How Calendars Work: Taming the Sun, the Moon and Time Itself

What a Calendar Really Is

A calendar is a system for organizing days by giving names and numbers to longer periods of time: weeks, months and years. Within such a system, a date points to one single, specific day, such as 14 July 1789 or 1 January 2000. The word is also used for the physical object that records the system, like a printed wall calendar or the app on a phone, and for lists of planned events, such as a school calendar or a court calendar. Historians even speak of a "calendar of wills" or a "calendar of letters", meaning a chronological list of documents.

The English word comes from the Latin kalendae, the name the Romans gave to the first day of every month. On the kalends, debts and interest were due, so a Roman account book was called a calendarium. From that bookkeeping term grew the word we now use for the whole system of counting days.

Calendars matter because almost everything in organized society depends on them: when to plant and harvest, when to celebrate religious festivals, when taxes are due, when school begins and how old a person is. Yet building a good calendar turns out to be surprisingly hard, because nature does not cooperate.

The Problem: Nature Does Not Divide Evenly

Most calendars are built on three natural cycles that anyone can observe in the sky.

• The day: one rotation of the Earth relative to the Sun, the alternation of light and darkness.
• The month: the cycle of the Moon's phases, from new moon to new moon, which lasts on average about 29.53 days. This is called the synodic month.
• The year: the cycle of the seasons. The tropical year, measured for example from one March equinox to the next, lasts about 365.2422 days.

The trouble is that none of these numbers fits neatly into the others. A year is not a whole number of days, and it is not a whole number of months either: twelve lunar months add up to only about 354 days, roughly 11 days short of a solar year. Every calendar in history is a compromise between these awkward fractions. Calendar makers have had to decide which cycle matters most to them and how to correct the errors that pile up over time.

Three basic types

Depending on which cycle they follow, calendars fall into three main families.

• Solar calendars keep in step with the seasons and ignore the Moon. The Gregorian calendar used worldwide today is solar.
• Lunar calendars follow the phases of the Moon and ignore the seasons. The Islamic calendar is the best-known example.
• Lunisolar calendars try to follow both, using lunar months but adding an extra month from time to time so that the year stays aligned with the seasons. The Hebrew and traditional Chinese calendars work this way.

The First Calendars: Watching the Sky

Long before writing, people tracked time by watching the Sun, the Moon and the stars. Many prehistoric monuments are aligned with key moments of the solar year. At Stonehenge in England, the main axis lines up with sunrise at the summer solstice and sunset at the winter solstice, which suggests that its builders paid close attention to the turning points of the year.

Egypt and the star that announced the flood

Ancient Egypt developed one of the earliest known civil calendars. It had 12 months of 30 days each, grouped into three seasons of four months named after the life of the Nile: Akhet (inundation), Peret (growing) and Shemu (harvest). Five extra days were added at the end of the year, giving a total of 365. The Egyptians also noticed that the annual flood of the Nile came around the time when the bright star Sirius first reappeared in the dawn sky after a period of invisibility.

Because the Egyptian year had exactly 365 days, with no leap day, it slipped against the true solar year by about one day every four years. Over centuries, the months wandered slowly through all the seasons.

Mesopotamia and the 19-year cycle

In Mesopotamia, the Babylonians used a lunisolar calendar in which each month began with the first sighting of the thin crescent Moon after sunset. To keep the months in line with the seasons, they inserted a thirteenth month when needed. Over time, Babylonian astronomers settled on a regular pattern of seven extra months in every 19 years. The same relationship was described in Greece by Meton of Athens in the 5th century BC and is known as the Metonic cycle: 19 solar years contain almost exactly 235 lunar months. This clever coincidence still underlies the Hebrew calendar and the method for calculating the date of Easter.

From Rome to the Whole World

The calendar most people use today has its roots in ancient Rome, and its history explains many of its odd features.

