What is the oldest calendar still actively used? That is the Jewish or Hebrew calendar. And with the year 2020 in the Common Era dating, the Jewish or Hebrew calendar date is the year 5780. The Hebrew calendar is an ancient lunisolar calendar that can trace its origins back to the Torah, with the book of Genesis.
In the book of Genesis, it is implied that months are 30 days (Genesis 8:3-4) and that cycles were 12 months annually. Originally an observational calendar, that Hebrew calendar would end each day at sundown. Eventually the calendar was replaced with a mathematically calculated one. This was done to include an additional month to reconcile for the solar year.
With the Hebrew calendar being used for the observance of Jewish religious practices and holidays the calendar never went out of use nor left the area which would become Israel. With the founding of Israel, the Hebrew calendar dating was used on the issuance of currency and coins. Starting in 1948 or JE5708, coins began to be issued using the Hebrew calendar date exclusively.
The full date doesn’t appear on the coins until JE5741 or 1981 Common Era, but a partial date in Hebrew of the last three years of the Hebrew calendar date. The Hebrew calendar date is 3760 years greater than the Common Era conversion, so to convert simply subtract 3760 from the Hebrew date.
Some coins, especially commemorative issues, will have both Common Era and Hebrew calendar dates on the coin. Since the calendar is a state-used calendar it is accepted as Hebrew rather than Jewish alone keeping with a more secularized context.
Today in Israel the Hebrew calendar is still used for religious purposes, but the Common Era date is greatly favored for everyday use. Yet, coins are still issued using the Hebrew calendar dating. After 5780 years the calendar continues being used and is the oldest actively used dating system.