Jewish Calendar In Canada

First Posted on Friday, September 3, 2021 / Yom Shishi, 26 Elul , 5781

By: David Orenstein

Back on March 5 I wrote about the Mi’kmaw Calendar in the CSTHA post “Mi’kmaw Calendar and Traditional Astronomy: A Two-Eyed Seeing Partnership”. So now it’s time to reflect on my own calendric tradition.

The last Jewish Sabbath of 5781 starts at sunset today, 7:28 pm EDT, here in Toronto and 7:10 pm EDT, in Montreal. And at the differing sunset times across the country. It will be Shabbat, 27 Elul, 5781. In synagogue, we’ll be continuing with our regular weekly Torah reading, Nitsavim = D’varim / Deutoronomy 29.9-30.20. The last day of the month is 29 Elul, so that means Rosh Ha-Shonah (literally “The Head of the Year” in Hebrew) is just around the corner. Also, since this holiday marks the Jewish New Year, it’s almost 5782.

To help to explain the Jewish calendar and its use in Canada, luckily, I have the work of retired University of Ottawa mathematics professor, Edward L. Cohen to rely on. Since at least the mid-1990s he’s been working on calendrics, covering a wide range over time and space of the world’s calendars. Not only has he been studying the Jewish calendar, but also the Gregorian, Islamic, Mayan, and French Revolutionary calendars, to name just a few.

5782 is a leap year, that means it has thirteen instead of twelve months.

In order (days of the month): Tishrei (30) Cheshvan (29) Kislev (30) Tevet (29) Shevat (30) Adar I (30) Adar II (29) Nisan (30) Iyar (29) Sivan (30) Tammuz (29) Av (30) Elul (29). For a total of 384 days, making it a regular leap year.

A regular non-leap year has 354 days, a difference of 30 days, the length of the leap month Adar I. There are also defective years of 353 and 383 days respectively and excessive years, 355 and 385 days.

So, Rosh Ha-Shonah must be the first of Tishrei. That is the first day of Rosh Ha-Shonah. Since Canada is in the Diaspora, not in Eretz Israel (the Land of Israel), Rosh ha-Shonah is a two-day holiday.

So, when was Rosh Ha-Shonah for 5781 our current year? When will it be in 5783? That’s easy: 1 Tishrei and 2 Tishrei, of course. But if we want to determine the date of Rosh Ha-Shona in the modified Gregorian Calendar that we use in Canada as our civil calendar, here’s what we have to do.

The Jewish calendar is based on the Moon and regulated by the Sun. The time from one New Moon to the next was known to be 29 days, 2 hours, 44 minutes, 3 1/3 seconds (a molad in Hebrew, pl. moladot).

Thus, every month has either 29 or 30 days, as exemplified above by 5782. Except, for Cheshvan and Kislev which can have either 29 or 20 days, all the months have the same length as they do for 5782.

In combination with the length of the solar year, the Jewish Calendar as a Metonic cycle of 19 years in which the lunar and solar calendars eventually match up again. The seven leap years with the extra month are in italics:


Cohen has provided a table for us, running from 1883/5644 to 2110/5871, and from Metonic Cycle 298 to 309. Note that the Gregorian year is that of the Jewish year’s Rosh Ha-Shonah. Thus, we have 2020/5781 and 2021/5782 on the list.

In this table 2021/5782 is listed as S07-T, K. this means that the first day Rosh Ha-Shonah is September 7, 2021, and it’s on a Tuesday. “K” is the type of year. “K” is one of the seven types of leap year, in this case with the first day of Rosh Ha-Shonah on a Tuesday and the first Day of Pesach (Passover) on Shabbat (Saturday). A “K” year is also a regular leap year of 384 days.

For 2020/5781 and 2022/5782 we have listings of S19-S, B and S26-M, E, respectively. So here we have Rosh ha-Shonah starting on September 19 (a Saturday) and September 26 (a Monday). “B” and “E” are both types of ordinary (non-leap ) years, with “B” defective (353 days) and “E” excessive 355 days.

Cohen also shows how he generates this table, but that’s another story.

There will be many more Jewish holidays for us to commemorate throughout the month of Tishrei (September 6 – October 6, 2021), such as:

Yom Kippur – The Day of Atonement: 10 Tishrei (September 16-17),

Sukkot – Fall Harvest Festival: 15-20 Tishrei (September 20-26),

Simchat Torah – Anniversary of Receiving the Torah at Mount Sinai: 23 Tishrei (September 28-29).

But these are many more stories.



Edward L. Cohen

(1994) “The Hebrew Calendar Simplified” Proceedings of the Canadian Sociiety for the History and Philosophy of Mathematics, 7: 50-57

(1996) “Gregorian Dates for the Jewish New Year” Proceedings of the Canadian Society for the History and Philosophy of Mathematics, 9: 79-90

(2000) “Adoption and Reform of the Gregorian Calendar” Math Horizons 7(3): 5- 11

(2001) “The French Republican Calendar” Proceedings of the Canadian Society for the History and Philosophy of Mathematics, 14: 32-40

(2002) “The Mayan Calendars” Proceedings of the Canadian Society for the History and Philosophy of Mathematics, 15: 36-57

(2003a) “Calendars of the Dead-Sea-Scroll Sect” Cubo Matemática Educacional, 5(2): 1-16

(2003b) “The Islamic Calendar” Proceedings of the Canadian Society for the History and Philosophy of Mathematics 16: 116-130



March 5, 2021, CSTHA Mi’kmaw Calendar blog post:

Canadian Society for the History and Philosophy of Mathematics (CSHPM) website: