Calendar reform

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Calendar reform or calendrical reform is any significant revision of a calendar system. The term sometimes is used instead for a proposal to switch to a different calendar design.



The prime objective of a calendar is to unambiguously identify any day in past, present and future by a specific date in order to record or organize social, religious, commercial or administrative events. Recurring periods that contain multiple days, like weeks, months and even years, are secondary, convenient features of a calendar. Most cultures adopt a primary dating system, but different cultures have always needed to align multiple calendars with each other, because they coexisted in the same space (e.g. secular and religious groups with different demands) or had established trading relations.

Once specified, a calendar design cannot be altered without becoming a new design. If a proposed design is sufficiently close to the legacy one, i.e. compatible with it, a reform of the local calendar system is possible without disruption. Examples of this include the changes to the Chinese calendar due to problems between regions in China and practical changes in religious calendars such as the Islamic calendar where the start of the month is now derived from astronomical data rather than sightings by religious leaders. [1]

Some design changes, however, will yield date identifiers different from the previous design for some days, often in the distant past or future. The calendar system must clarify whether dates are changed to the new design retroactively (using a proleptic calendar) or whether the design in use then and there shall be respected. Calendar schisms happen if not all cultures that adopted a common calendar system before perform a calendar reform at the same time. If date identifiers are similar but different, confusion and mistakes are unavoidable.

Most calendars have several rules which could be altered by reform:

Historical reforms

Historically, most calendar reforms have been made in order to synchronize the calendar with the astronomical year (either solar or sidereal) and/or the synodic month in lunar or lunisolar calendars. Most reforms for calendars have been to make them more accurate. This has happened to various lunar and lunisolar calendars, and also the Julian calendar when it was altered to the Gregorian calendar.

The fundamental problems of the calendar are that the astronomical year has neither a whole number of days nor a whole number of lunar months; neither does the lunar month have a whole number of days: in each case there are fractions "left over". (In some physical circumstances the rotations and revolutions of a planet and its satellite(s) can be phase-locked —for example the same side of the moon always faces us— but this has not operated to lock together the lengths of the Earth's year, day and month.) Such remainders could accumulate from one period to the next, thereby driving the cycles out of synchronization.

A typical solution to force synchronization is intercalation. This means occasionally adding an extra day (or month) into the cycle. An alternative approach is to ignore the mismatch and simply let the cycles continue to drift apart. The general approaches include:

An obvious disadvantage of the lunisolar method of inserting a whole extra month is the large irregularity of the length of the year from one to the next. The simplicity of a lunar calendar has always been outweighed by its inability to track the seasons, and a solar calendar is used in conjunction to remedy this defect. Identifying the lunar cycle month requires straightforward observation of the Moon on a clear night. However, identifying seasonal cycles requires much more methodical observation of stars or a device to track solar day-to-day progression, such as that established at places like Stonehenge. After centuries of empirical observations, the theoretical aspects of calendar construction could become more refined, enabling predictions that identified the need for reform.

Reform of lunar and lunisolar calendars

There have been 50 to 100 reforms of the traditional Chinese calendar over 2500 years, most of which were intended to better fit the calendar months to astronomical lunations and to more accurately add the extra month so that the regular months maintain their proper seasonal positions, even though each seasonal marker can occur anywhere within its month. There have been at least four similar reforms of the lunisolar version of the Hindu calendar, all intended to make the month a better match to the lunation and to make the year a better fit to the sidereal year. There have been reforms of the solar version of the Hindu calendar which changed the distribution of the days in each month to better match the length of time that the Sun spends in each sidereal zodiacal sign. The same applies to the Buddhist calendar. The first millennium reform of the Hebrew calendar changed it from an observational calendar into a calculated calendar. The Islamic calendar was a reform of the preceding lunisolar calendar which completely divorced it from the solar year.

Another reform was performed in Seljuk Persia by Omar Khayyam and others, developing the precisely computed Jalali calendar.

