converting Long Count

Mesoamerican Long Count calendar

The Mesoamerican Long Count calendar is a non-repeating, vigesimal and base-18 calendar used by several Pre-Columbian Mesoamerican cultures, most notably the Maya. For this reason, it is sometimes known as the Maya Long Count calendar...

 dates (1st century BC – 10th century). However, neither astronomer

Astronomer

An astronomer is a scientist who studies celestial bodies such as planets, stars and galaxies.Historically, astronomy was more concerned with the classification and description of phenomena in the sky, while astrophysics attempted to explain these phenomena and the differences between them using...

s nor non-Maya historian

Historian

A historian is a person who studies and writes about the past and is regarded as an authority on it. Historians are concerned with the continuous, methodical narrative and research of past events as relating to the human race; as well as the study of all history in time. If the individual is...

s generally use it.

For these calendars we can distinguish two systems of numbering years BC. Bede

Bede

Bede , also referred to as Saint Bede or the Venerable Bede , was a monk at the Northumbrian monastery of Saint Peter at Monkwearmouth, today part of Sunderland, England, and of its companion monastery, Saint Paul's, in modern Jarrow , both in the Kingdom of Northumbria...

 and later historians did not use the Latin zero, nulla, as a year (see Year zero

Year zero

"Year zero" does not exist in the widely used Gregorian calendar or in its predecessor, the Julian calendar. Under those systems, the year 1 BC is followed by AD 1...

), 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

Proleptic Julian calendar

The proleptic Julian calendar is produced by extending the Julian calendar to dates preceding AD 4 when its quadrennial leap year stabilized. The leap years actually observed between its official implementation in 45 BC and AD 4 were erratic, see the Julian calendar article for details.A 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

Astronomical year numbering

Astronomical year numbering is based on AD/CE year numbering, but follows normal decimal integer numbering more strictly. Thus, it has a year 0, the years before that are designated with negative numbers and the years after that are designated with positive numbers...

 and in the international standard date system, ISO 8601. In these systems, the year 0 is a leap year

Leap year

A leap year is a year containing one extra day in order to keep the calendar year synchronized with the astronomical or seasonal year...

.

Although the nominal Julian calendar

Julian calendar

The Julian calendar began in 45 BC as a reform of the Roman calendar by Julius Caesar. It was chosen after consultation with the astronomer Sosigenes of Alexandria and was probably designed to approximate the tropical year .The Julian calendar has a regular year of 365 days divided into 12 months...

 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

Computer software

Computer software, or just software, is a collection of computer programs and related data that provide the instructions for telling a computer what to do and how to do it....

 to simplify the handling of older dates. For example, it is the calendar used by MySQL

MySQL

MySQL officially, but also commonly "My Sequel") is a relational database management system that runs as a server providing multi-user access to a number of databases. It is named after developer Michael Widenius' daughter, My...

, SQLite

SQLite

SQLite is an ACID-compliant embedded relational database management system contained in a relatively small C programming library. The source code for SQLite is in the public domain and implements most of the SQL standard...

, PHP

PHP

PHP is a general-purpose server-side scripting language originally designed for web development to produce dynamic web pages. For this purpose, PHP code is embedded into the HTML source document and interpreted by a web server with a PHP processor module, which generates the web page document...

, CIM

Common Information Model (computing)

The Common Information Model is an open standard that defines how managed elements in an IT environment are represented as a common set of objects and relationships between them...

, Delphi, and COBOL

COBOL

COBOL is one of the oldest programming languages. Its name is an acronym for COmmon Business-Oriented Language, defining its primary domain in business, finance, and administrative systems for companies and governments....

.

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 is undefined for few days. This table 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

Latin

Latin is an Italic language originally spoken in Latium and Ancient Rome. It, along with most European languages, is a descendant of the ancient Proto-Indo-European language. Although it is considered a dead language, a number of scholars and members of the Christian clergy speak it fluently, and...

 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 (beginning of quadrennial leap years) 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