Gregorian calendar starting from 15
The Gregorian calendar
is the internationally
accepted civil calendar
. It was first
proposed by the Calabrian
doctor Aloysius Lilius
, and decreed by Pope Gregory XIII
, after whom the calendar
was named, on 24 February 1582 by the papal
. It was adopted later that year by a handful
of countries, with other countries adopting it over the following
It is a reform of the Julian
. Gregory's bull does not ordain any particular
year-numbering system, but uses the Anno
system which counts years from the traditional
, and which had spread throughout Europe during
the Middle Ages
. That is the same
year-numbering system that is the de facto
The Gregorian calendar modifies the Julian calendar's regular cycle
of leap years
, years exactly divisible by
four, including all centurial years, as follows:
Every year that is exactly divisible by four is a leap
year, except for years that are exactly divisible by 100; the
centurial years that are exactly divisible by 400 are still leap
For example, the year 1900 is not a leap year; the year
2000 is a leap year.
The Gregorian solar calendar is an arithmetical
calendar. It counts days as the
basic unit of time, grouping them into years of 365 or 366 days;
and repeats completely every 146,097 days, which fill 400 years,
and which also happens to be 20,871 seven-day weeks
. Of these 400 years, 303 (the "common years")
have 365 days, and 97 (the leap years) have 366 days. This gives an
average year length of exactly 365.2425 days, or 365 days, 5 hours,
49 minutes and 12 seconds.
A Gregorian year is divided into twelve months
of irregular length, with no regular relationship among their
A calendar date is fully specified by the year (numbered by some
scheme beyond the scope of the calendar itself), the month
(identified by name or number), and the day of the month (numbered
sequentially starting at 1).
Leap years add a 29th day to February, which normally has 28 days.
The essential ongoing differentiating feature of the Gregorian
calendar, as distinct from the Julian calendar with a leap day
every four years, is that the Gregorian omits 3 leap days every 400
years. This difference would have been more noticeable in modern
memory were it not that the year 2000 was a leap year in both the
Julian and Gregorian calendar systems.
day in a leap year is
known as a leap day
. Since Roman times 24
) was counted as the
leap day, but now 29 February is regarded as the leap day in most
Although the calendar year runs from 1 January to 31 December,
sometimes year numbers were based on a different starting point
within the calendar. Confusingly, the term "Anno Domini" is not
specific on this point, and actually refers to a family of year
numbering systems with different starting points for the years.
(See the section below for more on this issue.)
The Catholic Church
a tabular lunar calendar, which was primarily to calculate the date
, and the lunar calendar required
reform as well. A perpetual lunar calendar was created, in the
sense that 30 different arrangements (lines in the expanded table
) for lunar months were created. One
of the 30 arrangements applies to a century (for this purpose, the
century begins with a year divisible by 100). When the arrangement
to be used for a given century is communicated, anyone in
possession of the tables can find the age of the moon on any date,
and calculate the date of Easter.
The motivation of the Catholic Church in adjusting the calendar was
to celebrate Easter at the time it thought the First Council of Nicaea
upon in 325. Although a canon of the council implies that all
churches used the same Easter, they did not. The Church of
Alexandria celebrated Easter on the Sunday after the 14th day of
the moon (computed using the Metonic
) that falls on or after the vernal equinox
, which they placed on 21
March. However, the Church of Rome still regarded 25 March as the
equinox (until 342) and used a different cycle to compute the day
of the moon. In the Alexandrian system, since the 14th day of the
Easter moon could fall at earliest on 21 March its first day could
fall no earlier than 8 March and no later than 5 April. This meant
that Easter varied between 22 March and 25 April. In Rome, Easter
was not allowed to fall later than 21 April, that being the day of
or birthday of Rome and
a pagan festival. The first day of the Easter moon could fall no
earlier than 5 March and no later than 2 April. Easter was the
Sunday after the 15th day of this moon, whose 14th day was allowed
to precede the equinox. Where the two systems produced different
dates there was generally a compromise so that both churches were
able to celebrate on the same day. By the tenth century all
churches (except some on the eastern border of the Byzantine Empire
) had adopted the
Alexandrian Easter, which still placed the vernal equinox on 21
March, although Bede
had already noted its
drift in 725—it had drifted even further by the sixteenth
Worse, the reckoned Moon that was used to compute Easter
was fixed to the Julian year by a
19 year cycle
. However, that
approximation built up an error of one day every 310 years, so by
the sixteenth century the lunar calendar was out of phase with the
real Moon by four days.
The Council of Trent
plan in 1563 for correcting the calendrical errors, requiring that
the date of the vernal equinox
restored to that which it held at the time of the First Council of
Nicaea in 325 and that an alteration to the calendar be designed to
prevent future drift. This would allow for a more consistent and
accurate scheduling of the feast of Easter
The fix was to come in two stages. First, it was necessary to
approximate the correct length of a solar year. The value chosen
was 365.2425 days in decimal notation. Although close to the
mean tropical year
days, it is even closer to the vernal equinox year
of 365.2424 days;
this fact made the choice of approximation particularly appropriate
as the purpose of creating the calendar was to ensure that the
vernal equinox would be near a specific date (21 March). (See
The second stage was to devise a model based on the approximation
which would provide an accurate yet simple, rule-based calendar.
