What is the Julian calendar?

The Julian calendar was introduced by Julius Caesar (bust at right) in 45 B.C.E. Author David Duncan says the Julian calendar was born of Caesar's tryst with Cleopatra.

Before the Julian calendar was introduced, priests in the Roman Empire exploited the calendar for political ends, inserting days and even months into the calendar to keep the politicians they favored in office. Tired of the chaos that this undependable system eventually gave rise to, Julius Caesar finally set out to put the long-abused calendar back on track.

It was in common use until the late 1500s, when countries started changing to the Gregorian calendar (section the modern year). However, some countries (for example, Greece and Russia) used it into the early 1900s, and the Orthodox church in Russia still uses it, as do some other Orthodox churches.

In the Julian calendar, the tropical year is approximated as 365 1/4 days = 365.25 days. This gives an error of 1 day in approximately 128 years.

The approximation 365 1/4 is achieved by having 1 leap year every 4 years.

What years are leap years?

The Julian calendar has 1 leap year every 4 years:

Every year divisible by 4 is a leap year.

However, the 4-year rule was not followed in the first years after the introduction of the Julian calendar in 45 B.C.E. Due to a counting error, every 3rd year was a leap year in the first years of this calendar's existence. The leap years were:

45 B.C.E., 42 B.C.E., 39 B.C.E., 36 B.C.E., 33 B.C.E., 30 B.C.E., 27 B.C.E., 24 B.C.E., 21 B.C.E., 18 B.C.E., 15 B.C.E., 12 B.C.E., 9 B.C.E., C.E. 8, C.E. 12, and every 4th year from then on.

Authorities disagree about whether 45 B.C.E. was a leap year or not.

There were no leap years between 9 B.C.E. and C.E. 8 (or, according to some authorities, between 12 B.C.E. and C.E. 4). This period without leap years was decreed by emperor Augustus in order to make up for the surplus of leap years introduced previously, and it earned him a place in the calendar as the 8th month was named after him.

It is a curious fact that although the method of reckoning years after the (official) birthyear of Christ was not introduced until the 6th century, by some stroke of luck the Julian leap years coincide with years of our Lord that are divisible by 4.

What consequences did the use of the Julian calendar have?

The Julian calendar introduces an error of 1 day every 128 years. So every 128 years the tropical year shifts one day backwards with respect to the calendar. Furthermore, the method for calculating the dates for Easter was inaccurate and needed to be refined.

In order to remedy this, two steps were necessary: 1) The Julian calendar had to be replaced by something more adequate. 2) The extra days that the Julian calendar had inserted had to be dropped.

The solution to problem 1 was the Gregorian calendar described in the section about the modern year.

The solution to problem 2 depended on the fact that it was felt that 21 March was the proper day for vernal equinox (because 21 March was the date for vernal equinox during the Council of Nicaea in C.E. 325). The Gregorian calendar was therefore calibrated to make that day vernal equinox.

By 1582 vernal equinox had moved (1582-325)/128 days = approximately 10 days backwards. So 10 days had to be dropped.

What is the Roman calendar?

Before Julius Caesar introduced the Julian calendar in 45 B.C.E., the Roman calendar was a mess, and much of our so-called "knowledge" about it seems to be little more than guesswork.

Originally, the year started on 1 March and consisted of only 304 days or 10 months (Martius, Aprilis, Maius, Junius, Quintilis, Sextilis, September, October, November, and December). These 304 days were followed by an unnamed and unnumbered winter period. The Roman king Numa Pompilius (c. 715-673 B.C.E., although his historicity is disputed) allegedly introduced February and January (in that order) between December and March, increasing the length of the year to 354 or 355 days. In 450 B.C.E., February was moved to its current position between January and March.

In order to make up for the lack of days in a year, an extra month, Intercalaris or Mercedonius, (allegedly with 22 or 23 days though some authorities dispute this) was introduced in some years. In an 8 year period the length of the years were:

1: 12 months or 355 days
2: 13 months or 377 days
3: 12 months or 355 days
4: 13 months or 378 days
5: 12 months or 355 days
6: 13 months or 377 days
7: 12 months or 355 days
8: 13 months or 378 days

A total of 2930 days corresponding to a year of 366 1/4 days. This year was discovered to be too long, and therefore 7 days were later dropped from the 8th year, yielding 365.375 days per year.