Julian and Gregorian reforms

William Hogarth's An Election Entertainment includes a banner with the protest slogan against the Gregorian calendar: "Give us our Eleven days" (on floor at lower right) William Hogarth 028.jpg
William Hogarth’s An Election Entertainment includes a banner with the protest slogan against the Gregorian calendar: "Give us our Eleven days" (on floor at lower right)

When Julius Caesar took power in Rome, the Roman calendar had ceased to reflect the year accurately. [2]

The Julian reform made 46 BC 445 days long and replaced the intercalary month with an intercalary day to be inserted within February every four years. This produced a noticeably more accurate calendar, but it had an average year length of 365 days and 6 hours (365.25 d). This had the effect of adding about three-quarters of an hour every four years. The effect accumulated from inception in 45 BC until by the 16th century the northward equinox was falling on March 10 or 11.

Under Pope Gregory XIII, the leap year rule was altered: century years which are not divisible by 400 would be common years. The years 2000 and 2400 are leap years, but not 1700, 1800, 1900, 2100, 2200, 2300 and 3000. This rule makes the mean year 365.2425 days (365 d, 5 h, 49 min, 12 s) long. While this does not synchronize the years entirely, it would require a few thousand years to accumulate a day. [3]

So that the northward equinox would have the same date in the new Gregorian calendar as it had when the Council of Nicaea made recommendations in AD 325 (March 21), ten days were dropped so that October 5 became October 15 in 1582.

Julian to Gregorian Date Change Julian to Gregorian Date Change.png
Julian to Gregorian Date Change

This reform took a few centuries to spread through the nations that used the Julian calendar, although the Russian church year still uses the Julian calendar. Those nations that adopted this calendar on or after 1700 had to drop more than ten days: Great Britain, for instance, dropped 11. [4]

In 1923, Milutin Milanković proposed to a synod of some Eastern Orthodox Churches at Constantinople that only those centennial years (those ending in 00) that leave a remainder of 200 or 600 upon division by 900 would be leap years, decreasing the average year length to 365.242 days. These remainders were chosen to delay as much as possible the first year (after 1923) that this calendar would disagree with the Gregorian calendar, until 2800. It was adopted by some Eastern Orthodox Churches under the names Revised Julian calendar or New calendar, but was rejected by others.


The Gregorian calendar is currently used by most of the world. There is also an international standard describing the calendar, ISO 8601, with some differences from traditional conceptions in many cultures.

Since the papal reform in 1582, several proposals have been offered to make the Gregorian calendar more useful or regular. Very few reforms have gained official acceptance. The rather different decimal French Republican Calendar was one such official reform, but was abolished twelve years later by Napoleon. After World War II, the newly formed United Nations continued efforts of its predecessor, the League of Nations, to establish the proposed World Calendar but postponed the issue after a veto from the government of the United States, which was mainly based upon concerns of religious groups about the proposed days that would be outside the seven-day week cycle ("blank days") and thus disrupt having a sabbath every seven days. Independently the World Council of Churches still tries to find a common rule for the date of Easter, [5] which might be eased by a new common calendar.

Reformers cite several problems with the Gregorian calendar:

It is hard or even impossible to solve all these issues in just one calendar.

Most plans evolve around the solar year of a little more than 365 days. This number does not divide well by seven or twelve, which are the traditional numbers of days per week and months per year respectively. The nearby numbers 360, 364 and 366 are divisible in better ways. There are also lunar-centric proposals.

Perennial calendars

Many calendar reforms have offered solutions to make the Gregorian calendar perennial. These reforms would make it easy to work out the day of the week of a particular date, and would make changing calendars each year unnecessary. There are, roughly speaking, two options to achieve this goal: leap week calendars and intercalary days. Leap week calendars add a leap week of seven days to the calendar every five or six years to keep the calendar roughly in step with the tropical year. They have years of either 364 days (52 weeks) or 371 days (53 weeks), thus preserving the 7-day week.

Proposals mainly differ in their selection of a leap rule, placing of the leap item (usually middle or end of the year), in the start day of the week and year, in the number (12 or 13) and size of months and in connected naming; some are compatible to the week date of ISO 8601.