The formula designed by Aloysius
was ultimately successful. It proposed a 10-day
correction to revert the drift since Nicaea, and the imposition of
a leap day in only 97 years in 400 rather than in 1 year in 4. To
implement the model, it was provided that years divisible by
100 would be leap years only if they were
divisible by 400 as well
. So, in the last millennium, 1600 and
2000 were leap years, but 1700, 1800 and 1900 were not. In this
millennium, 2100, 2200, 2300 and 2500 will not be leap years, but
2400 will be. This theory was expanded upon by Christopher Clavius
in a closely argued,
800 page volume. He would later defend his and Lilius's work
The 19-year cycle used for the lunar calendar was also to be
corrected by one day every 300 or 400 years (8 times in 2500 years)
along with corrections for the years (1700, 1800, 1900, 2100 et
cetera) that are no longer leap years. In fact, a new method for
computing the date of Easter was introduced.
In 1577 a Compendium
was sent to expert mathematicians
outside the reform commission for comments. Some of these experts,
and Giuseppe Moleto, believed Easter should be
computed from the true motions of the sun and moon, rather than
using a tabular method, but these recommendations were not
Gregory dropped 10 days to bring the calendar back into
synchronization with the seasons. Lilius originally proposed that
the 10-day correction should be implemented by deleting the Julian
leap day on each of its ten occurrences during a period of 40
years, thereby providing for a gradual return of the equinox to 21
March. However, Clavius's opinion was that the correction should
take place in one move and it was this advice which prevailed with
Gregory. Accordingly, when the new calendar was put in use, the
error accumulated in the 13 centuries since the Council of Nicaea
was corrected by a deletion of ten days. The last day of the Julian
calendar was Thursday, 4 October 1582 and this was followed by the
first day of the Gregorian calendar, Friday, 15 October 1582 (the
cycle of weekdays was not affected).
Gregory's reform was enacted in the most solemn of forms available
to the Church, in fact the bull had no
authority beyond the Catholic Church and the Papal States.
The changes which he was proposing were
changes to the civil calendar
which he had no authority. The changes required adoption by the
civil authorities in each country to have legal effect.
The Nicene Council
sought to devise rules whereby all Christians would celebrate
on the same day. In fact it took a
very long time before Christians achieved that objective (see
for the issues which arose). However,
the bull Inter
became the law of the Catholic Church
. It was not recognised,
however, by Protestant Churches
Consequently, the days on which Easter and related holidays were
celebrated by different Christian Churches again diverged.
Adoption in Europe
Only four Catholic countries adopted the new calendar on the date
specified by the bull. Other Catholic countries experienced some
delay before adopting the reform; and non-Catholic countries, not
being subject to the decrees of the Pope, initially rejected or
simply ignored the reform altogether, although they all eventually
adopted it. Hence, the dates 5 October 1582 to 14 October 1582
(inclusive) are valid dates in many countries.
Spain, Portugal, the
Commonwealth, and most of Italy implemented
the new calendar on Friday, 15 October 1582, following Julian
Thursday, 4 October 1582.
The Spanish and Portuguese
colonies adopted the calendar later because of the slowness of
communication. France adopted the
new calendar on Monday, 20 December 1582, following Sunday, 9
provinces of Brabant, Zeeland and the Staten-Generaal also adopted
it on 25 December of that year, the provinces forming the Southern
Netherlands (modern Belgium) on 1 January 1583, and the province of
Holland followed suit on 12 January 1583.
Many Protestant countries initially objected to adopting a Catholic
invention; some Protestants
new calendar was part of a plot to return them to the Catholic
fold. In the Czech lands
Protestants resisted the calendar imposed by the Habsburg Monarchy
. In parts of Ireland, Catholic
rebels until their defeat in the Nine Years' War kept the "new"
Easter in defiance of the English-loyal authorities; later,
Catholics practising in secret petitioned the Propaganda Fide for dispensation from observing
the new calendar, as it signalled their disloyalty.
Denmark, which then
included Norway and some
Protestant states of Germany, adopted the
solar portion of the new calendar on Monday, 1 March 1700,
following Sunday, 18 February 1700, because of the influence of
Ole Rømer, but did not adopt the
decided to calculate the date of Easter astronomically using the
instant of the vernal equinox and the full moon according to
's Rudolphine Tables
of 1627. They
finally adopted the lunar portion of the Gregorian calendar in
1776. The remaining provinces of the Dutch Republic
also adopted the Gregorian
calendar in July 1700 (Gelderland), December 1700 (Utrecht and
Overijssel) and January 1701 (Friesland and Groningen).
relationship with the Gregorian Calendar was a difficult
Sweden started to make the change from the Julian
calendar and towards the Gregorian calendar in 1700, but it was
decided to make the (then 11-day) adjustment gradually, by
excluding the leap days (29 February) from each of 11 successive
leap years, 1700 to 1740. In the meantime, the Swedish calendar
would be out of step with both the Julian calendar and
Gregorian calendar for 40 years; also, the difference would not be
constant but would change every 4 years. This strange system
clearly had great potential for endless confusion when working out
the dates of Swedish events in this 40-year period. To make matters
worse, the system was poorly administered and the leap days that
should have been excluded from 1704 and 1708 were not excluded. The
Swedish calendar (according to the transition plan) should now have
been 8 days behind the Gregorian, but was still in fact 10 days
behind. King Charles XII
recognised that the gradual change to the new system was not
working, and he abandoned it.