This is all theory. In practice it was the duty of the priesthood to keep track of the calendars, but they failed miserably, partly due to ignorance, partly because they were bribed to make certain years long and other years short. Furthermore, leap years were considered unlucky and were therefore avoided in time of crisis, such as the Second Punic War.

In order to clean up this mess, Julius Caesar made his famous calendar reform in 45 B.C.E. We can make an educated guess about the length of the months in the years 47 and 46 B.C.E.:

	47 B.C.E.	46 B.C.E.
January	29	29
February	28	24
Intercalaris		27
March	31	31
April	29	29
May	31	31
June	29	29
Quintilis	31	31
Sextilis	29	29
September	29	29
October	31	31
November	29	29
Undecember		33
Duodecember		34
December	29	29
Total	355	445

The length of the months from 45 B.C.E. onward were the same as the ones we know today.

Occasionally one reads the following story:

"Julius Caesar made all odd numbered months 31 days long, and all even numbered months 30 days long (with February having 29 days in non-leap years). In 44 B.C.E. Quintilis was renamed 'Julius' (July) in honor of Julius Caesar, and in 8 B.C.E. Sextilis became 'Augustus' in honor of emperor Augustus. When Augustus had a month named after him, he wanted his month to be a full 31 days long, so he removed a day from February and shifted the length of the other months so that August would have 31 days."

This story, however, has no basis in actual fact. It is a fabrication, possibly invented by the English-French scholar Johannes de Sacrobosco in the 13th century.

How did the Romans number days?

The Romans did not number the days sequentially from 1. Instead they had three fixed points in each month:

"Kalendae"

(or "Calendae"), which was the first day of the month.

"Idus,"

which was the 13th day of January, February, April, June, August, September, November, and December, or the 15th day of March, May, July, or October.

"Nonae,"

which was the 9th day before Idus (counting Idus itself as the 1st day).

The days between Kalendae and Nonae were called "the 5th day before Nonae," "the 4th day before Nonae," "the 3rd day before Nonae," and "the day before Nonae." (There was no "2nd day before Nonae." This was because of the inclusive way of counting used by the Romans: To them, Nonae itself was the first day, and thus "the 2nd day before" and "the day before" would mean the same thing.)

Similarly, the days between Nonae and Idus were called "the Xth day before Idus," and the days after Idus were called "the Xth day before Kalendae (of the next month)."

Julius Caesar decreed that in leap years the "6th day before Kalendae of March" should be doubled. So in contrast to our present system, in which we introduce an extra date (29 February), the Romans had the same date twice in leap years. The doubling of the 6th day before Kalendae of March is the origin of the word bissextile. If we create a list of equivalence between the Roman days and our current days of February in a leap year, we get the following:

7th day before Kalendae of March	23	February
6th day before Kalendae of March	24	February
6th day before Kalendae of March	25	February
5th day before Kalendae of March	26	February
4th day before Kalendae of March	27	February
3rd day before Kalendae of March	28	February
The day before Kalendae of March	29	February
Kalendae of March	1	March

You can see that the extra 6th day (going backwards) falls on what is today 24 February. For this reason 24 February is still today considered the "extra day" in leap years. However, at certain times in history, the second 6th day (25 Feb) has been considered the leap day.

Why did Caesar choose to double the 6th day before Kalendae of March? It appears that the leap month Intercalaris/Mercedonius of the pre-reform calendar was not placed after February, but inside it, namely between the 7th and 6th day before Kalendae of March. It was therefore natural to have the leap day in the same position.

What is the proleptic calendar?

The Julian calendar was introduced in 45 BC, but when historians date events prior to that year, they normally extend the Julian calendar backward in time. This extended calendar is known as the "Julian Proleptic Calendar".

Similarly, it is possible to extend the Gregorian calendar backward in time before 1582. However, this "Gregorian Proleptic Calendar" is not commonly used.

If someone refers to, for example, 15 March 429 BC, they are probably using the Julian proleptic calendar.

In the Julian proleptic calendar, year X BC is a leap year, if X-1 is divisible by 4. This is the natural extension of the Julian leap year rules.

What is Easter?

In the Christian world, Easter (and the days immediately preceding it) is the celebration of the death and resurrection of Jesus in (approximately) C.E. 30.

See additional information on Easter.

What is the Indiction?

The Indiction was used in the middle ages to specify the position of a year in a 15 year taxation cycle. It was introduced by emperor Constantine the Great on 1 September 312 and ceased to be used in 1806.

