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2. The Christian calendarThe ``Christian calendar'' is the term I use to designate the calendar commonly in use, although its connection with Christianity is highly debatable. The Christian calendar has years of 365 or 366 days. It is divided into 12 months that have no relationship to the motion of the moon. In parallel with this system, the concept of weeks groups the days in sets of 7. Two main versions of the Christian calendar have existed in recent times: The Julian calendar and the Gregorian calendar. The difference between them lies in the way they approximate the length of the tropical year and their rules for calculating Easter.
2.1 What is the Julian calendar?The Julian calendar was introduced by Julius Caesar in 45 BC. It was in common use until the 1500s, when countries started changing to the Gregorian calendar (section 2.2). However, some countries (for example, Greece and Russia) used it into this century, 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.
2.1.1 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, this rule was not followed in the first years after the introduction of the Julian calendar in 45 BC. 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 BC, 42 BC, 39 BC, 36 BC, 33 BC, 30 BC, 27 BC, 24 BC, 21 BC, 18 BC, 15 BC, 12 BC, 9 BC, AD 8, AD 12, and every 4th year from then on. Authories disagree about whether 45 BC was a leap year or not. There were no leap years between 9 BC and AD 8 (or, according to some authorities, between 12 BC and AD 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.
2.1.2 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 section 2.2. 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 AD 325). The Gregorian calendar was therefore calibrated to make that day vernal equinox. By 1582 vernal equinox had moved (1582325)/128 days = approximately 10 days backwards. So 10 days had to be dropped.

Nonleap year  Leap year 
22 February  22 February 
23 February  23 February 
24 February (extra day)  
24 February  25 February 
25 February  26 February 
26 February  27 February 
27 February  28 February 
28 February  29 February 
For example, the feast of St. Leander has been celebrated on 27 February in nonleap years and on 28 February in leap years.
The EU (European Union) in their infinite wisdom have decided that starting in the year 2000, 29 February is to be the leap day. This will affect countries such as Sweden and Austria that celebrate ``name days'' (i.e. each day is associated with a name).
It appears that the Roman Catholic Church already uses 29 February as the leap day.
In the Julian calendar the relationship between the days of the week and the dates of the year is repeated in cycles of 28 years. In the Gregorian calendar this is still true for periods that do not cross years that are divisible by 100 but not by 400.
A period of 28 years is called a Solar Cycle. The Solar Number
of a year is found as:
In the Julian calendar there is a onetoone relationship between the Solar Number and the day on which a particular date falls.
(The leap year cycle of the Gregorian calendar is 400 years, which is 146,097 days, which curiously enough is a multiple of 7. So in the Gregorian calendar the equivalent of the ``Solar Cycle'' would be 400 years, not 7×400=2800 years as one might be tempted to believe.)
To calculate the day on which a particular date falls, the following algorithm may be used (the divisions are integer divisions, in which remainders are discarded):
Example: On what day of the week was the author born?
My birthday is 2 August 1953 (Gregorian, of course).
I was born on a Sunday.
Before Julius Caesar introduced the Julian calendar in 45 BC, the Roman calendar was a mess, and much of our socalled ``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. 715673 BC, 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 BC, 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 daysA 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.
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
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 BC. We can make an educated guess about the length of the months in the years 47 and 46 BC:
47 BC  46 BC  
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 BC 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 nonleap years). In 44 BC Quintilis was renamed `Julius' (July) in honour of Julius Caesar, and in 8 BC Sextilis became `Augustus' in honour 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 dating back to the 14th century.
The Romans didn't number the days sequentially from 1. Instead they had three fixed points in each month:
The days between Kalendae and Nonae were called ``the 4th day before Nonae'', ``the 3rd day before Nonae'', and ``the 2nd day before Nonae''. (The 1st day before Nonae would be Nonae itself.)
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 equivalences 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 
2nd 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 (see section 2.3). 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 prereform 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.
For the man in the street, yes. When Julius Caesar introduced his calendar in 45 BC, he made 1 January the start of the year, and it was always the date on which the Solar Number and the Golden Number (see section 2.9.3) were incremented.
However, the church didn't like the wild parties that took place at the start of the new year, and in AD 567 the council of Tours declared that having the year start on 1 January was an ancient mistake that should be abolished.
Through the middle ages various New Year dates were used. If an ancient document refers to year X, it may mean any of 7 different periods in our present system:
Choosing the right interpretation of a year number is difficult, so much more as one country might use different systems for religious and civil needs.
The Byzantine Empire used a year starting on 1 Sep, but they didn't count years since the birth of Christ, instead they counted years since the creation of the world which they dated to 1 September 5509 BC.
Since about 1600 most countries have used 1 January as the first day of the year. Italy and England, however, did not make 1 January official until around 1750.