However, rather than proceeding directly to the Gregorian calendar,
it was decided to revert to the Julian calendar. This was achieved
by introducing the unique date 30
in the year 1712, adjusting the discrepancy in the
calendars from 10 back to 11 days. Sweden finally adopted the
Gregorian calendar in 1753, when Wednesday, 17 February was
followed by Thursday, 1 March. Since Finland was under
Swedish rule at that time, it did the same.
Britain and the British
Empire (including the eastern part of what is now the United States) adopted the Gregorian calendar in 1752 by which
time it was necessary to correct by 11 days.
September 1752 was followed by Thursday, 14 September 1752 to
account for 29 February 1700 (Julian). Claims that rioters demanded
"Give us our eleven days"
grew out of a misinterpretation of a
painting by William Hogarth
1753, the British tax year in Britain continued to operate on the
Julian calendar and began on 5 April, which was the "Old
" new tax year of 25 March. A 12th skipped Julian leap day
in 1800 changed its start to 6 April. It was not changed
when a 13th Julian leap day was skipped in 1900, so the tax year in
Kingdom still begins on 6 April.
Alaska, the change
took place when Friday, 6 October 1867 was followed again by
Friday, 18 October after the US purchase of Alaska from Russia,
which was still on the Julian calendar. Instead of 12 days,
only 11 were skipped, and the day of the week was repeated on
successive days, because the International Date Line was shifted from Alaska's eastern to western
boundary along with the change to the Gregorian
Gregorian calendar was accepted after the October Revolution (so named because it
took place in October 1917 in the Julian calendar).
January 1918 the Council of People's
issued a Decree
Wednesday, 31 January 1918 was to be followed by Thursday, 14
country of Eastern Orthodox Europe to adopt the Gregorian calendar
was Greece on Thursday,
1 March 1923, following Wednesday, 15 February 1923.
Adoption in Eastern Asia
Japan, the first
eastern Asia country adopting the western calendar, replaced its
traditional lunisolar calendar with the Gregorian calendar on 1
January 1873, and changed its traditional month names into numbered
months, but continued to use Gengo, reign
names, instead of the Common Era or
Anno Domini system: Meiji
1=1868, Taisho 1=1912, Showa 1=1926,
Heisei 1=1989, and so on.
The "Western calendar"
) using western year numbers, is also widely
accepted by civilians and to a lesser extent by government
China (ROC) formally adopted the Gregorian calendar at
its founding on 1 January 1912, but China soon descended into a
period of warlordism with different
warlords using different calendars.
With the unification
of China under the
in October 1928, the Nationalist Government
effective 1 January 1929 the Gregorian calendar would be used.
China retained the Chinese traditions of numbering the months and a
modified Era System, backdating the first
year of the ROC to 1912; this system is still in use in Taiwan where this
ROC government retains control. Upon its foundation
in 1949, the People's Republic of China continued to use the Gregorian calendar with
numbered months, but abolished the ROC Era System and adopted
Western numbered years.
In 1645, the director of the Bureau of Astronomy and Meteorology
Kim Yuk (1580-1658) "successfully urged the throne to adopt the
Western methods of calendrical science. As a result, "Korea began
calculating its calendar with those new techniques in 1653." Korea
continued to primarily utilize the lunisolar Korean calendar
that was based on the
lunisolar Chinese calendar
Adoption by Orthodox Churches
Despite all the civil adoptions, none of the national Orthodox
Churches have recognized it for church or religious purposes.
Instead, a Revised Julian
was proposed in May 1923 which dropped 13 days in 1923
and adopted a different leap year rule. There will be no difference
between the two calendars until 2800. The Orthodox churches
of Constantinople, Alexandria, Antioch, Greece, Cyprus, Romania, and Bulgaria adopted the Revised
Julian calendar, so until 2800 these New calendarists would celebrate Christmas on 25 December in the Gregorian
calendar, the same day as the Western churches.
The Orthodox churches of Jerusalem
, the Republic of Macedonia
and the Greek Old Calendarists
did not accept
the Revised Julian calendar, and continue to celebrate Christmas on
25 December in the Julian calendar, which is 7 January in the
Gregorian calendar until 2100. The refusal to accept the Gregorian
reforms also has an impact on the date of Easter
. This is because the date of Easter is
determined with reference to 21 March as the functional equinox,
which continues to apply in the Julian calendar, even though the
civil calendar in the native countries now use the Gregorian
All of the other Eastern churches, the Oriental Orthodox
and the Armenian Apostolic Church
continue to use their own calendars, which usually result in fixed
dates being celebrated in accordance with the Julian calendar but
the Assyrian Church
the Gregorian Calendar as enacted by Mar Dinkha, causing a schism;
the Ancient Assyrian Church of the East continues to use the Julian
All Eastern churches continue to use the Julian Easter with the
sole exception of the Finnish
, which has adopted the Gregorian Easter.
