What is the Gregorian calendar?

What is the Gregorian calendar?

The Gregorian calendar is the solar civil calendar in use across the world for ordinary dating, named for Pope Gregory XIII, who proclaimed it on 24 February 1582 by the papal bull Inter gravissimas.¹ It is a minor correction to the older Julian calendar of Julius Caesar (46 b.c.), with the same twelve months, the same names for the months, the same length for the common year of 365 days, and the same insertion of an extra day — 29 February — in leap years. The single change is to the leap-year rule, and the single founding event that distinguishes it from the Julian calendar is the deletion of ten days from October 1582.²³

The reform replaced the Julian centurial leap years — every year divisible by four was a Julian leap year, with no exceptions — with the rule that centurial years are leap years only if they are also divisible by 400. Three out of every four century years that the Julian calendar treated as leap are now common years in the Gregorian: 1700, 1800, and 1900 lost their leap day; 1600 and 2000 kept theirs. The result is a calendar that loses three days every four centuries against the Julian and that runs much closer to the astronomical year. The Julian average year is 365.25 days, longer than the tropical year by about 11 minutes 14 seconds; the Gregorian average year is 365.2425 days, longer by about 27 seconds.²³

Because it is a civil calendar, the Gregorian calendar is the object of international standards rather than of a single legal text. It is the calendar referenced — implicitly or by name — by the international standard for date strings, by the internet timestamp standard, by every operating system's date-handling code, and by every modern programming language's date arithmetic.⁶ In Wikidata it is the entity Q12138, recorded as the "internationally accepted civil calendar".⁸

Why did the Julian calendar need to be reformed?

The Julian calendar of 46 b.c. set the year length to 365.25 days by intercalating a leap day every fourth year without exception. That value is about 11 minutes 14 seconds longer than the mean tropical year — the time the Sun takes to return to the same point relative to the celestial equator — so the Julian calendar runs slow against the seasons by approximately one day every 128 years.² By the late sixteenth century the Julian calendar had been in use for more than sixteen hundred years and the cumulative drift was visible.

The drift was a problem because the Christian church anchored the date of Easter to the vernal equinox. The First Council of Nicaea, in 325, had ruled that Easter should be celebrated on the Sunday following the first full moon on or after the vernal equinox, and had assumed an equinox date of 21 March.²³ By 1582 the astronomical vernal equinox was occurring on 11 March — ten days earlier than the Nicaean date — and the church's tables for computing the lunar age were also wrong. Easter was, in effect, being celebrated on a Sunday that the rule was no longer producing correctly.²

Pope Gregory XIII convened a calendar commission in 1572.³ The commission adopted a proposal originated by the Italian physician and astronomer Aloysius Lilius and worked out in detail by the Jesuit mathematician Christopher Clavius. The bull Inter gravissimas, issued ten years later, made the commission's decisions law for the Catholic Church and the states that recognised papal authority. It did three things at once: it deleted ten days from October 1582 to bring the equinox back to 21 March; it changed the leap-year rule going forward; and it issued new tables for computing Easter against the corrected calendar.¹

What did the 1582 reform actually change?

The reform was, in its operative content, three short rules. They are still in force, almost unchanged, and they are the entirety of what distinguishes the Gregorian calendar from the Julian calendar it superseded.

Ten days shall be removed from the month of October of the year 1582 … so that the day which would have been called the fifth of October shall be called the fifteenth. Every fourth year shall continue to be bissextile, as the custom is now, except that of centurial years only every fourth shall be bissextile, thus the years 1700, 1800 and 1900 shall not be bissextile.¹

The first rule was a one-time correction. Thursday 4 October 1582 was followed directly by Friday 15 October 1582 — the dates between them simply did not exist in any country that observed the reform that year. The day of the week ran straight through the gap, unaffected: the 4th was a Thursday, the 15th was a Friday, and the seven-day cycle that the day of the week sits in continued without interruption. The Julian calendar's accumulated 10-day surplus over the Nicaean equinox date was simply taken back.¹²

The second rule is the leap-year correction that the reform is now remembered for. Every fourth year remained a leap year — the basic Julian rule — but three out of every four centurial years lost their leap day. The first centurial years to be common years rather than leap years under the new rule were 1700, 1800, and 1900; the first one to remain a leap year was 1600, and the next was 2000.¹⁴ In its most compact form the rule is the one quoted by the U.S. Naval Observatory: "Every year that is exactly divisible by four is a leap year, except for years that are exactly divisible by 100, but these centurial years are leap years if they are exactly divisible by 400."³

The third rule replaced the medieval Easter tables with new ones based on a cycle of epacts — small numerical corrections that track the difference between the calendar and the astronomical Moon — rather than the older "golden number" method. The new tables are the operational reason the church accepted the calendar change at all; the leap-year rule is the structural reason the reform has lasted. The Easter rule itself is not part of the civil calendar that secular states adopted, and most of the world treats Inter gravissimas's contribution as the two civil rules: the date correction and the leap-year rule.¹²

How accurate is the Gregorian calendar?

