thumb|upright=1.25|alt=Museum of the Roman Theater of Caesaraugusta in Zaragoza, Spain|A reproduction of the ', a painted wall-calendar from the late Roman Republic
thumb|upright=1.25|Another reproduction of the fragmentary ' , with the seventh and eighth months still named [[Quintilis ("QVI") and Sextilis ("SEX") and an intercalary month ("INTER") in the far right-hand column]]
The Roman calendar was used by the Roman Kingdom and Roman Republic. Although the term is primarily used for Rome's pre-Julian calendars, it is often used inclusively of the Julian calendar established by Julius Caesar in 46 BC.
According to most Roman accounts, their original calendar was established by their legendary first king Romulus. It consisted of ten months, beginning in spring with March and leaving winter as an unassigned span of days before the next year. These months each had 30 or 31 days and ran for 38 nundinal cycles, each forming a kind of eight-day weeknine days counted inclusively in the Roman mannerand ending with religious rituals and a public market. This fixed calendar bore traces of its origin as an observational lunar one. In particular, the most important days of each monthits kalends, nones, and idesseem to have derived from the new moon, the first-quarter moon, and the full moon respectively. To a late date, the College of Pontiffs formally proclaimed each of these days on the Capitoline Hill and Roman dating counted down inclusively towards the next such day in any month. (For example, the year-end festival of Terminalia on 23February was called , the 6th day before the March kalends.)
Romulus's successor Numa Pompilius is usually credited with a revised calendar that divided winter between the two months of January and February, shortened most other months, and established rough alignment with the solar year by some system of intercalation. This is a typical feature of lunisolar calendars and was necessary to keep the Roman religious festivals and other activities within their proper seasons.
Modern historians dispute various points of this account. It is possible the original calendar was agriculturally based, observational of the seasons and stars rather than of the moon, with ten months of varying length filling the entire year. If this ever existed, it would have changed to the lunisolar system later credited to Numa during the kingdom or early Republic under the influence of the Etruscans and of Pythagorean Southern Italian Greeks. After the establishment of the Republic, years began to be dated by consulships but the calendar and its rituals were otherwise very conservatively maintained until the Late Republic. Even when the nundinal cycles had completely departed from correlation with the moon's phases, a pontiff was obliged to meet the sacred king, to claim that he had observed the new moon, and to offer a sacrifice to Juno to solemnize each kalends.
It is clear that, for a variety of reasons, the intercalation necessary for the system's accuracy was not always observed. Astronomical events recorded in Livy show the civil calendar had varied from the solar year by an entire season in and was still two months off in . By the or before, control of intercalation was given to the pontifex maximus butas these were often active political leaders like Caesarpolitical considerations continued to interfere with its regular application.
Victorious in his civil war, Caesar reformed the calendar in 46 BC, making the year of his third consulship last for 446days. This new Julian calendar was an entirely solar one, influenced by the Egyptian calendar. In order to avoid interfering with Rome's religious ceremonies, the reform distributed the unassigned days among the months (towards their ends) and did not adjust any nones or ides, even in months which came to have 31days. The Julian calendar was designed to have a single leap day every fourth year by repeating February 24 (a doubled or ) but, following Caesar's assassination, the priests mistakenly added the bissextile () leap day every three years due to their inclusive counting. In order to bring the calendar back to its proper place, Augustus was obliged to suspend intercalation for one or two decades.
At 365.25 days, the Julian calendar remained slightly longer than the solar year (365.24 days).<!--Two decimal places is adequately precise for the lead. --> By the 16th century, the date of Easter had shifted so far away from the vernal equinox that Pope Gregory XIII ordered a further correction to the calendar method, resulting in the establishment of the modern Gregorian calendar.
History
thumb|right|250px|The remains of the ', containing the months of January, March, April, and December and a portion of February.
Prehistoric calendar
The original Roman calendar is usually believed to have been an observational lunar calendar whose months ended and began from the new moon. Because a lunar cycle is about 29.5 days long, such months would have varied between . Roman works on agriculture including those of Cato, Varro, Vergil, Columella, and Pliny invariably date their practices based on suitable conditions or upon the rising of stars, with only occasional supplementary mention of the civil calendar of their times until the 4th or 5th century author Palladius. Augury, formal Roman ornithomancy, continued to be the focus of a prestigious dedicated priesthood until at least the end of the 4th century. Although most Roman festivals in the historical record were closely tied to the nundinal cycle of the later calendar, there remained several moveable feasts (, "proclaimed festivals") like the Sementivae that were dependent on local conditions. Michels suggests this was the original state of all ancient festivals, marking divisions between the seasons and occasions within them.