The early Roman calendar

According to Roman tradition, the earliest Roman calendar had only ten months, starting in March and ending in December, with the winter period left uncounted. January and February were added later. This is why September, October, November and December are named after the Latin words for seven, eight, nine and ten, even though they are now the ninth to twelfth months. Roman months were divided not by weeks but by three fixed points: the Kalends (the first day), the Nones and the Ides, which fell in the middle of the month. The Ides of March, the 15th, became famous as the day Julius Caesar was assassinated in 44 BC.

The pre-Julian Roman year had only 355 days, and officials were supposed to insert an extra month from time to time. Because this was often done irregularly, sometimes for political reasons, the calendar drifted badly out of step with the seasons.

Julius Caesar's reform

Julius Caesar fixed the problem with the help of the Alexandrian astronomer Sosigenes. His new Julian calendar took effect in 45 BC. It had 365 days, with one extra day added every fourth year, giving an average year of 365.25 days. To bring the calendar back in line with the seasons, the year 46 BC was stretched to 445 days, and it is sometimes called the "year of confusion". Later, the month Quintilis was renamed July in Caesar's honour, and Sextilis became August after the emperor Augustus.

Pope Gregory XIII and the missing ten days

The Julian year was very close to the real solar year, but not exact. It was about 11 minutes too long, an error that adds up to roughly one day every 128 years. By the 16th century, the spring equinox was arriving about ten days earlier on the calendar than it had at the time of the Council of Nicaea in 325, which mattered greatly to the Church because the date of Easter depends on the equinox.

In 1582, Pope Gregory XIII issued the papal bull Inter gravissimas, introducing what we now call the Gregorian calendar. The plan was based mainly on the work of the Italian physician Aloysius Lilius and was promoted by the Jesuit astronomer Christopher Clavius. Two changes were made:

1. Ten days were removed at once. In the countries that adopted the reform first, Thursday 4 October 1582 was followed directly by Friday 15 October 1582.
2. The leap-year rule was refined. A year divisible by 4 is still a leap year, except for century years, which are leap years only if divisible by 400. So 1600 and 2000 were leap years, but 1700, 1800 and 1900 were not.

This gives an average year of 365.2425 days, so close to the tropical year that the error amounts to only about one day in more than 3,000 years.

A slow adoption

Spain, Portugal, Poland-Lithuania and the Italian states switched in 1582, but many Protestant and Orthodox countries were suspicious of a reform coming from Rome. Great Britain and its colonies changed only in 1752, by which time 11 days had to be dropped: Wednesday 2 September was followed by Thursday 14 September. Russia adopted the Gregorian calendar in 1918, which is why the October Revolution of 1917 is commemorated in November. Greece switched in 1923.

Several Orthodox churches, including the Georgian, Russian and Serbian churches, still use the Julian calendar for their religious feasts. Because the two calendars are now 13 days apart, their Christmas, 25 December in the Julian calendar, falls on 7 January in the Gregorian calendar. In 2023 the Orthodox Church of Ukraine moved its fixed feasts to the new style, and Ukraine's official Christmas holiday moved to 25 December.

Calendars That Follow the Moon

Not every culture chose to keep pace with the seasons. For many, the Moon was the more natural clock, because its phases are easy to see and a new month can be recognized by anyone with a clear view of the sky.

The Islamic calendar

The Islamic, or Hijri, calendar is purely lunar. It has 12 months of 29 or 30 days, making a year of 354 or 355 days. Its years are counted from the Hijra, the migration of the Prophet Muhammad from Mecca to Medina in 622 CE. Because the Islamic year is about 11 days shorter than the solar year, its months move steadily through the seasons. The fasting month of Ramadan, for example, can fall in summer or in winter, and it takes about 33 years to travel all the way around the solar year.

The Hebrew calendar

The Hebrew calendar is lunisolar. Its months follow the Moon, but seven times in every 19-year cycle a thirteenth month is added so that festivals such as Passover always fall in spring. Years are counted from the traditional date of the creation of the world: the Jewish New Year, Rosh Hashanah, in September 2026 began the year 5787.

