The Gregorian calendar: Julian and Gregorian

Fact sheet

Scientific classification

• Solar: it measures the tropical year (the cycle of the seasons) alone; its twelve months are fixed divisions inherited from the old Roman lunar calendar that no longer follow the moon.
• Arithmetical: fixed rules that depend on no observation and no true position of the sun, so any date in it can be computed with integer operations.
• Its accuracy: the Julian year is about 11 minutes longer than the tropical year, so the seasons fall behind it by a day about every 128 years. The Gregorian year is about 27 seconds longer than the mean tropical year — a day in 3,000 to 3,300 years depending on the value adopted for the tropical year.
• Its standing: the Gregorian is the international civil calendar, and the ISO 8601 standard for writing dates rests on it. Calendar scholars call the Gregorian form “proleptic” when it is extended before 1582, as astronomers do in their tables.

Rules

1. The day begins at midnight, as the Roman civil day did.
2. The months are twelve of fixed length: 31 days for January, March, May, July, August, October and December; 30 days for April, June, September and November; and 28 for February (29 in a leap year).
3. The Julian leap rule: a year is a leap year if divisible by 4. So every four years have 1461 days.
4. The Gregorian leap rule: a year is a leap year if divisible by 4, except century years, which are leap years only if divisible by 400: so 1700, 1800 and 1900 are common, 1600 and 2000 are leap, and 2100 is common. Every 400 years therefore have 146,097 days, i.e. exactly 20,871 weeks, so the calendar repeats with its weekdays every 400 years.

A curiosity of the arithmetic: the difference between the two forms was zero in the 3rd century CE (between 1 March 200 and 1 March 300), and has grown by a day in every century year not divisible by 400.

Months and their names

The old Roman year began with March, which is why September, October, November and December mean “seventh, eighth, ninth and tenth” in Latin. In the Arab world the months have three common sets of names:

The Syriac names in the Levant and Iraq are inherited from the Babylonian calendar and are the same as the Hebrew lunar month names (Nisan, Iyar, Tammuz, Av, Elul…), but here they name solar months. As for the popular story that Augustus took a day from February so that his month would equal Julius’s, it has no basis in Roman sources; the first to tell it was a 13th-century writer, Sacrobosco.

Counting the years

• Before the Christian era: the Romans named the year after its two consuls, or counted it from the founding of Rome (753 BCE by Varro’s reckoning).
• The Christian era: proposed by the monk Dionysius Exiguus in 525 for computing Easter, it spread in Western Europe after the English historian Bede adopted it in the 8th century. The reckoning does not match what historians consider likely for the birth of Christ (a few years before year 1).
• No year zero: the year before 1 CE is 1 BCE. Since the 18th century astronomers have used a count with a year zero (0 = 1 BCE, −1 = 2 BCE) to simplify calculation, which the ISO 8601 standard adopts.
• The year did not always begin on 1 January: the Romans made it 1 January from 153 BCE, but medieval Europe began the year on 25 March, 25 December or Easter; England kept beginning the year on 25 March until 1752.

History: from Rome to Rome

1. Before 46 BCE

   The Roman Republican calendar

   The Roman year had 12 months and 355 days, to which an intercalary month of 27 or 28 days was sometimes added after February. Intercalation was decided by the pontiffs, many of them politicians, who lengthened and shortened years to suit themselves, until the calendar drifted about three months from the seasons.

2. 46 BCE

   The reform of Julius Caesar

   On the advice of the astronomer Sosigenes of Alexandria, Caesar made the year 365 days, added a day every four years, and abolished the intercalary month. To bring the calendar back to the seasons he made 46 BCE 445 days long (“the last year of confusion”), and the new calendar took effect on 1 January 45 BCE. The leap day was a repeated day before 24 February (the “sixth day twice” before the first of March), whence the European name of the leap year, bissextile.

3. 44–8 BCE

   The pontiffs’ error and Augustus’s correction

   After Caesar’s death the pontiffs mistakenly intercalated every three years (counting the first and last year together), adding 12 days instead of 9 in 36 years. In 8 BCE Augustus ordered intercalation to be skipped for some years until the count was right, and the four-year leap rule resumed in 4 or 8 CE depending on how historians order those years. During this period the seventh and eighth months were named after Julius and Augustus.