The World Calendar, favored by the UN in the 1950s, and the International Fixed Calendar, quite popular among economists between the World Wars, are proposals that start each year on a Sunday. The 364 days within the week system form 52 weeks of 7 days. The World Calendar has every quarter beginning on the same day of the week. In the World Calendar, the 365th and 366th day are considered holidays and named Worlds Day and Leap Year Day. These "off-calendar" days stand outside the seven-day week and caused some religious groups to strongly oppose adoption of the World Calendar. Such concerns helped prevent the World Calendar from being adopted. Supporters of the World Calendar, however, argue that the religious groups' opposition overlooked every individual's right to celebrate these holidays as extra days of worship, or Sabbaths. This option, they reason, maintained the seven-day worship cycle for those who share that concern, while allowing benefits of a perennial calendar to be shared by all.

Some calendar reform ideas, such as the Pax Calendar, Symmetry454 calendar and the Hanke-Henry Permanent Calendar, were created to solve this problem by having years of either 364 days (52 weeks) or 371 days (53 weeks), thus preserving the 7-day week. The 53-week calendar, used in government and in business for fiscal years, is a variant of this concept. Each year of this calendar can be up to 371 days long.

Some calendars have quarters of regularly patterned uneven months e.g., a 35-day (five-week) month and a pair of 28-day (four-week) months, with a leap week appended to the final month when needed. The Common Civil Calendar and Time calendar has months of 30 and 31 days, but inserts a leap week in the middle of the year, when needed, whereas its successor, the Hanke-Henry Permanent Calendar, moves the extra week to the end of the year.

In the World Season Calendar, months are discarded altogether; instead, the year is divided into four seasons of 13 weeks each. An extra day (two days during leap year) is added to the calendar that is not assigned a day of the week in order to perennialize the calendar. The same calendar of 91 days is used for each season of every year.

10-month calendars

A decimal calendar is a calendar which includes units of time based on the decimal system.

The French Republican Calendar was introduced (along with decimal time) in 1793. [6] It consisted of twelve months, each divided into three décades of ten days, with five or six intercalary days called sansculottides . [6] The calendar was abolished by Napoleon on January 1, 1806. [6]

12-month calendars

The lengths of the months inherited from the old Roman calendar as reformed by Julius Caesar do not follow any apparent logic systematically. Many reform proposals seek to make the pattern more uniform. When keeping the traditional dozen months and the close approximation of a solar year, this usually yields four equal quarters of three months each where one month is longer than the other two. World Calendar and Hanke–Henry Permanent Calendar follow this with 31∶30∶30 and 30∶30∶31 days per month, respectively. On the other hand, Symmetry454 uses 4∶5∶4 weeks per month. They all result in 364 systematically distributed days and hence have to add either one extra and one leap day or a leap week.

13-month calendars

Some calendar reformers seek to equalize the length of each month in the year. This is often accomplished by creating a calendar that has 13 months of 4 weeks (28 days) each, making 364 days. The earliest known proposal of this type was the Georgian Calendar (1745) [7] by Rev. Hugh Jones.

The Positivist calendar (1849), created by Auguste Comte, was based on a 364-day year which included one or two “blank” days. Each of the 13 months had 28 days and exactly four weeks, and each started on a Monday. The International Fixed Calendar is a more modern descendant of this calendar.

Around 1930, one James Colligan invented the Pax Calendar, which avoids off-calendar days by adding a 7-day leap week to the 364-day common year for 71 out of 400 years.

Lunisolar calendars

Lunisolar calendars usually have 12 or 13 months of 29 or 30 days.

The Hermetic Lunar Week Calendar is a lunisolar calendar proposal which has 12 or 13 lunar months of 29 or 30 days a year, and begins each year near the vernal equinox. [8]

The Meyer-Palmen Solilunar Calendar has 12 lunar months with 29 or 30 days plus a leap month called Meton every 3 or 2 years with 30 or 31 days. 60 years together are called a cycle. It uses a leap cycle which has equal number of days, weeks, months, years and cycles. 2498258 days, 356894 weeks, 84599 months, 6840 years and 114 cycles nearly all equal each other. It is called an era, although time isn't divided into it in this calendar. [9]

Some propose to improve leap rules of existing calendars, such as the Hebrew calendar. The Rectified Hebrew calendar uses a more accurate leap cycle of 4366 months per 353-year cycle, with 130 leap years per cycle, and a progressively shorter molad interval, intended to replace the 19-year leap cycle and the constant molad interval of the traditional fixed arithmetic Hebrew calendar, respectively.