The Chinese calendar

The traditional Chinese calendar is also lunisolar, with leap months inserted according to astronomical rules. It divides the solar year into 24 solar terms that once guided farmers' work. Chinese New Year always falls between 21 January and 20 February. Years are named in a 60-year cycle that combines ten Heavenly Stems with twelve Earthly Branches, and the twelve branches are linked to the famous animals of the Chinese zodiac, from the Rat to the Pig.

Weeks, Eras and Other Inventions

Why seven days?

Unlike the day, month and year, the week is not tied to any astronomical cycle. The seven-day week has roots in ancient Mesopotamia and in Jewish tradition, with its weekly Sabbath. In the Roman world, the seven days became linked to the seven "planets" visible to the naked eye: the Sun, the Moon, Mars, Mercury, Jupiter, Venus and Saturn. In 321 the emperor Constantine made Sunday an official day of rest. These planetary names survive in many languages. In English, Sunday, Monday and Saturday honour the Sun, Moon and Saturn, while Tuesday, Wednesday, Thursday and Friday are named after the Germanic gods Tiw, Woden, Thor and Frigg.

Some governments tried to abolish the seven-day week. Revolutionary France introduced a calendar with 12 months of 30 days, each divided into three ten-day "decades", plus five or six extra days at the end of the year. The months received poetic names linked to nature, such as Brumaire (the month of mist) and Thermidor (the month of heat). It was used from 1793 until Napoleon abolished it at the start of 1806. The Soviet Union also experimented with five-day and six-day weeks between 1929 and 1940 before returning to seven.

Counting the years

A calendar also needs a starting point, or epoch, from which years are counted. The Romans sometimes counted from the legendary founding of their city; the ancient Greeks used Olympiads, four-year periods between Olympic Games. The system of counting years Anno Domini, "in the year of the Lord", was devised by the monk Dionysius Exiguus in the 6th century and spread widely thanks to the English historian Bede. It has a curious gap: there is no year zero. The year 1 BC is followed directly by AD 1, which is why, strictly speaking, the 21st century began on 1 January 2001. Astronomers avoid the problem by using a year 0 in their calculations. Today many people use the neutral terms BCE and CE, which count the years in exactly the same way.

Remarkable Calendars Around the World

• The Maya calendars: The Maya of Mesoamerica ran several cycles at once. The Tzolk'in had 260 days, and the Haab' had 365 days, made of 18 months of 20 days plus 5 extra days. The two cycles came back to the same combination only every 52 years, a period known as the Calendar Round. For longer spans they used the Long Count, and the completion of one of its great cycles on 21 December 2012 inspired many myths about the end of the world, though for the Maya it simply marked the turn of a new period.
• The Ethiopian calendar: It has 13 months: twelve of 30 days and a short thirteenth month of five or six days. Its year count runs about seven to eight years behind the Gregorian one.
• The Iranian calendar: The Solar Hijri calendar used in Iran and Afghanistan begins its year at Nowruz, at the moment of the March equinox, which is determined by astronomical observation. This makes it one of the most accurate solar calendars in use.

Calendars in the Modern World

Today the Gregorian calendar is the international standard for business, science, travel and communication, even in countries that also keep a traditional calendar for religious or cultural purposes. To avoid confusion between formats such as 03/04 (which can mean 3 April or 4 March depending on the country), the international standard ISO 8601 writes dates from the largest unit to the smallest, as in 2026-10-30, and counts Monday as the first day of the week.

The Gregorian calendar is still not perfect. Months have unequal lengths, from 28 to 31 days, and a given date falls on a different weekday every year. Over the past two centuries, reformers have proposed alternatives such as the International Fixed Calendar, with 13 months of exactly 28 days, and the World Calendar, in which every year would begin on the same weekday. None has been adopted, mainly because changing a system that the whole world relies on would be enormously difficult.

There is also a small, lasting curiosity: people born on 29 February have a real birthday on the calendar only once every four years. Their unusual birthdays are a reminder that even our most familiar way of measuring time is a human invention, a clever and ancient compromise between the day, the Moon and the Sun.