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from:1582 till:1582 text:"1582~France, Netherlands (Brabant, Zeeland and the Staten-Generaal), Savoy, Luxembourg"
from:1583 till:1583 text:"1583~Austria, Netherlands (Holland and modern Belgium), Catholic Switzerland and Germany"
from:1587 till:1587 text:"1587~Hungary"
from:1605 till:1710 text:"1605-1710~Nova Scotia" color:bleuclair anchor:from
from:1610 till:1610 text:"1610~Prussia"
from:1582 till:1735 text:"1582-1735~Duchy of Lorraine" color:bleuclair anchor:from
from:1648 till:1648 text:"1648~Alsace"
from:1682 till:1682 text:"1682~Strasbourg"
from:1700 till:1701 text:"1700~Protestant Germany, Netherlands (the northern provinces), Switzerland;~Denmark (incl. Norway and Iceland)" shift:(2,5)
from:1753 till:1753 text:"1753~Sweden (incl. Finland)"
#To start again the indentation in top
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#To start again the indentation in top
from:1811 till:1811 text:"1811~Swiss canton of Grisons"
from:1867 till:1867 text:"1867~Alaska (Russia -> USA)"
from:1873 till:1873 text:"1873~Japan"
from:1875 till:1875 text:"1875~Egypt"
from:1896 till:1896 text:"1896~Korea"
from:1912 till:1912 text:"1912~Albania"
from:1915 till:1915 text:"1915~Latvia, Lithuania"
from:1916 till:1916 text:"1916~Bulgaria"
from:1918 till:1918 text:"1918~Russia, Estonia"
from:1919 till:1919 text:"1919~Romania, Yugoslavia
from:1922 till:1922 text:"1922~USSR"
from:1923 till:1923 text:"1923~Greece"
from:1926 till:1926 text:"1926~Turkey"
#To start again the indentation in top
from:1912 till:1912 text:"1912 & 1929~China" shift:(2,5)
Difference between Gregorian and Julian calendar dates
Since the introduction of the Gregorian calendar, the difference
between Gregorian and Julian calendar dates has increased by three
days every four centuries:
|From 15 October 1582
to 28 February 1700
|From 5 October 1582
to 18 February 1700
|From 12 March 1700
to 28 February 1800
|From 1 March 1700
to 17 February 1800
|From 13 March 1800
to 28 February 1900
|From 1 March 1800
to 16 February 1900
|From 14 March 1900
to 28 February 2100
|From 1 March 1900
to 15 February 2100
|From 15 March 2100
to 28 February 2200
|From 1 March 2100
to 14 February 2200
Note that the difference is not well defined when it spans the end
of a February that has a different number of days in the two
calendars. Therefore such dates are excluded from the table.
Beginning of the year
The ancient Roman calendar
its year on 1 March. The year used in dates during the Roman Republic
and the Roman Empire
was the consular year, which began
on the day when consuls first entered office — probably 1 May
before 222 BC, 15 March from 222 BC and 1 January from 153 BC. In
45 BC, Julius Caesar
, which continued to
use 1 January as the first day of the new year. Even though the
year used for dates changed, the civil year always displayed its
months in the order January through December from the Roman
Republican period until the present.
the Middle Ages, under the influence of
the Christian Church, many Western European countries moved the
start of the year to one of several important Christian festivals —
25 December (the Nativity of
Jesus), 25 March (Annunciation), or
Easter (France), while the
Byzantine Empire began its year on
1 September and Russia did so on 1
March until 1492 when the year was moved to 1
In common usage, 1 January was regarded as New Year's Day and
celebrated as such, but from the 12th century until 1751 the
year in England began on 25 March (Lady Day
).Nørby, Toke. The
Perpetual Calendar: What about England
Version 29 February 2000
So, for example, the Parliamentary record records the execution of
(as the year did not end until 24 March),
although modern histories adjust the start of the year to 1 January
and record the execution as occurring in
Most Western European countries changed the start of the year to 1
January before they adopted the Gregorian calendar. For example,
Scotland changed the start of the Scottish New Year to 1 January in
1600 (this means that 1599 was a short year). England, Ireland and
the British colonies changed the start of the year to 1 January in
1752 (so 1751 was a short year with only 282 days). Later that year
in September the Gregorian calendar was introduced throughout
Britain and the British colonies (see the section Adoption
). These two reforms were implemented by
the Calendar Act
In some countries, an official decree or law specified that the
start of the year should be 1 January. For such countries we can
identify a specific year when a 1 January-year became the norm. But
in other countries the customs varied, and the start of the year
moved back and forth as fashion and influence from other countries
dictated various customs.
Neither the papal bull nor its attached canons explicitly fix such
a date, though it is implied by two tables of saint
's days, one labeled 1582 which ends on 31
December, and another for any full year that begins on 1 January.
It also specifies its epact
relative to 1
January, in contrast with the Julian calendar, which specified it
relative to 22 March. These would have been the inevitable result
of the above shift in the beginning of the Julian year.
During the period between 1582, when the first countries adopted
the Gregorian calendar, and 1923, when the last European country
adopted it, it was often necessary to indicate the date of some
event in both the Julian calendar and in the Gregorian calendar,
for example, "10/21 February 1750/51", where the dual year
accounts for some countries already beginning their numbered year
on 1 January while others were still using some other date. Even
before 1582, the year sometimes had to be double dated because of
the different beginnings of the year in various countries. Woolley,
writing in his biography of John Dee
(1527–1608/9), notes that
immediately after 1582 English letter writers "customarily" used
"two dates" on their letters, one OS and one NS.