The Gregorian average year is 365.2425 days, compared to a current mean tropical year of about 365.24219 days.² The calendar therefore runs long by about 27 seconds per year against the actual astronomical year. That residual error accumulates to a full day in roughly 3,300 years on its own, or — phrased a little more conservatively, since the tropical year itself is slowly shortening — to a one-day discrepancy with the vernal equinox after about another 8,000 years from the year 2000.²⁴

The accuracy gain over the Julian calendar is an order of magnitude. The Julian calendar runs long by about 11 minutes 14 seconds per year, accumulating one day every 128 years; the Gregorian runs long by about 27 seconds per year, accumulating one day in millennia.² Across the four centuries since 1582, the two calendars have drifted apart by exactly three days — the three centurial leap days the Gregorian rule skipped (1700, 1800, 1900) and the Julian kept. The current gap between a Gregorian date and the same Julian date is therefore thirteen days, after a fourth Julian centurial leap day in 2100 that the Gregorian will not match.²

The numerical character of the Gregorian rule is straightforward to verify by counting. In any 400-year span the calendar contains 100 multiples of 4. Four of those are also multiples of 100, and three of those four are not multiples of 400. Those three are the centurial leap days the rule drops. The 400-year cycle therefore contains 100 − 3 = 97 leap years and 303 common years: 303 × 365 + 97 × 366 = 146,097 days, which is a mean calendar year of exactly 365.2425 days.² Because 146,097 is also divisible by 7, the entire civil calendar — dates, leap days, and weekdays — repeats exactly every 400 years.²

Various proposals to refine the rule have been made over the centuries — typically by dropping the leap day in years divisible by some larger number, such as 4,000 — but none has been adopted. The 2,000-year track record of the Julian rule and the post-1582 track record of its Gregorian successor both suggest that the world is more comfortable with a calendar that drifts slowly and predictably than with one that is repeatedly tweaked.²

How was the calendar adopted around the world?

The Gregorian calendar was promulgated in 1582 by a papal bull, and so it was adopted first by the states that recognised papal authority and only gradually by the rest of the world. The pattern of staggered adoption — and the resulting need to be careful with historical dates — is one of the lasting consequences of the reform.²

The Catholic states moved first. Spain, Portugal, Poland, and most of Italy switched in October 1582, on the dates the bull specified. The Catholic principalities of the Holy Roman Empire and the German Catholic states followed in 1583 and 1584. France adopted the calendar in December 1582, dropping ten days from that month rather than from October.²

Protestant Europe accepted the calendar only after long resistance. The Protestant German states adopted it in 1700, after a near-century of running parallel calendars; Sweden adopted it in 1753, after a celebrated false start in which it abandoned the Julian calendar in 1700 only to reinstate it in 1712 by inserting a 30 February into that year.² Britain and her American colonies held out the longest among Protestant Western Europe, switching only when the Calendar (New Style) Act 1750 took effect in September 1752: Wednesday 2 September 1752 was followed directly by Thursday 14 September 1752, dropping eleven days because the eighteenth century had added one more centurial leap day to the Julian–Gregorian gap.⁵ The same Act moved the start of the legal year from 25 March to 1 January, so that 1751 was a short year of 282 days running from 25 March to 31 December.⁵

The Eastern Orthodox countries adopted the Gregorian civil calendar later still. Bulgaria switched in 1916, Russia in 1918 (skipping thirteen days in February), and Greece — the last European state to make the switch — in 1923, also skipping thirteen days.² Outside Europe, Japan adopted the calendar in 1873, China in 1912 (for the new republic) and 1949 (operationally for the People's Republic), and Saudi Arabia in 2016 for civil administration, retaining the Islamic Hijri calendar for religious purposes. By the early twentieth century the Gregorian calendar was the de facto international standard for civil dating, with national religious and liturgical calendars running alongside it.²³

Old Style and New Style

The staggered adoption introduced a convention that historians still use. A date written in the form "1 February 1700 O.S." or "O.S." alone is an Old Style date — a date as recorded in a jurisdiction still using the Julian calendar. A date marked N.S. is New Style, recorded under the Gregorian calendar. The two differ by 10 days in the 16th century, 11 in the 18th, 12 in the 19th, and 13 from 1900 onward.² George Washington was born on 11 February 1732 in the Julian calendar then in use in the British colonies; modern American convention reckons his birthday as 22 February 1732, the Gregorian date eleven days later. The same convention is the reason Russian sources still refer to the October Revolution of 1917 — which the Gregorian calendar dates to 7 November.²

What is the difference between the Gregorian, Julian, and Revised Julian calendars?