In England (but not Scotland) three different years were used:
A lot of languages, including English, use month names based on Latin. Their meaning is listed below. However, some languages (Czech and Polish, for example) use quite different names.
In the Christian world, Easter (and the days immediately preceding it) is the celebration of the death and resurrection of Jesus in (approximately) AD 30.
Easter Sunday is the first Sunday after the first full moon after vernal equinox.
The calculation of Easter is complicated because it is linked to (an inaccurate version of) the Hebrew calendar.
Jesus was crucified immediately before the Jewish Passover, which is a celebration of the Exodus from Egypt under Moses. Celebration of Passover started on the 14th or 15th day of the (spring) month of Nisan. Jewish months start when the moon is new, therefore the 14th or 15th day of the month must be immediately after a full moon.
It was therefore decided to make Easter Sunday the first Sunday after the first full moon after vernal equinox. Or more precisely: Easter Sunday is the first Sunday after the ``official'' full moon on or after the ``official'' vernal equinox.
The official vernal equinox is always 21 March.
The official full moon may differ from the real full moon by one or two days.
(Note, however, that historically, some countries have used the real (astronomical) full moon instead of the official one when calculating Easter. This was the case, for example, of the German Protestant states, which used the astronomical full moon in the years 17001776. A similar practice was used Sweden in the years 17401844 and in Denmark in the 1700s.)
The full moon that precedes Easter is called the Paschal full moon. Two concepts play an important role when calculating the Paschal full moon: The Golden Number and the Epact. They are described in the following sections.
The following sections give details about how to calculate the date for Easter. Note, however, that while the Julian calendar was in use, it was customary to use tables rather than calculations to determine Easter. The following sections do mention how to calcuate Easter under the Julian calendar, but the reader should be aware that this is an attempt to express in formulas what was originally expressed in tables. The formulas can be taken as a good indication of when Easter was celebrated in the Western Church from approximately the 6th century.
Each year is associated with a Golden Number.
Considering that the relationship between the moon's phases and the days of
the year repeats itself every 19 years (as described in chapter 1),
it is natural to associate a number between 1 and 19 with each year. This number
is the socalled Golden Number. It is calculated thus:
New moon will fall on (approximately) the same date in two years with the same Golden Number.
Each year is associated with an Epact.
The Epact is a measure of the age of the moon (i.e. the number of days that have passed since an ``official'' new moon) on a particular date.
In the Julian calendar, 8 + the Epact is the age of the moon at the start of the year. In the Gregorian calendar, the Epact is the age of the moon at the start of the year.
The Epact is linked to the Golden Number in the following manner:
Under the Julian calendar, 19 years were assumed to be exactly an integral
number of synodic months, and the following relationship exists between the
Golden Number and the Epact:
If this formula yields zero, the Epact is by convention frequently designated by the symbol * and its value is said to be 30. Weird? Maybe, but people didn't like the number zero in the old days.
Since there are only 19 possible golden numbers, the Epact can have only 19 different values: 1, 3, 4, 6, 7, 9, 11, 12, 14, 15, 17, 18, 20, 22, 23, 25, 26, 28, and 30.
The Julian system for calculating full moons was inaccurate, and under the
Gregorian calendar, some modifications are made to the simple relationship
between the Golden Number and the Epact.
In the Gregorian calendar the Epact should be calculated thus (the divisions are integer divisions, in which remainders are discarded):
(For the purpose of this calculation century=20 is used for the years 1900 through 1999, and similarly for other centuries, although this contradicts the rules in section 2.10.3.)
(This adds one to the Epact 8 times every 2500 years.)
In the Gregorian calendar, the Epact can have any value from 1 to 30.
Example: What was the Epact for 1992?
The Epact for 1992 was 25.
To find Easter the following algorithm is used:
An Epact of 25 requires special treatment, as it has two dates in the above table. There are two equivalent methods for choosing the correct full moon date:
The proof that these two statements are equivalent is left as an exercise to the reader. (The frustrated ones may contact me for the proof.)
Example: When was Easter in 1992?
In the previous section we found that the Golden Number for 1992 was 17 and the Epact was 25. Looking in the table, we find that the Paschal full moon was either 17 or 18 April. By rule B above, we choose 17 April because the Golden Number >11.
17 April 1992 was a Friday. Easter Sunday must therefore have been 19 April.
This is an attempt to boil down the information given in the previous sections (the divisions are integer divisions, in which remainders are discarded):
This algorithm is based in part on the algorithm of Oudin (1940) as quoted in ``Explanatory Supplement to the Astronomical Almanac'', P. Kenneth Seidelmann, editor.
People who want to dig into the workings of this algorithm, may be interested to know that
 G
 is the Golden Number1
 H
 is 23Epact (modulo 30)
 I
 is the number of days from 21 March to the Paschal full moon
 J
 is the weekday for the Paschal full moon (0=Sunday, 1=Monday, etc.)
