This page covers the properties of various calendars used in the world.
PROPERTIES OF THE GREGORIAN CALENDAR
There are several interesting quirks in the Gregorian calendar (the calendar we use in
the United States). Here is a list of the more interesting ones:
Days of the week behave strangely. Here is a list of the first days in each month that
are on the day of the week that January 1 is on, and the number of days in each month:
||7||same day of week
||31||days in month
||May||Months with same
days of week
||6||same day of week
||31||days in month
||May||Months with same
days of week
Leap years also behave strangely in the Gregorian calendar. It leaves out
leapyear days in year numbers that are divisible by 100, but not divisible by
HISTORY OF THE GREGORIAN CALENDAR
We have a strange calendar because the history of our calendar is strange. This is
because politicians controlled much of its development. Here is an account of this
- The original Roman calendar was designed with two 30-day months and one 31-day
month in each quarter. But one quarter had to have two 31-day months to make 365
- Politicians used to move days from one month to another to lengthen their own
terms of office, and shorten the terms of their opponents. The year numbers of the
Roman calendar dated from the founding of Rome.
- March was the first month of the year. This explains the names September,
October, November, and December, which were the 7th, 8th, 9th, and 10th
- Leapyear day was the last day of the year, in February. It stayed in
February when the beginning of the year was moved to January.
- In 45 BC, Julius Caesar changed the name of Quintillus to July, in his own
honor, stole a day from February to make it a long month, and claimed that he made
summer longer and winter shorter. In doing so, he created the Julian
- Julius added a leap year every three years until spring started where it
belonged (March 1), then he changed it to occur every four years.
- Not to be outdone, Augustus Caesar changed Sextillus to August, stole another
day from February, made August a long month, and again claimed a longer summer and
a shorter winter.
- In 404 AD, The Catholic Church tried to reset the year numbers so that the
year 1 was the year Jesus Christ was born. But they missed, because they did not
understand that Octavian Caesar and Augustus Caesar were the same man. They referred
the date to the year Octavian changed his name, instead of the year he took the
throne. Jesus was born between 4 and 8 BC by today's Gregorian calendar.
- There is no year numbered 0. The year after 1 BC is 1 AD. This is because
there is no zero in the Roman numeral system. One has to be careful when
calculating times that span this dividing line, because a year must be subtracted
from the expected number of years between two dates. The importance of zero in
numeric systems was not recognized until the 17th Century AD.
- Because there is no year numbered 0, multiple year groups do not have the
- Decades begin in years with 1 as the right digit.
Decades end in years with 0 as the right digit.
- Centuries begin in years with 01 as the right digits.
Centuries end in years with 00 as the right digits.
- Millennia begin in years with 001 as the right digits.
Millennia end in years with 000 as the right digits.
- Astronomers DO include a year zero when they calculate the positions of
stars and planets. So every BC year has one added to the year number in the
astronomical calendar, compared to the reverse-extended Julian calendar we use
for BC dates. Thus, 3 BC Julian is 2 BC astronomical.
- In France, the first month of the year was April for many years. A change
decided by the Council of Trent in 1563 initiated Pope Gregory's calendar reforms.
The Catholic calendar was changed in 1564 to have January 1 be the beginning of
the year. The French calendar was changed to match the Catholic calendar, but
some people would not agree to the change. They continued to celebrate the new
year on April 1, and were called "April Fools" for doing so.
- The year did not quite fit the length of a day, and by 1582 AD, spring was
starting 10 days early. The calendar instituted by Pope Gregory fixed both the
10-day offset and the creep of spring toward a winter month. It leaves out
leapyear days in year numbers divisible by 100, but not divisible by 400. This is
the calendar in use today in the United States, and most of the western world,
although only the Catholic countries adopted it in 1582 AD. This calendar is
accurate to one day in 3323 years.
- As a result of the change, October 1582 lost 10 days, with October 4
immediately followed by October 15. This time was chosen to not leave out any
major Catholic holidays.
- Germany and the Netherlands made the change to the Gregorian calendar in
- In 1752 AD, the British Empire made the calendar change, dropping 11 days
from the month of September in that year, and adopting the Gregorian calendar.
September 2 was followed immediately by September 14. The change sparked riots
when landlords charged for a full month's rent for the shortened month.
- The American colonies made the change the same year. This changed George
- Greece made the change to the Gregorian calendar in 1923.
OTHER CALENDARS AND CALENDAR CHANGES
- From 1793 through 1805, the French Revolutionary Calendar was used in
- The year began on our September 23 (autumnal equinox), had 12 30-day
months, and 5 intercalary (between months) days at the end of the year (plus
one more intercalary day in a leap year).