Old Style and New Style dates
"Old Style" (OS) and "New Style" (NS) are sometimes added to dates
to identify which system is used in the British Empire
and other countries that did
not immediately change. Because the Calendar Act of 1750
altered the start
of the year, and also aligned the British calendar with the
Gregorian calendar, there is some confusion as to what these terms
mean. They can indicate that the start of the Julian year
has been adjusted to
start on 1 January (NS) even though contemporary documents use a
different start of year (OS); or to indicate that a date conforms
to the Julian calendar (OS), formerly in use in many countries,
rather than the Gregorian calendar (NS). Death warrant of Charles I
web page of the
. A demonstration of New Style meaning Julian
calendar with a start of year adjustment. The October (November) Revolution
encyclopaedia, A demonstration of New Style meaning the Gregorian
Use of dates from historical documents
There was a great deal of confusion when the calendar changed, and
the confusion continues today. In some cases, historians did not
differentiate between the years, forcing some researchers to guess
between two years when interpreting the information.
When "translating" dates from historical documents to current
documents for dates that have been incorrectly
dated by historians, both years should be entered into present-day
documents until a copy of the original primary source verifies
which year was written in the official record. Often errors have
been perpetuated from the early 19th century and still exist today.
When translating dates from historical documents to current
documents for dates that have been correctly
by historians, the standard practice is to enter the earlier year
first, and the later year second.
Proleptic Gregorian calendar
The Gregorian calendar can, for certain purposes, be extended
backwards to dates preceding its official introduction, producing
the proleptic Gregorian
. However, this proleptic calendar should be used with
For ordinary purposes, the dates of events occurring prior to 15
October 1582 are generally shown as they appeared in the Julian
calendar, with the year starting on 1 January, and no conversion to
their Gregorian equivalents. The Battle of Agincourt is universally known to have been fought on 25
October 1415 which is Saint Crispin's
Usually, the mapping of new dates onto old dates with a start of
year adjustment works well with little confusion for events which
happened before the introduction of the Gregorian Calendar. But for
the period between the first introduction of the Gregorian calendar
on 15 October 1582 and its introduction in Britain on 14 September
1752, there can be considerable confusion between events in
continental western Europe and in British domains in English
language histories. Events in continental western Europe are
usually reported in English language histories as happening under
the Gregorian calendar. For example the Battle of
Blenheim is always given as 13 August 1704.
confusion occurs when an event affects both. For example William III of England arrived at
Brixham in England on 5 November (Julian calendar), after
setting sail from the Netherlands on 11 November (Gregorian calendar).
apparently died on exactly the
same date (23 April 1616), but in fact Cervantes predeceased
Shakespeare by ten days in real time (for dating these events,
Spain used the Gregorian calendar, but Britain used the Julian
calendar). This coincidence, however, has allowed
UNESCO to make 23
April the World Book and
Astronomers avoid this ambiguity by the use of the Julian day number
For dates before the year 1, unlike the proleptic Gregorian
calendar used in the international standard ISO 8601
, the traditional proleptic Gregorian
calendar (like the Julian calendar) does not have a year 0
and instead uses the ordinal numbers 1, 2,
… both for years AD and BC. Thus the traditional timeline is 2 BC,
1 BC, AD 1, and AD 2. ISO 8601 uses astronomical year numbering
which includes a year 0 and negative numbers before it. Thus the
ISO 8601 timeline is -0001, 0000, 0001, and 0002.
Months of the year
English speakers sometimes remember the number of days in each
month by the use of the traditional mnemonic
- Thirty days hath September,
- April, June, and November.
- All the rest have thirty-one,
- Excepting February alone,
- Which hath twenty-eight days clear,
- And twenty-nine in each leap year.
For variations and alternate endings, see Thirty days hath September
A language-independent alternative used in many countries is to
hold up your two fists with the index knuckle of your left hand
against the index knuckle of your right hand. Then, starting with
January from the little knuckle of your left hand, count knuckle,
space, knuckle, space through the months. A knuckle represents a
month of 31 days, and a space represents a short month (a 28- or
29-day February or any 30-day month). The junction between the
hands is not counted, so the two index knuckles represent July and
August. This method also works by starting the sequence on the
right hand's little knuckle, and continue toward to the left. You
can also use just one hand; after counting the fourth knuckle as
July, start again counting the first knuckle as August. A similar
mnemonic can be found on a piano
: starting on the key F for January, moving up the
keyboard in semitones
, the black notes give
the short months, the white notes the long ones.
The Origins of English naming used by the Gregorian calendar:
- January: Janus (Roman god of
gates, doorways, beginnings and endings)
- February: Februus (Etruscan god of death) Februarius
(mensis) (Latin for "month of purification (rituals)" it is said to
be a Sabine word, the last month of ancient pre-450 BC Roman calendar). It is related to fever.