 L
 is the number of days from 21 March to the Sunday on or before the Paschal full moon (a number between 6 and 28)
Suppose you know the Easter date of the current year, can you easily find the Easter date in the next year? No, but you can make a qualified guess.
If Easter Sunday in the current year falls on day X and the next year is not a leap year, Easter Sunday of next year will fall on one of the following days: X15, X8, X+13 (rare), or X+20.
If Easter Sunday in the current year falls on day X and the next year is a leap year, Easter Sunday of next year will fall on one of the following days: X16, X9, X+12 (extremely rare), or X+19. (The jump X+12 occurs only once in the period 18002099, namely when going from 2075 to 2076.)
If you combine this knowledge with the fact that Easter Sunday never falls before 22 March and never falls after 25 April, you can narrow the possibilities down to two or three dates.
The sequence of Easter dates repeats itself every 532 years in the Julian calendar. The number 532 is the product of the following numbers:
19 (the Metonic cycle or the cycle of the Golden Number)
28 (the Solar cycle, see section 2.4)
The sequence of Easter dates repeats itself every 5,700,000 years in the Gregorian calendar. The number 5,700,000 is the product of the following numbers:
19 (the Metonic cycle or the cycle of the Golden Number)
400 (the Gregorian equivalent of the Solar cycle, see section 2.4)
25 (the cycle used in step 3 when calculating the Epact)
30 (the number of different Epact values)
The Greek Orthodox Church does not always celebrate Easter on the same day as the Catholic and Protestant countries. The reason is that the Orthodox Church uses the Julian calendar when calculating Easter. This is case even in the churches that otherwise use the Gregorian calendar.
When the Greek Orthodox Church in 1923 decided to change to the Gregorian calendar (or rather: a Revised Julian Calendar), they chose to use the astronomical full moon as the basis for calculating Easter, rather than the ``official'' full moon described in the previous sections. And they chose the meridian of Jerusalem to serve as definition of when a Sunday starts. However, except for some sporadic use the 1920s, this system was never adopted in practice.
At at meeting in Aleppo, Syria (510 March 1997), organised by the World Council of Churches and the Middle East Council of Churches, representatives of several churches and Christian world communions suggested that the discrepancies between Easter calculations in the Western and the Eastern churches could be resolved by adopting astronomically accurate calculations of the vernal equinox and the full moon, instead of using the algorithm presented in section 2.9.5. The meridian of Jerusalem should be used for the astronomical calculations.
The new method for calculating Easter should take effect from the year 2001. In that year the Julian and Gregorian Easter dates coincide (on 15 April Gregorian/2 April Julian), and it is therefore a reasonable starting point for the new system.
Whether this new system will actually be adopted, remains to be seen. So the answer to the question heading this section is: I don't know.
If the new system is introduced, churches using the Gregorian calendar will hardly notice the change. Only once during the period 20012025 will these churches note a difference: In 2019 the Gregorian method gives an Easter date of 21 April, but the proposed new method gives 24 March.
Note that the new method makes an Easter date of 21 March possible. This date was not possible under the Julian or Gregorian algorithms. (Under the new method, Easter will fall on 21 March in the year 2877. You're all invited to my house on that date!)
In about AD 523, the papal chancellor, Bonifatius, asked a monk by the name of Dionysius Exiguus to devise a way to implement the rules from the Nicean council (the socalled ``Alexandrine Rules'') for general use.
Dionysius Exiguus (in English known as Denis the Little) was a monk from Scythia, he was a canon in the Roman curia, and his assignment was to prepare calculations of the dates of Easter. At that time it was customary to count years since the reign of emperor Diocletian; but in his calculations Dionysius chose to number the years since the birth of Christ, rather than honour the persecutor Diocletian.
Dionysius (wrongly) fixed Jesus' birth with respect to Diocletian's reign in such a manner that it falls on 25 December 753 AUC (ab urbe condita, i.e. since the founding of Rome), thus making the current era start with AD 1 on 1 January 754 AUC.
How Dionysius established the year of Christ's birth is not known (see section 2.10.1 for a couple of theories). Jesus was born under the reign of king Herod the Great, who died in 750 AUC, which means that Jesus could have been born no later than that year. Dionysius' calculations were disputed at a very early stage.
When people started dating years before 754 AUC using the term ``Before Christ'', they let the year 1 BC immediately precede AD 1 with no intervening year zero.
Note, however, that astronomers frequently use another way of numbering the years BC. Instead of 1 BC they use 0, instead of 2 BC they use 1, instead of 3 BC they use 2, etc.
See also section 2.10.2.
