The Nile’s swell was an outstanding for Egyptians event that coincided with the rise of Sirius (Greek Sotis, Egyptian Sopdet ) above the dawn horizon. Heliacal rise of Sirius takes place on the19th of July in Julian calendar and on the 15th of June according to modern calendar. For Egyptians it was the sign that begins a new-year. Because Egyptian year comprised 365 days while solar year (or rather Sotis year) is 365.25 days long, every fourth year the calendar would be in error of 1 day. Egyptians were aware of it and that is why the beginning of a new- year was moveable, every time formally acclaimed.
To equalize the calendar with astronomic year in the Late Period there were 5 days more added (called by Greeks epagomenal) to the end of each year. Egyptians named the days as follows: Osiris, Horus, Seth, Isis, Nephtys. Names of the months, coming from the names of more important ceremonies, had been introduced in the Late Period too. The months in Pharaohs era were just numerated. 
Apart from the calendar described above, there was a ritual calendar, based on lunar cycles. It was also divided into 12 alternate month of 29 or 30 days each. Thus the two successive months made up together 59 days. The year was being prolonged every 5 years thus two last months of a year comprised together 60 days. One of the most important tasks of Egyptian priests was to synchronise terms of religious ceremonies and festivals relevant to lunar cult and assigned according to lunar phases with those of Sotis calendar and then – to state their dates. The Carlsberg papyrus describes a mode of re-calculation of moveable feasts from lunar year to dates from Sotis calendar. The consistence of a 25 year long cycle was achieved after dividing 309 lunar months into 16 common years (12 month each) and 9 great years (13 months each).
A system of years’ calculation had never been continuous. Under the reign of first dynasties any memorable event was a starting-point of a new-year. In time of the Dynasties V and VI for instance years were counted due to the general cattle register. It was only with the approach of the New Kingdom that the beginning of a new-year was in keeping with the beginning of new kingship. Thus the following inscription:      meant king of Upper and Lower Egypt Menmaatre first year of kingship. Years of reign and calendar years did not agree. The second year of reign started with the crowning anniversary and not with a day of a new year.

Two Egyptian textual records of Sothic rising form the basis of the conventional chronology of Egypt, which, in turn, influences that of the whole Mediterranean region. These two documents are XIIth Dynasty letter from the site el-Lahun, written on day 16, month 4, of the second season in year 7 of the reign of Senweseret III, and an XVIIIth Dynasty Theban medical papyrus (Papyrus Ebers), written on day 9, month 3, of the third season of year 9 in the reign of Amenhotep I. By assigning absolute dates to each of these documents (1872 BC for the el-Lahun rising in year 7 of Senweseret III, and 1541 BC for the Ebers rising in regnal year 9 of Amenhotep I - by I. Shaw "The Oxford History of Ancient Egypt"), Egyptologists have been able to extrapolate a set of absolute dates for the whole of the pharaonic period, on the basis of records of the lengths of reign of the other kings of the Middle and New Kingdoms.
It is not possible, however, to be totally confident of the  absolute dates cited above, since the precise dating is dependent on our knowledge of the location (or locations) where the astronomical observations were made. It used to be assumed - without any real evidence - that such observations were made at Memphis or perhaps, Thebes, but Detlef Franke and Rolf Krauss have argued that they were all made at Elephantine. William Ward, on the other hand, suggested that they are all more likely to have been separate local observations, which would have resulted in a time lag in terms of the various 'national' religious festivals (that is, both the observations and the corresponding festivals may actually have taken place at different times and in different parts of the country). This continuing uncertainty means that our astronomical linchpins are in reality somewhat floating, although it should be noted that the differences between the 'high' and 'low' chronologies (based largely on assumptions concerning different observation points) are usually only a few decades at most.