- March: Mars (Roman god of
- April: "Modern scholars associate the name with an ancient root
meaning 'other', i.e the second month of a year beginning in
- May: Maia Maiestas (Roman
- June: Juno (Roman goddess, wife
- July: Julius Caesar (Roman
dictator) (month was formerly named Quintilis, the fifth month of
the calendar of Romulus)
- August: Augustus (first Roman emperor)
(month was formerly named Sextilis, the sixth month of
- September: septem (Latin for seven, the seventh month of
- October: octo (Latin for eight, the eighth month of
- November: novem (Latin for nine, the ninth month of
- December: decem (Latin for ten, the tenth month of
In conjunction with the system of months there is a system of
. A physical or electronic calendar
provides conversion from a given date to the weekday
, and shows multiple dates for a given
weekday and month. Calculating the day of the
is not very simple, because of the irregularities in the
Gregorian system. When the Gregorian calendar was adopted by each
country, the weekly cycle continued uninterrupted. So, using the
original proposed adoption date, Thursday, 4 October 1582 would be
followed by Friday 15 October.
Distribution of dates by day of the week
Since the 400-year cycle of the Gregorian calendar consists of a
whole number of weeks, each cycle has a fixed distribution of
weekdays among calendar dates. It then becomes possible that this
distribution is not even.
Indeed, because there are 97 leap years in every 400 years in the
Gregorian Calendar, there are on average 13 for each starting
weekday in each cycle. This already shows that the frequency is not
the same for each weekday, which is due to the effects of the
"common" centennial years (1700, 1800, 1900, 2100, 2200
The absence of an extra day in such years causes the following leap
year (1704, 1804, 1904, 2104 etc.) to start on the same day of
the week as the leap year twelve years before
1892, 2092 etc.). Similarly, the leap year eight years after a
"common" centennial year (1708, 1808, 1908, 2108 etc.) starts on
the same day of the week as the leap year immediately prior to
the "common" centennial year
(1696, 1796, 1896, 2096 etc.).
Thus, those days of the week on which such leap years begin gain an
extra year or two in each cycle. In each cycle there are:
Note that as a cycle, this pattern is symmetric with respect to the
low Saturday value.
A leap year starting on Sunday means the next year does not start
on Monday, so more leap years starting on Sunday means fewer years
starting on Monday, etc. Thus the pattern of number of years
starting on each day is inverted and shifted by one weekday: 58,
56, 58, 57, 57, 58, 56 (symmetric with respect to the high Sunday
The number of common years starting on each day is found by
subtraction: 43, 43, 44, 43, 44, 43, 43.
The frequency of a particular date being on a particular weekday
can easily be derived from the above (for dates in March and later,
relate them to the next
See also the cycle of
The Gregorian calendar improves the approximation made by the
by skipping three
Julian leap days in every 400 years, giving an average year of
365.2425 mean solar day
approximation has an error of about one day
with respect to the mean tropical year
, but less than half
this error with respect to the vernal equinox year
of 365.24237 days.
With respect to both solstices the Gregorian Calendar gives an
average year length that is actually shorter than the true length.
By any criterion, the Gregorian calendar is substantially more
accurate than the one day in 128 years error of the Julian calendar
(average year 365.25 days).
In the 19th century, Sir John Herschel
proposed a modification to the Gregorian calendar with 969 leap
days every 4000 years, instead of 970 leap days that the Gregorian
calendar would insert over the same period. This would reduce the
average year to 365.24225 days. Herschel's proposal would make the
year 4000, and multiples thereof, common instead of leap. While
this modification has often been proposed since, it has never been
On timescales of thousands of years, the Gregorian calendar falls
behind the seasons because the slowing down of the Earth's rotation
makes each day slightly longer over time
(see tidal acceleration
) while the year maintains a
more uniform duration. Borkowski reviewed mathematical models in
the literature, and found the results generally fall between a
model by McCarthy and Babcock, and another by Stephenson and
Morrison. If so, in the year 4000, the calendar will fall behind by
at least 0.8, but less than 1.1 days. In the year 12,000 the
calendar would fall behind at least 8, but less than 12 days.
Calendar seasonal error
This image shows the difference between the Gregorian calendar and
-axis and the x
-axis is Gregorian calendar
Each point is the date and time of the June Solstice
on that particular year. The
error shifts by about a quarter of a day per year. Centurial years
are ordinary years, unless they are divisible by 400, in which case
they are leap years. This causes a correction on years 1700, 1800,
1900, 2100, 2200, and 2300.
For instance, these corrections cause 23 December 1903 to be the
latest December solstice, and 20 December 2096 to be the earliest
solstice—2.25 days of variation compared with the seasonal
Leap seconds and other aspects
Since 1972, some years may also contain one or more leap seconds
, to account for cumulative
irregularities in the Earth's rotation. So far, these have always
been positive and have occurred on average once every 18
The day of the year is somewhat inconvenient to compute, partly
because the leap day does not fall at the end of the year. But the
calendar exhibits a repeating pattern for the number of days in the
months March through July and August through December: 31, 30, 31,
30, 31, for a total of 153 days each. In fact, any five consecutive
months not containing February contain exactly 153 days.
