The Babylonian calendar is one of the greatest achievements of Antiquity: it combines a solar and a lunar cycle in such a way that the beginning of the year never wanders far from the Spring equinox. The basic theoretical principle is well-known: in a cycle of nineteen years, we have twelve years of twelve lunar months and seven years of thirteen months. Theoretically, dates in ancient Babylonian texts can be converted to our calendar; there are several webpages that offer converters, which are also useful for dates on Jewish calendars.
And that’s the problem. The Babylonian calendar is not exactly the same. In the end, a new month started when the new moon was actually observed, which means that the months could sometimes be one day longer or shorter, depending on the circumstances in Babylon or Jerusalem.
A more or less correct conversion is mentioned in the tables of Parker & Dubberstein, Babylonian Chronology 626 B.C. – A.D. 75 (1956; update 1971). Now, Dutch astronomer Rob van Gent of Utrecht University has made a calendar converter that’s not derived from the Jewish calendar, but is directly based on Babylonian information.