Thirty days hath September, April, June and November. The uneven length of the months is not a mistake. It is the leftover of a calendar that was reformed, adjusted and patched for over two thousand years.
The ten-month calendar
According to tradition, the oldest Roman calendar had only ten months and 304 days, starting in March. This explains why September, October, November and December have names that come from the Latin words for seven, eight, nine and ten, although they are now the ninth to twelfth months. The winter after December was simply not counted.
The details of this early calendar are uncertain, because the Romans themselves wrote about it centuries later.
January and February
King Numa Pompilius is said to have added January and February to cover the winter gap, which gave a year of about 355 days. Because 355 days is ten days short of a solar year, the Romans had to insert an extra month from time to time, and the priests who controlled this had political reasons to make the year longer or shorter.
By the time of Julius Caesar, the calendar was so far out of step with the seasons that the harvest festivals no longer fell in autumn.
Julius Caesar's reform
In 46 BC Caesar, advised by the astronomer Sosigenes of Alexandria, reformed the calendar. To bring the year into line with the seasons, 46 BC was made 445 days long, which is known as the year of confusion. From 45 BC the year had 365 days, with an extra day every fourth year.
Caesar distributed the days among the months in the pattern we still use, apart from February, which kept the leftover days. January became the first month of the year.
Two months named after emperors
The fifth month, Quintilis, was renamed July in honor of Julius Caesar after his death. The sixth month, Sextilis, was renamed August for the emperor Augustus. A popular story says that August was given 31 days so as not to be shorter than July, and a day was taken from February. This story is probably a later invention, because the lengths were set already under Caesar.
The other names are older: January is named after the god Janus, March after Mars, May after the goddess Maia and June after Juno.
Gregory's correction
Caesar's year of 365.25 days was slightly too long, and by the 1500s the calendar was ten days behind the seasons. In 1582 Pope Gregory XIII removed ten days, so that October 4 was followed by October 15, and refined the leap year rule. Protestant and Orthodox countries accepted it much later.
Britain and its colonies changed in 1752, when September 2 was followed by September 14. Russia changed in 1918, after the revolution, when February 1 was followed by February 14.
The rhyme and the knuckles
To remember the months with 31 days, you can use your knuckles. Make a fist and count along the knuckles and the gaps between them. The months that fall on a knuckle have 31 days, and those that fall in a gap have 30, or 28 in the case of February. The rhyme works too: thirty days hath September, April, June and November, all the rest have thirty-one, except February alone.
Seven months have 31 days, four have 30, and one has 28 or 29.
Calendars that work differently
Other calendars are built on other principles. The Islamic calendar is purely lunar, with twelve months of 29 or 30 days and a year of about 354 days, so its holidays move through the seasons. The Jewish and Chinese calendars are lunisolar, and add a leap month to keep in step with the sun. The Persian calendar is solar and very accurate.
The Gregorian calendar is now the standard for civil use almost everywhere, even in countries that also use their traditional calendars for religious holidays.
A year in numbers
A common year has 365 days, which is 52 weeks and one day. It has twelve months, seven of which have 31 days. The longest span between two month starts is 31 days, and the shortest is 28, so the first of the month can fall on any weekday, and any month with 31 days has five of at least three different weekdays. That is why some months have five Fridays, Saturdays and Sundays, and others do not.
Could we have a better calendar?
Reformers have proposed calendars with equal months or a fixed weekday for each date, such as the International Fixed Calendar with thirteen months of 28 days. They have never been adopted, mainly because changing the weekday cycle would disturb religious practice and because the current system, however odd, works.
For the dates and day counts in any calendar year, the tools on this site take care of the arithmetic.