See also common year
starting on Sunday
The 400-year cycle of the Gregorian calendar has 146,097 days and
hence exactly 20,871 weeks. So, for example, the days of the week
in Gregorian 1603 were exactly the same as for 2003. The years that
are divisible by 400 begin on a Saturday. In the 400-year cycle,
more months begin on a Sunday (and hence have Friday the 13th
) than any other day of the
week (see above under Week
for a more detailed
explanation of how this happens). 688 out of every 4800 months (or
172/1200) begin on a Sunday, while only 684 out of every 4800
months (171/1200) begin on each of Saturday and Monday, the least
A smaller cycle is 28 years (1,461 weeks), provided that there is
no dropped leap year in between. Days of the week in years may also
repeat after 6, 11, 12, 28 or 40 years. Intervals of 6 and 11 are
only possible with common years, while intervals of 28 and 40 are
only possible with leap years. An interval of 12 years only occurs
with common years when there is a dropped leap year in
The Doomsday algorithm
method by which you can discern which of the 14 calendar variations
should be used in any given year (after the Gregorian reformation).
It is based on the last day in February, referred to as the
Day of week
Common years always begin and end on the same day of the week,
since 365 is one more than a multiple of 7 (52 [number of weeks in
a year] × 7 [number of days in a week] = 364). For example, 2003
began on a Wednesday and ended on a Wednesday. Leap years end on
the next day of the week from which they begin. For example, 2004
began on a Thursday and ended on a Friday.
Not counting leap years, any calendar date will move to the next
day of the week the following year. For example, if your birthday
fell on a Tuesday in 2002, it fell on a Wednesday in 2003. Leap
years make things a little more complicated. 2004 was a leap year,
so calendar days of 1 March or later in the year, moved two days of
the week from 2003. However, calendar days occurring before 1 March
do not make the extra day of the week jump until the year following
a leap year. So, if your birthday is 15 June, then it must have
fallen on a Sunday in 2003 and a Tuesday in 2004. If, however, your
birthday is 15 February, then it must have fallen on a Saturday in
2003, a Sunday in 2004 and a Tuesday in 2005.
In any year (even a leap year), July always begins on the same day
of the week that April does. Therefore, the only difference between
a July calendar page and an April calendar page in the same year is
the extra day July has. The same relationship exists between
September and December as well as between March and November. Add
an extra day to the September page and you've got December. Take a
day away from the March page and you've got November. In common
years only, there are additional matches: October duplicates
January, and March and November duplicate February in their first
28 days. In leap years only, there is a different set of additional
matches: July is a duplicate of January while February is
duplicated in the first 29 days of August.
English names for year numbering system
The Anno Domini
(Latin for "in the year of the/our Lord")
system of numbering years, in which the leap year rules are
written, and which is generally used together with the Gregorian
calendar, is also known in English as the Common Era or Christian
Era. Years before the beginning of the era are known in English as
Before Christ, Before the Common Era, or Before the Christian Era.
The corresponding abbreviations AD, CE, BC, and BCE are used. There
is no year 0; AD 1 immediately follows 1 BC.
Naturally, since Inter gravissimas
was written in Latin,
it does not mandate any English language nomenclature. Two era
names occur within the bull, "anno Incarnationis dominicæ
("in the year of the Incarnation of the Lord") for the year it was
signed, and "anno à Nativitate Domini nostri Jesu Christi
("in the year from the Nativity of our Lord Jesus Christ") for the
year it was printed. Nevertheless, "anno Domini" and its
inflections "anni Domini" and "annus Domini" are used many times in
the canons attached to the bull.
- Blackburn, B. & Holford-Strevens, L. (1999). The Oxford
Companion to the Year. Oxford University Press ISBN
0-19-214231-3. Pages 98–99.
- Coyne, G. V., Hoskin, M. A., and Pedersen, O.(Eds.) (1983).
Gregorian reform of the calendar: Proceedings of
the Vatican conference to commemorate its 400th anniversary,
1582-1982. Vatican City: Pontifical Academy of Sciences,
- Duncan, D. E. (1999). Calendar: Humanity's Epic Struggle To Determine A True And
Accurate Year. Harper
Perennial. ISBN 0-380-79324-5.
- Gregory XIII. (2002). Inter Gravissimas (W. Spenser & R.
T. Crowley, Trans.). International
Organization for Standardization. (Original work published
- Moyer, G. (May 1982). "The Gregorian Calendar". Scientific
American", pp. 144–152.
- Lee, P.H. & de Bary, W. T. (Eds., with Yongho Ch'oe &
Kang, H.H.W.). (2000). Sources of Korean Tradition, (Vol.
2). New York: Columbia University Press, 2000.
Etymology Dictionary retrieved 23 August 2006
- Seidelmann, P. K. (Ed.). (1992). Explanatory Supplement to
the Astronomical Almanac. Sausalito, CA: University Science
- Introduction to Calendars. United States Naval
Observatory. Accessed 15 January 2009.
- Calendars by L. E. Doggett. Section 2.
- The international standard for the representation of dates and
times ISO 8601 uses
the Gregorian calendar. Section 3.2.1.
- This era was created in the year 525 by the Roman monk
Dionysius Exiguus. See Nineteen-Year Cycle of Dionysius. Introduction and
- Stating the rule this way is an anachronism, since the Anno
Domini year numbering was not invented until about 570 years after
Julius Caesar established his calendar
- Introduction to Calendars. (13 September 2007).
United States Naval
- "Lastly, in consideration of the quarter of a day, which he
regarded as completing the true year, he established the rule that,
at the end of every four years, a single day should be intercalated
where the month had been hitherto inserted, that is, immediately
after the terminalia; which day is now called the
bissextum". Censorinus:The Natal Day.