It is frequently claimed that it was the venerable Bede (673735) who introduced BC dating. This is probably not true.
In this section I have used AD 1 = 754 AUC. This is the most likely equivalence between the two systems. However, some authorities state that AD 1 = 753 AUC or 755 AUC. This confusion is not a modern one, it appears that even the Romans were in some doubt about how to count the years since the founding of Rome.
There are quite a few theories about this. And many of the theories are presented as if they were indisputable historical fact.
Here are two theories that I personally consider likely:
No.
There are two reasons for this:
 There is no year 0.
 Jesus was born before 4 BC.
The concept of a year ``zero'' is a modern myth (but a very popular one). Roman numerals do not have a figure designating zero, and treating zero as a number on an equal footing with other numbers was not common in the 6th century when our present year reckoning was established by Dionysius Exiguus (see section 2.10). Dionysius let the year AD 1 start one week after what he believed to be Jesus' birthday.
Therefore, AD 1 follows immediately after 1 BC with no intervening year zero. So a person who was born in 10 BC and died in AD 10, would have died at the age of 19, not 20.
Furthermore, Dionysius' calculations were wrong. The Gospel of Matthew tells us that Jesus was born under the reign of king Herod the Great, and he died in 4 BC. It is likely that Jesus was actually born around 7 BC. The date of his birth is unknown; it may or may not be 25 December.
The first century started in AD 1. The second century must therefore have started a hundred years later, in AD 101, and the 21st century must start 2000 years after the first century, i.e. in the year 2001.
This is the cause of some heated debate, especially since some dictionaries and encyclopaedias say that a century starts in years that end in 00.
Let me propose a few compromises:
Any 100year period is a century. Therefore the period from 23 June 1998 to 22 June 2098 is a century. So please feel free to celebrate the start of a century any day you like!
Although the 20th century started in 1901, the 1900s started in 1900. Similarly, we can celebrate the start of the 2000s in 2000 and the start of the 21st century in 2001.
Finally, let's take a lesson from history:
When 1899 became 1900 people celebrated the start of a new century.Two parties! Let's do the same thing again!
When 1900 became 1901 people celebrated the start of a new century.
Years before the birth of Christ are in English traditionally identified using the abbreviation BC (``Before Christ'').
Years after the birth of Christ are traditionally identified using the abbreviation AD (``Anno Domini'', that is, ``In the Year of the Lord'').
Some people, who dislike the reference to Christianity that is implied in these terms, prefer the abbreviations BCE (``Before the Common Era'') and CE (``Common Era'').
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 abolished [whatever that means] in 1806.
The Indiction may be calculated thus:
The Indiction has no astronomical significance.
The Indiction did not always follow the calendar year. Three different Indictions may be identified:
The Julian period (and the Julian day number) must not be confused with the Julian calendar.
The French scholar Joseph Justus Scaliger (15401609) was interested in assigning a positive number to every year without having to worry about BC/AD. 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 (14841558).
Scaliger's Julian period starts on 1 January 4713 BC (Julian calendar) and lasts for 7980 years. AD 1998 is thus year 6711 in the Julian period. After 7980 years the number starts from 1 again.
Why 4713 BC and why 7980 years? Well, in 4713 BC the Indiction (see section 2.11), the Golden Number (see section 2.9.3) and the Solar Number (see section 2.4) were all 1. The next times this happens is 15×19×28=7980 years later, in AD 3268.
Astronomers have used the Julian period to assign a unique number to every day since 1 January 4713 BC. This is the socalled Julian Day (JD). JD 0 designates the 24 hours from noon UTC on 1 January 4713 BC to noon UTC on 2 January 4713 BC.
This means that at noon UTC on 1 January AD 2000, JD 2,451,545 will start.
This can be calculated thus:
From 4713 BC to AD 2000 there are 6712 years.
In the Julian calendar, years have 365.25 days, so 6712 years correspond to 6712×365.25=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 AD 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.
Try this one (the divisions are integer divisions, in which remainders are discarded):
JDN 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 algorith 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, JDN, to a day, month, and year) these formulas can be used (again, the divisions are integer divisions):
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.
The answer to this question depends on what you mean by ``correct''. Different countries have different customs.
Most countries use a daymonthyear format, such as:
25.12.1998 25/12/1998 25/121998 25.XII.1998
In the U.S.A. a monthdayyear format is common:
12/25/1998 12251998
International standard IS8601 mandates a yearmonthday format, namely either
19981225 or 19981225.
In all of these systems, the first two digits of the year are frequently omitted:
25.12.98 12/25/98 981225
This confusion leads to misunderstandings. What is 020304? To most people it is 2 Mar 2004; to an American it is 3 Feb 2004; and to a person using the international standard it would be 4 Mar 2002.
If you want to be sure that people understand you, I recommend that you
