Like all other calendars, the Babylonian calendar had twelve lunar months (about 354 days) and a problem to make these fit the solar year (about 365 days). In the western calendar, this is solved by cutting the tie between the lunar phase and the calendar month; the Babylonians found a different solution by adding leap months.

Originally, the king decided which month had to be added ("intercalated"), and when. This was not very satisfying, and the Babylonian astronomers, often called Chaldaeans, gradually developed rules to create the nearly perfect calendar. The key was the discovery, in the mid-eighth century, that 235 lunar months are almost identical to 19 solar years. (The difference is only two hours.) The Chaldaeans concluded that seven out of nineteen years ought to be leap years with an extra month.


From now on, intercalary months were still announced by the king, but he was advised by an astronomer. After Babylon had been captured by the Persian king Cyrus the Great in 539, priestly officials took over. The Chaldaeans now started to look for a standard procedure for the intercalation of months. It was introduced in 503 BCE by Darius I the Great (if not earlier).


As this table shows, there are six years when a second month Addaru is added, and one year with an extra Ulûlu. The result is that the first day of the month Nisannu (New year's day) was never far from the vernal equinox (the first day of spring), so that the civil calendar and the seasons were never out of step. This system is often called the cycle of Meton, to commemorate the Greek astronomer who tried to introduce it in the West. It is still used in the Jewish calendar.


At an unknown moment in the fourth century, an even better procedure for the intercalation of months was invented. This time, a cycle of 76 years was used, one day was left out, and the limits of variability in the start of the year were further narrowed. The new system was already known in 331, because in that year the Macedonian conqueror Alexander the Great captured Babylon and ordered the Astronomical diaries to be translated into Greek. The new knowledge was immediately applied in Greece: the astronomer Callippus of Cyzicus, a pupil of the philosopher Aristotle of Stagira, recalculated the length of the lunar month and proposed a new calendar, in which he applied the longer cycle. His new era, which was used by all later Greek astronomers, started at 28 June 330, eight months after the capture of Babylon.


One final remark: the Babylonians did not develop a calendar era until the last years of the fourth century. It was only then that people started to date with formulae like "in the year 162 of the Seleucid era". Until then, regnal years were used, and it was very important to use the name of the correct king. In the Diadochi Chronicle, we find the charming piece of information that the Macedonian general Seleucus I Nicator, after he had expelled his rival Antigonus Monophthalmus, "declared that Year 7 of Antigonus-the-general had to be counted as Year 6 of Alexander, son of Alexander, and Seleucus-the-general."