Legendary 10-month calendar
The Romans themselves usually described their first organized year as one with ten fixed months, a decimal division fitting general Roman practice. There were four months of "31" daysMarch, May, Quintilis, and Octobercalled "full months" () and six months of "30" daysApril, June, Sextilis, September, November, and Decembercalled "hollow months" ('). These "304" days made up exactly 38 nundinal cycles. The months were kept in alignment with the moon, however, by counting the new moon as the last day of the first month and simultaneously the first day of the next month. The system is usually said to have left the remaining two to three months of the year as an unorganized "winter", since they were irrelevant to the farming cycle. Macrobius claims the 10-month calendar was fixed and allowed to shift until the summer months were completely misplaced, at which time additional days belonging to no month were simply inserted into the calendar until it seemed things were restored to their proper place. Licinius Macer's lost history apparently similarly stated that even the earliest Roman calendar employed intercalation.
Later Roman writers usually credited this calendar to Romulus, their legendary first king and culture hero, although this was common with other practices and traditions whose origin had been lost to them. Censorinus considered him to have borrowed the system from Alba Longa, Rüpke also finds the coincidence of the length of the supposed "Romulan" year with the length of the first ten months of the Julian calendar to indicate that it is an interpretation by late Republican writers.
| style="font-weight: bold;" | 31
|-
| June || Mensis Iunius || Month of Juno
| 30
|-
| July || Mensis Quintilis<br>Mensis Quinctilis || Fifth Month
| style="font-weight: bold;" | 31
|-
| August || Mensis Sextilis || Sixth Month
| 30
|-
| September || Mensis September || Seventh Month
| 30
|-
| October || Mensis October || Eighth Month
| style="font-weight: bold;" | 31
|-
| November || Mensis November || Ninth Month
| 30
|-
| December || Mensis December || Tenth Month
| 30
|-
! scope="row" colspan="3" style="text-align: right;" | Length of the year:
! style="text-align: left;" | 304
|}
Other traditions existed alongside this one, however. Plutarch's Parallel Lives recounts that Romulus's calendar had been solar but adhered to the general principle that the year should last for 360 days. Months were employed secondarily and haphazardly, with some counted as 20 days and others as 35 or more.
Rome's 8-day week, the nundinal cycle, was shared with the Etruscans, who used it as the schedule of royal audiences. It was presumably a part of the early calendar and was credited in Roman legend variously to Romulus and Servius Tullius.
Republican calendar
The attested calendar of the Roman Republic was quite different. It had twelve months, already including January and February during the winter.
According to Livy, it was Numa Pompilius, the second king of Rome who divided the year into twelve lunar months (History of Rome, I.19). Fifty days, says Censorinus, were added to the calendar and a day taken from each month of thirty days to provide for the two winter months: Januarius (January) and Februarius (February), both of which had 28 days (The Natal Day, XX). This was a lunar year of 354 days but, because of the Roman superstition about even numbers, an additional day was added to January to make the calendar 355 days long. Auspiciously, each month now had an odd number of days: Martius (March), Maius (May), Quinctilis (July), and October continued to have 31; the other months, 29, except for February, which had 28 days. Considered unlucky, it was devoted to rites of purification (februa) and expiation appropriate to the last month of the year. (Although these legendary beginnings attest to the venerability of the lunar calendar of the Roman Republic, its historical origin probably was the publication of a revised calendar by the Decemviri in as part of the Twelve Tables, Rome's first code of law.)
The inequality between the lunar year of 355 days and the tropical year of 365.25 days led to a shortfall over four years of (10.25 × 4) = 41 days. on account of them being actually named and counted inclusively in days before the kalends of March; they were traditionally part of the celebration for the new year. There was occasionally a delay of one day (a being inserted between February 23 and the start of the ) for the purpose of avoiding a clash between a particular festival and a particular day of the week (see for another example). The Roman superstitions concerning the numbering and order of the months seem to have arisen from Pythagorean superstitions concerning the luckiness of odd numbers.
These Pythagorean-based changes to the Roman calendar were generally credited by the Romans to Numa Pompilius, Romulus's successor and the second of Rome's seven kings, as were the two new months of the calendar.