Calendar proposals that introduce a thirteenth month or change the Julian-Gregorian system of months often also propose new names for these months. New names have also been proposed for days out of the week cycle (e.g., 365th and leap) and weeks out of the month cycle.

Proposals to change the traditional month and weekday names are less frequent. The Gregorian calendar obtains its names mostly from gods of historical religions (e.g., Thursday from Nordic Thor or March from Roman Mars) or leaders of vanished empires (July and August from the first Caesars), or ordinals that got out of synchronization (September through December, originally seventh through tenth, now ninth through twelfth).


Comte’s Positivist calendar, for example, proposed naming the 13 months in his calendar after figures from religion, literature, philosophy and science. Similarly, the Hermetic Lunar Week Calendar uses 12 or 13 lunar months named after 13 contributors to research on psychoactive plants and chemicals. [8]

Specific proposals

There have been many specific calendar proposals to replace the Gregorian calendar:

The following count one or more days outside the standard seven-day week:

The following are leap week calendars:

There have also been proposals to revise the way years are numbered:

Reform of the Islamic calendar:

See also

Precursors of the Gregorian reform

Related Research Articles

Calendar System for organizing the days of year

A calendar is a system of organizing days. This is done by giving names to periods of time, typically days, weeks, months and years. A date is the designation of a single, specific day within such a system. A calendar is also a physical record of such a system. A calendar can also mean a list of planned events, such as a court calendar or a partly or fully chronological list of documents, such as a calendar of wills.

Generally speaking, a calendar year begins on the New Year's Day of the given calendar system and ends on the day before the following New Year's Day, and thus consists of a whole number of days. A year can also be measured by starting on any other named day of the calendar, and ending on the day before this named day in the following year. This may be termed a "year's time", but not a "calendar year". To reconcilie the calendar year with the astronomical cycle certain years contain extra days.

Chinese calendar Lunisolar calendar from China

The traditional Chinese calendar, is a lunisolar calendar which reckons years, months and days according to astronomical phenomena. In China it is defined by the Chinese national standard GB/T 33661–2017, "Calculation and promulgation of the Chinese calendar", issued by the Standardisation Administration of China on May 12, 2017.

Intercalation or embolism in timekeeping is the insertion of a leap day, week, or month into some calendar years to make the calendar follow the seasons or moon phases. Lunisolar calendars may require intercalations of both days and months.

The Julian calendar, proposed by Julius Caesar in AUC 708, was a reform of the Roman calendar. It took effect on 1 January AUC 709 , by edict. It was designed with the aid of Greek mathematicians and astronomers such as Sosigenes of Alexandria.

A leap year is a calendar year that contains an additional day added to keep the calendar year synchronized with the astronomical year or seasonal year. Because astronomical events and seasons do not repeat in a whole number of days, calendars that have a constant number of days in each year will unavoidably drift over time with respect to the event that the year is supposed to track, such as seasons. By inserting an additional day or month into some years, the drift between a civilization's dating system and the physical properties of the solar system can be corrected. A year that is not a leap year is a common year.

A lunisolar calendar is a calendar in many cultures whose date indicates both the Moon phase and the time of the solar year. If the solar year is defined as a tropical year, then a lunisolar calendar will give an indication of the season; if it is taken as a sidereal year, then the calendar will predict the constellation near which the full moon may occur. As with all calendars which divide the year into months there is an additional requirement that the year have a whole number of months. In this case ordinary years consist of twelve months but every second or third year is an embolismic year, which adds a thirteenth intercalary, embolismic, or leap month.

A month is a unit of time, used with calendars, that is approximately as long as a natural orbital period of the Moon; the words month and Moon are cognates. The traditional concept arose with the cycle of Moon phases; such lunar months ("lunations") are synodic months and last approximately 29.53 days. From excavated tally sticks, researchers have deduced that people counted days in relation to the Moon's phases as early as the Paleolithic age. Synodic months, based on the Moon's orbital period with respect to the Earth-Sun line, are still the basis of many calendars today, and are used to divide the year.