Three solar civil calendars are worth distinguishing. The Julian calendar, introduced by Julius Caesar in 46 b.c., intercalates a leap day every four years with no exceptions; its average year is 365.25 days. The Gregorian calendar, introduced by Pope Gregory XIII in 1582, drops three centurial leap days out of every four to give an average year of 365.2425 days. The Revised Julian calendar, proposed by the Serbian astronomer Milutin Milanković and adopted at a 1923 synod in Constantinople, replaces the Gregorian centurial rule with a finer one: centurial years are leap years only when divided by 900 they leave a remainder of 200 or 600.⁹²

The Revised Julian calendar agrees with the Gregorian for every date between 1600 and 2800 — the two calendars disagree for the first time only in 2800, which the Gregorian rule keeps as a leap year and the Revised Julian rule drops. Its mean year is 365 + 218/900 = 365.24222… days, slightly shorter than the Gregorian's 365.2425 and a slightly better fit to the current mean tropical year. The differences are too small to matter for civil dating within any human planning horizon, and the Revised Julian calendar is best understood as an Orthodox-church attempt to bring the Julian-calendar-based liturgical calendar back into line with the seasons without copying the Catholic-church reform of 1582 wholesale.⁹

The Revised Julian calendar was adopted at the 1923 Synod of Constantinople by several autocephalous Orthodox churches, including the Ecumenical Patriarchate of Constantinople and the churches of Greece, Romania, and Cyprus, for fixed-date observances. Easter and other movable feasts remained tied to the Julian calendar — Bulgaria followed in 1968, and the Finnish Orthodox Church is the one church now using the Gregorian Easter computation. The Russian, Serbian, Georgian, and Jerusalem patriarchates retain the unrevised Julian calendar in full, which is why Orthodox Christmas is celebrated on 7 January by the Gregorian reckoning of those communities (it remains 25 December on their internal Julian reckoning).⁹²

What is the proleptic Gregorian calendar?

Most modern date-handling software does not care about the historical date the Gregorian rule was adopted. It applies the rule to every year it is asked about, including years before 1582 and indeed before the year 1, treating the Gregorian calendar as if it had always been in use. The result is called the proleptic Gregorian calendar, and it is the calendar referenced by the standard for date-and-time strings on the internet, by the IANA Time Zone Database used by every major operating system to map UTC to local time, and by the date arithmetic in nearly every modern programming language.⁶⁷

The convention works for two reasons. First, computer software that does date arithmetic almost never needs the difference of "what calendar was a 14th-century European document actually written in"; it needs a single consistent year-month-day-to-day-count function, and the proleptic Gregorian rule is the simplest such function whose answers match modern dates. Second, the alternative — switching from Julian to Gregorian on different dates depending on jurisdiction (1582 in Italy, 1752 in Britain, 1918 in Russia, and so on) — would make every program that handles historical dates a regional history exam.⁷

The internet timestamp standard pins the proleptic rule down with the same wording the Gregorian reform used: a leap year is a year divisible by four, except centuries, unless they are divisible by 400.⁶ Negative and zero years follow the astronomical convention introduced by Jacques Cassini in 1740: the year a.d. 1 is preceded by year 0, which is preceded by year −1, with no gap.² In this scheme the year 0 is divisible by 400, so it is a (proleptic) leap year. Historical writing instead labels years 1 b.c. and skips zero, which is convenient for chronologists and inconvenient for everyone doing arithmetic; the international date-string standard explicitly uses the astronomical convention.⁶

One small consequence to watch for: a proleptic Gregorian date for an event before 1582 does not correspond to any date a contemporary would have written. 12 October 1492 in modern computer databases is the proleptic Gregorian rendering of the date Columbus recorded as 12 October in his Julian-calendar log. The "historical" Gregorian rendering — what the Catholic Church now uses for pre-1582 events — adds the appropriate Julian-to-Gregorian offset; the proleptic rendering does not. The disagreement is small (10 days in the 16th century, slightly less in earlier ones) but enough to derail historical date arithmetic that does not declare which convention it is using.²⁷

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