Ab Urbe condita (related with Anno Urbis conditae: AUC or a.u.c.) is Latin for "from the founding of the City (Rome)", traditionally set in 753 BC. It was used to identify the Roman year by a few Roman historians. Modern historians use it much more frequently than the Romans themselves did; the dominant method of identifying Roman years was to name the two consuls who held office that year. Before the advent of the modern critical edition of historical Roman works, AUC was indiscriminately added to them by earlier editors, making it appear more widely used than it actually was. The regnal year of the emperor was also used to identify years, especially in the Byzantine Empire after Justinian required its use in 537. Examples of usage are principally found in German authors, for example Mommsen's History of Rome.
From Emperor Claudius onwards, Varro's calculation (see below) superseded other contemporary calculations. Celebrating the anniversary of the city became part of imperial propaganda. Claudius was the first to hold magnificent celebrations in honour of the city's anniversary, in 47, eight hundred years after the founding of the city. In 121, Hadrian, and in 147/8, Antoninus Pius held similar celebrations.
In 248, Philip the Arab celebrated Rome's first millennium, together with Ludi saeculares for Rome's alleged tenth saeculum. Coins from his reign commemorate the celebrations. A coin by a contender for the imperial throne, Pacatianus, explicitly states "Year one thousand and first", which is an indication that the citizens of the Empire had a sense of the beginning of a new era, a Saeculum Novum.
...1 ab urbe condita = 753 before Christ
...2 ab urbe condita = 752 BC
...3 ab urbe condita = 751 BC ...
750 ab urbe condita = 4 BC (Death of Herod the Great)
751 ab urbe condita = 3 BC
752 ab urbe condita = 2 BC
753 ab urbe condita = 1 BC
754 ab urbe condita = 1 Anno Domini
755 ab urbe condita = 2 AD
2761 ab urbe condita = 2008 AD
However, according to Lucius Tarrutius of Firmum, Romulus and Remus were conceived in the womb on the 23rd day of the Egyptian month Choiac, at the time of a total eclipse of the Sun. (This eclipse occurred on June 15, 763 BC, with a magnitude of 62.5% at Rome. Its beginning took place at 6:49, its middle at 7:47 and its end at 8:51.) He was born on the 21st day of the month Thoth. The first day of Thoth fell on March 2 in that year. Rome was founded on the ninth day of the month Pharmuthi, which was April 21, as universally agreed. The Romans add that about the time Romulus started to build the city, an eclipse of the Sun was observed by Antimachus, the Teian poet, on the 30th day of the lunar month. This eclipse on June 25, 745 BC (see above) had a magnitude of 54.6% at Teos, Asia Minor. It started at 17:49; it was still eclipsed at sunset, at 19:20. Romulus vanished in the 54th year of his life, on the Nones of Quintilis (July), on a day when the Sun was darkened. The day turned into night, which sudden darkness was believed to be an eclipse of the Sun. It occurred on July 17, 709 BC, with a magnitude of 93.7%, beginning at 5:04 and ending at 6:57. (All these eclipse data have been calculated by Prof. Aurél Ponori-Thewrewk, retired director of the Planetarium of Budapest.) Plutarch placed it in the 37th year from the foundation of Rome, on the fifth of our July, then called Quintilis, also states that Romulus ruled for 37 years. He was slain by the senate or disappeared in the 38th year of his reign. Most of these have been recorded by Plutarch, Florus, Cicero, Dio (Dion) Cassius and Dionysius of Halicarnassus (L. 2). Dio in his Roman History (Book I) confirms this data by telling that Romulus was in his 18th year of age when he had founded Rome. Thus, three eclipse calculations may support the suggestion that Romulus reigned from 746 BC to 709 BC, and Rome was founded in 745 BC.
Q. Fabius Pictor (c. 250 BC) tells that Roman consuls started for the first time 239 years after Rome's foundation (Enciclopedia Italiana, XIV, 1951: 173). Livy (I, 60) gives almost the same, 240 years for that interval. Polybius tells that 28 years after the expulsion of the last Persian king Xerxes crossed over to Greece, and that event is fixed to 478 BC by two solar eclipses.