Metonic cycle

The Metonic cycle or enneadecaeteris is a period of approximately 19 years after which the phases of the moon recur at the same time of the year. The recurrence is not perfect, and by precise observation the Metonic cycle defined as 235 synodic lunar months is just 1 hour, 27 minutes and 33 seconds longer than 19 tropical years. Meton of Athens, in the 5th century BC, judged the cycle to be a whole number of days, 6,940. Using these whole numbers facilitates the construction of a luni-solar calendar.

Roman calendar Calendar used by the Roman Kingdom and Roman Republic

The Roman calendar was the calendar used by the Roman kingdom and republic. The term often includes the Julian calendar established by the reforms of the dictator Julius Caesar and emperor Augustus in the late 1st century BC and sometimes includes any system dated by inclusive counting towards months' kalends, nones, and ides in the Roman manner. The term usually excludes the Alexandrian calendar of Roman Egypt, which continued the unique months of that land's former calendar; the Byzantine calendar of the later Roman Empire, which usually dated the Roman months in the simple count of the ancient Greek calendars; and the Gregorian calendar, which refined the Julian system to bring it into still closer alignment with the tropical year.

The World Calendar is a proposed reform of the Gregorian calendar created by Elisabeth Achelis of Brooklyn, New York in 1930.

A solar calendar is a calendar whose dates indicate the season or almost equivalently the apparent position of the Sun relative to the stars. The Gregorian calendar, widely accepted as a standard in the world, is an example of a solar calendar. The main other type of calendar is a lunar calendar, whose months correspond to cycles of Moon phases. The months of the Gregorian calendar do not correspond to cycles of the Moon phase.

The history of calendars, that is, of people creating and using methods for keeping track of days and larger divisions of time, covers a practice with ancient roots.

A leap week calendar is a calendar system with a whole number of weeks every year, and with every year starting on the same weekday. Most leap week calendars are proposed reforms to the civil calendar, in order to achieve a perennial calendar. Some, however, such as the ISO week date calendar, are simply conveniences for specific purposes.

Buddhist calendar

The Buddhist calendar is a set of lunisolar calendars primarily used in mainland Southeast Asian countries of Cambodia, Laos, Myanmar and Thailand as well as in Sri Lanka and Chinese populations of Malaysia and Singapore for religious or official occasions. While the calendars share a common lineage, they also have minor but important variations such as intercalation schedules, month names and numbering, use of cycles, etc. In Thailand, the name Buddhist Era is a year numbering system shared by the traditional Thai lunisolar calendar and by the Thai solar calendar.

The Symmetry454 calendar (Sym454) is a proposal for calendar reform created by Irv Bromberg of the University of Toronto, Canada. It is a perennial solar calendar that conserves the traditional month pattern and 7-day week, has symmetrical equal quarters in 82% of the years in its 293-year cycle, and starts every month on Monday.

The Burmese calendar is a lunisolar calendar in which the months are based on lunar months and years are based on sidereal years. The calendar is largely based on an older version of the Hindu calendar, though unlike the Indian systems, it employs a version of the Metonic cycle. The calendar therefore has to reconcile the sidereal years of the Hindu calendar with the Metonic cycle's near tropical years by adding intercalary months and days at irregular intervals.

The Gregorian calendar is the calendar used in most of the world. It was introduced in October 1582 by Pope Gregory XIII as a minor modification of the Julian calendar, reducing the average year from 365.25 days to 365.2425 days, and adjusting for the drift in the 'tropical' or 'solar' year that the inaccuracy had caused during the intervening centuries.

The Hanke–Henry Permanent Calendar (HHPC) is a proposal for calendar reform. It is one of many examples of leap week calendars, calendars that maintain synchronization with the solar year by intercalating entire weeks rather than single days. It is a modification of a previous proposal, Common-Civil-Calendar-and-Time (CCC&T). With the Hanke–Henry Permanent Calendar, every calendar date always falls on the same day of the week. A major feature of the calendar system is the abolition of time zones.

A perennial calendar is a calendar that applies to any year, keeping the same dates, weekdays and other features.


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Further reading