- The months were named after weather or agricultural events, such as
"wine", "harvest", "frost", and "snow"
- The weeks were 10 days long, with one day of rest every 10 days. The years were
numbered 1 through 13, with 1 starting in 1792.
- People obeying the Bible quickly put an end to this calendar, by not obeying
the 10-day week.
- The Eastern Orthodox countries kept the Julian calendar until 1917 AD.
At that time, they made a change that drops 2 leapyears every 9 centuries (instead
of 1 every 4). But they did NOT remove the 12-day difference, so their calendar
is 12 days behind ours. This calendar is accurate to one day in 4200 years.
- The Soviet Union made the change to the Eastern Orthodox calendar in 1918.
- Many Eastern European countries never changed away from the Julian calendar.
- There have been two proposals to change the calendar so it repeats year after year.
- One proposal has one 31-day month followed by two 30-day months in each
quarter. The 31-day month always begins on Sunday. The last day of the year is an
intercalary day after Dec 30, but has no day of the week. Leapyear day is also an
intercalary day after Jun 30, and also has no day of the week.
- The other proposal has thirteen 28-day months, with the last day and the
leapyear day after it without a day number, a month, or a day of the week. Every
month starts on Sunday.
Christians and Jews will not accept these secular calendars, because they
interrupt the God-ordained 7 day week, so they will probably never be
- The Jewish calendar is a lunar calendar that works on alternating 29-day
and 30-day months. In every 7 of 19 years, an intercalary month is added to bring
the calendar back in step with the solar year. This calendar explains the shifting
dates of the Christian holidays Ash Wednesday, Palm Sunday, Easter, and
- The Islamic calendar is a lunar calendar that works on alternating 29-day
and 30-day months. But there are no resynchronizing intercalary months or days, so
the calendar actually rotates completely around the solar year over a period of
some thirty solar years, during which they experience one more year than we do.
So Islamic holidays occur in different parts of the Gregorian year in different
years. An Islamic holiday can occur on any Gregorian date.
CALENDAR FEATURES EXPLAINED
Here is why calendars have the features they have, and the physical reasons for
- Day - This is the smallest natural unit of time. It is one rotation of the
Earth. The mean solar day (mean time from midnight to midnight) is 24 hours, but
the sidereal (celestial) day is only 23 hours and 56 minutes. This is because the
earth has to turn farther to face the sun again, than it has to turn to face a
distant star again. This happens because the earth orbits the sun. So 366.2425
sidereal days equal 365.2425 solar days, as one rotation of the earth is canceled
out by the revolution of the earth around the sun.
- Week - there are two origins for a 7-day week:
- The command given by God to the Israelites.
- Approximately a quarter of a month, based on the number of wandering
objects seen in the sky. The ancients assigned a day to each, which is where we
get the names of our days of the week
|Day of Week||Name of god or planet
| English || Spanish
|| Norse || Roman || Greek
- Month - One lunation (a cycle of the moon phases) is about 29.5 solar days.
This is the time the Moon revolves around the Earth once relative to the Sun.
Since 12 lunations take only 354 days, 12 lunar months do not exactly make a
- The Moon revolves around the Earth 13 times in that period, but one of the
revolutions is canceled out by the Earth revolving around the Sun once a year. So
a sidereal month is only 27.5 days.
- Most solar calendars use an arbitrary month length that approximates the lunar
month. This keeps the calendar in step with the solar year.
- The Roman year began with March. The Gregorian year begins with January.
- The Roman names of the months are still used.
||Days in Month
| English || Spanish
|| Name Derivation ||Roman||Today
|March||marzo||start (was first month of year), also Mars
|June||junio||the family Junius
|July||julio||Julius Caesar (former name Quintillus)
|August||agosto||Augustus Caesar (former name Sextillus)
- Leapyear day is at the end of February because February was originally the
last month of the year. So the extra day was originally added to the end of the
- Season - The time between either solstice (point where the sun is exactly
over one of the tropic latitude lines) and either equinox (point where the sun is
exactly over the equator). It is a quarter of a tropical year.
- Year - This is the time it takes the Earth to revolve around the Sun once.
It is one cycle of the seasons. It is about 365.2425 solar days long.
- Due to precession, a tropical year (defined equinox to equinox) is slightly
shorter than a sidereal year. And a year has one more sidereal day than it has
solar days, because one rotation of the earth is canceled out by the revolution
around the sun, relative to the position of the sun.
- Astrological age - about 2200 years long. It is 1/12 of a
- Precession - The time it takes the tilt of the axis of the Earth to
precess once. This is the time it takes the location of the sun at the Vernal
Equinox to rotate once around the celestial sphere, or about 26000 years.
- Seconds, minutes, hours, fortnights, decades, centuries, and millennia
are arbitrary divisions or multiples of the natural values listed above.