- "Julius Caesar added ten days to the former number in order to
complete the 365 days which the sun takes to pass through the
zodiac; and to take account of the quarter of a day, he directed
the pontiffs, who were entrusted with the months and days, to
intercalate one day every four years in the same month and in the
same place the ancients had intercalated, that is, before the last
five days of February, hence this day was called bissextile."
- Coyne et al. (Eds), (1993), pp. 201–224.
- O. Pedersen. (1983). "The ecclesiastical calendar and the life
of the church." in G. V. Coyne et al., ed. 42–43.
- This is 365;14,33 days in sexagesimal notation—the length of the
year, rounded to two sexagesimal positions; this was the value
used in the major astronomical tables of the day.
- Coyne et al. (Eds), 1983, p. 211, 214.
- Toke Nørby. The Perpetual Calendar: What about
- Gordon Moyer. (May 1982). "The Gregorian Calendar".
Scientific American, May 1982, p. 144.
- Nørby, Toke. The Perpetual Calendar
- Mike Spathaky Old Style and New Style Dates and the change to the
Gregorian Calendar: A summary for genealogists
- Lee & de Bary 2000, 118.
- This is still reflected in the names of some months which
derive from Latin:
- Roman Dates: Eponymous Years
- S.I. Seleschnikow: Wieviel Monde hat ein Jahr?
(Aulis-Verlag, Leipzig/Jena/Berlin 1981, p. 149), which is a German
translation of С.И. Селешников: История календаря и
хронология (Издательство «Наука», Moscow 1977). The relevant
chapter is available online here: История
календаря в России и в СССР (Calendar history in Russia and the
USSR). Anno Mundi 7000 lasted from to .
- Tuesday 31 December 1661, Pepys Diary "I sat
down to end my journell for this year, ..."
- Herluf Nielsen: Kronologi (2nd ed., Dansk Historisk
Fællesforening, Copenhagen 1967), pp.48-50.
- Le calendrier grégorien en France
- Per decree of 16 June 1575. Hermann Grotefend, " Osteranfang" (Easter beginning), Zeitrechnung de Deutschen Mittelalters und der
Neuzeit (Chronology of the German Middle Ages and modern
- Blackburn & Holford-Strevens (1999), p. 784.
- John J. Bond, Handy-book of rules and tables for verifying dates
with the Christian era Scottish decree on pp.
- Roscoe Lamont, The reform of the Julian calendar, Popular
Astronomy 28 (1920) 18–32. Decree of Peter
the Great is on pp.23–24.
- Benjamin Woolley, The Queen's Conjurer: The science and
magic of Dr. John Dee, adviser to Queen Elizabeth I (New York:
Henry Holt, 2001) p.173
- In Scotland the legal start of year had been moved to 1 January
in 1600 (Mike Spathaky. Old Style New
Style dates and the change to the Gregorian calendar); and
as Ireland was not part of the union of Great Britain so separate
legislation was needed for Ireland.
- Spathaky, Mike Old Style New Style dates and the change to the
Gregorian calendar. "increasingly parish registers, in addition
to a new year heading after 24th March showing, for example '1733',
had another heading at the end of the following December indicating
'1733/4'. This showed where the New Style 1734 started even though
the Old Style 1733 continued until 24th March. ... We as historians
have no excuse for creating ambiguity and must keep to the notation
described above in one of its forms. It is no good writing simply
20th January 1745, for a reader is left wondering whether we have
used the Old or the New Style reckoning. The date should either be
written 20th January 1745 OS (if indeed it was Old Style) or as
20th January 1745/6. The hyphen (1745-6) is best avoided as it can
be interpreted as indicating a period of time."
- Stockton, J.R. Date Miscellany I: The Old and New Styles "The terms
'Old Style' and 'New Style' are now commonly used for both the
'Start of Year' and 'Leap Year' [(Gregorian calendar)] changes
(England & Wales: both in 1752; Scotland: 1600, 1752). I
believe that, properly and historically, the 'Styles' really refer
only to the 'Start of Year' change (from March 25th to January
1st); and that the 'Leap Year' change should be described as the
change from Julian to Gregorian."
- Adriana Rosado-Bonewitz, " Whats in a word?" (pdf, 1.3MB),
Intercambios: Quarterly Newsletter of the Spanish Language
Division of the American Translators, 9(1) (March 2005) 14-15,
ISSN 1550-2945 (in Spanish)
- Anatoly Liberman, " On A
Self-Congratulatory Note, Or, All The Year Round: The Names of The
Months" (filed in Oxford Etymologist, 7 March
- L.L. Neuru, " St. Valentine's Holiday" Labyrinth
64 (1996), Department of Classical Studies,
University of Waterloo, Ontario, Canada
- B. Blackburn & L. Holford-Strevens, (2003), The Oxford
Companion to the Year: An exploration of calendar customs and
time-reckoning, Oxford University Press, p. 140.
- Seidelmann, 1992, pp. 580–581.
- John Herschel, Outlines of Astronomy, 1849, p.
- Steel, D. (1999) Marking Time. Wiley. p. 185. Excerpt
viewed 22 June 2009 at http://books.google.com.
- Borkowski, K.M., (1991) "The tropical calendar and solar year", J.
Royal Astronomical Soc. of Canada 85(3) 121-130, pp.
- Les canons of Les textes fondateurs du calendrier