The Indiction may be calculated thus:

Indiction = (year + 2) mod 15 + 1

The Indiction has no astronomical significance.

The Indiction did not always follow the calendar year. Three different Indictions may be identified:

The Pontifical or Roman Indiction, which started on New Year's Day (being either 25 December, 1 January, or 25 March).
 

The Greek or Constantinopolitan Indiction, which started on 1 September.
 

The Imperial Indiction or Indiction of Constantine, which started on 24 September.

What is the Julian Period?

The Julian period (and the Julian day number) must not be confused with the Julian calendar.

The French scholar Joseph Justus Scaliger (1540-1609) was interested in assigning a positive number to every year without having to worry about B.C.E. / C.E. He invented what is today known as the Julian Period.

The Julian Period probably takes its name from the Julian calendar, although it has been claimed that it is named after Scaliger's father, the Italian scholar Julius Caesar Scaliger (1484-1558).

Scaliger's Julian period starts on 1 January 4713 B.C.E. (Julian calendar) and lasts for 7980 years. C.E. 2000 is thus year 6713 in the Julian period. After 7980 years the number starts from 1 again.

Why 4713 B.C.E. and why 7980 years? Well, in 4713 B.C.E. the Indiction (see above), the Golden Number (see section on Easter) and the Solar Number (see above) were all 1. The next times this happens is 15 x 19 x 28 = 7980 years later, in C.E. 3268.

Astronomers have used the Julian period to assign a unique number to every day since 1 January 4713 B.C.E. This is the so-called Julian Day (JD). JD 0 designates the 24 hours from noon UTC on 1 January 4713 B.C.E. to noon UTC on 2 January 4713 B.C.E.

This means that at noon UTC on 1 January C.E. 2000, JD 2,451,545 will start.

This can be calculated thus:

From 4713 B.C.E. to C.E. 2000 there are 6712 years.
In the Julian calendar, years have 365.25 days, so 6712 years correspond to 6712 x 365.25=2,451,558 days. Subtract from this the 13 days that the Gregorian calendar is ahead of the Julian calendar, and you get 2,451,545.

Often fractions of Julian day numbers are used, so that 1 January C.E. 2000 at 15:00 UTC is referred to as JD 2,451,545.125.

Note that some people use the term "Julian day number" to refer to any numbering of days. NASA, for example, use the term to denote the number of days since 1 January of the current year, counting 1 January as day 1.

Is there a formula for calculating the Julian day number?

Try this one (the divisions are integer divisions, in which remainders
are discarded):

   a = (14-month)/12
   y = year+4800-a
   m = month + 12*a - 3

For a date in the Gregorian calendar:
   JD = day + (153*m+2)/5 + y*365 + y/4 - y/100 + y/400 - 32045

For a date in the Julian calendar:
   JD = day + (153*m+2)/5 + y*365 + y/4 - 32083

JD is the Julian day number that starts at noon UTC on the specified date.

The algorithm works fine for AD dates. If you want to use it for BC dates, you must first convert the BC year to a negative year (e.g., 10 BC = -9). The algorithm works correctly for all dates after 4800 BC, i.e. at least for all positive Julian day numbers.

To convert the other way (i.e., to convert a Julian day number, JD, to a day, month, and year) these formulas can be used (again, the divisions are integer divisions):

For the Gregorian calendar:
   a = JD + 32044
   b = (4*a+3)/146097
   c = a - (b*146097)/4

For the Julian calendar:
   b = 0
   c = JD + 32082

Then, for both calendars:
   d = (4*c+3)/1461
   e = c - (1461*d)/4
   m = (5*e+2)/153

day = e - (153*m+2)/5 + 1
month = m + 3 - 12*(m/10)
year = b*100 + d - 4800 + m/10

What is the modified Julian day number?

Sometimes a modified Julian day number (MJD) is used which is 2,400,000.5 less than the Julian day number. This brings the numbers into a more manageable numeric range and makes the day numbers change at midnight UTC rather than noon.

MJD 0 thus started on 17 Nov 1858 (Gregorian) at 00:00:00 UTC.

What is the Lilian day number?

The Lilian day number is similar to the Julian day number, except that Lilian day number 1 started at midnight on the first day of the Gregorian calendar, that is, 15 October 1582.

The Lilian day number was invented by Bruce G. Ohms of IBM in 1986. It is named after Aloysius Lilius.