4. 321 CE

   The seven-day week

   Constantine made Sunday an official day of rest in 321, bringing the seven-day week into the Roman civil calendar alongside its old days.

5. 325 CE

   The Council of Nicaea and Easter

   The Council of Nicaea decided that Christian Easter be celebrated on a Sunday after the full moon following the spring equinox, and 21 March was taken as the fixed date of the equinox in church reckoning. Because the Julian year is longer than the tropical year, the true equinox came to fall before 21 March.

6. 525 CE

   The Christian era

   Dionysius Exiguus drew up Easter tables counted “from the Incarnation of the Lord,” giving birth to the Christian era that spread across Western Europe in the following centuries.

7. Middle Ages

   In the Islamic world: the “Rumi year”

   Muslim astronomers and historians knew the Julian calendar as the “Rumi (Roman) year” with its Syriac months, often paired with the “era of Alexander” (the Seleucid era), and it was used for land tax and agriculture. Al-Biruni described it, with others, in “The Remaining Signs of Past Centuries.”

8. 13th–16th c.

   The call for reform

   In the 8th century Bede estimated the drift of the equinox at more than three days, and Roger Bacon in the 13th at seven or eight. By the 16th century the equinox fell on 10 or 11 March, ten days earlier than its date at Nicaea; so the Council of Trent (1545) called for it to be restored to where it had been in 325. In 1560 Petrus Pitatus of Verona proposed the rule of 97 leap years in every 400.

9. 1582

   The reform of Gregory XIII

   By the bull Inter gravissimas (24 February 1582), based on the proposal of the Italian physician Aloysius Lilius — including a practical method for correcting the lunar tables — developed by the astronomer Christopher Clavius, the architect of the reform: ten days were dropped, so Thursday 4 October 1582 was followed by Friday 15 October, without breaking the sequence of weekdays; century years became common unless divisible by 400; and the lunar tables for computing Easter were adjusted. The equinox was thus restored to about 21 March as in the time of Nicaea, not as in Caesar’s time.

10. 1923

    The Revised Julian calendar

    A synod in Constantinople approved a form proposed by the Serbian astronomer Milutin Milanković: a century year is a leap year if the remainder of dividing its number of hundreds by 9 is 2 or 6. It matches the Gregorian until 2800, with a mean year of 365.24222 days; some Orthodox churches adopted it for fixed feasts, while all of them kept Easter on the Julian.

The spread of the Gregorian calendar

The Gregorian calendar was not adopted all at once: Catholic countries hurried to it, Protestant countries delayed more than a century, and Orthodox countries more than three centuries:

Ethiopia, Nepal, Iran and Afghanistan still officially use their own calendars.

The difference between the two forms

The difference grows by a day in every Gregorian common century year, on 1 March of that year (computed by the site’s engine):

That is why Christmas in the churches that follow the Julian calendar (25 December Julian) falls on 7 January Gregorian in the 20th and 21st centuries, and the “Julian New Year” on 14 January.

Current use

• Gregorian: the civil calendar in most countries of the world, and in trade, international relations and science.
• Julian: a church calendar for the Orthodox churches of Russia, Serbia, Georgia, North Macedonia and Jerusalem and on Mount Athos, and for the Ancient Assyrian Church of the East; nearly all Orthodox churches compute Easter by it.
• In the Maghreb: Amazigh farming still counts the “agricultural months” by the Julian calendar, including the Amazigh New Year “Yennayer” on 12–14 January.
• In science: astronomers count days by the “Julian Day Number” devised by Joseph Scaliger in 1583 — named after his father Julius Caesar Scaliger, not the Julian calendar.

On this site

• “Gregorian” on the site is the Gregorian extended before 1582 (proleptically) as in ISO 8601; and “Julian” uses its four-year rule throughout the range.
• European history written before 15 October 1582 (and in many countries long after) is entered in the Julian calendar, and the calculator warns about this.
• Years have no zero in the interface (the year before 1 is −1), and are computed internally as astronomical years.
• The Julian card in the date calculators shows its difference from the Gregorian on that day.

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