This page covers the properties of various calendars used in the world.


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:

Months:JanFebMarAprMay JunJulAugSepOctNovDec Next JanCase
Normal year15527 4263153 7same day of week
Normal year3128313031 30313130313031 31days in month
Normal yearOctMar
none AprnoneDec JanFeb
Sep MayMonths with same
days of week
Months:JanFebMarAprMay JunJulAugSepOctNovDec Next JanCase
Leap year15416 3152742 6same day of week
Leap year3129313031 30313130313031 31days in month
Leap yearApr
AugNov Jan
none Jan
FebDec noneMarSep MayMonths 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 400.


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 history:

  1. 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 days.
  2. 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.
  3. 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 months.
  4. 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.
  5. 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 calendar.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. Because there is no year numbered 0, multiple year groups do not have the expected boundaries:
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. Germany and the Netherlands made the change to the Gregorian calendar in 1698.
  16. 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.
  17. The American colonies made the change the same year. This changed George Washington's birthday.
  18. Greece made the change to the Gregorian calendar in 1923.


  1. From 1793 through 1805, the French Revolutionary Calendar was used in France.
  2. 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.
  3. The Soviet Union made the change to the Eastern Orthodox calendar in 1918.
  4. Many Eastern European countries never changed away from the Julian calendar.
  5. There have been two proposals to change the calendar so it repeats year after year.

    Christians and Jews will not accept these secular calendars, because they interrupt the God-ordained 7 day week, so they will probably never be adopted.

  6. 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 Pentecost.
  7. 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.


Here is why calendars have the features they have, and the physical reasons for them:

  1. 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.
  2. Week - there are two origins for a 7-day week:
  3. 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 year.
  4. 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.
  5. 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.
  6. Astrological age - about 2200 years long. It is 1/12 of a precession.
  7. 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.
  8. Seconds, minutes, hours, fortnights, decades, centuries, and millennia are arbitrary divisions or multiples of the natural values listed above.