How the Hebrew calendar works

Date calculations

Birthday

A Hebrew birthday is generally observed on the same Hebrew date each year. Two exceptions:

• Born in Adar of a non-leap year — in a leap year the birthday is observed in Adar II.
• Born on 30 Cheshvan or 30 Kislev — in years where that month has only 29 days, the birthday rolls forward to 1 Kislev (respectively 1 Tevet), which is Rosh Chodesh.

Yahrzeit

The yahrzeit is generally observed on the same Hebrew date each year. The exceptions differ from the birthday rule:

• Passed away in Adar of a non-leap year — most authorities today observe the yahrzeit in Adar I of a leap year, following the Rama; this is what we compute. The Shulchan Aruch and some Sephardic authorities rule Adar II. In the first year after passing, however, Adar I is preferred by many of those opinions who otherwise rule in favor of Adar II, since exactly 12 months must have elapsed (Magen Avraham there). See Shulchan Aruch OC 568:7¹.
• Passed away in Adar I of a leap year — subsequent leap years: Adar I; non-leap years: the sole Adar.
• Passed away in Adar II of a leap year — subsequent leap years: Adar II; non-leap years: the sole Adar.
• Passed away on 30 Cheshvan or 30 Kislev — the rule depends on what happened in the first year after death:
  • If that year had a 30th of the same month (a full month), then in future years with only 29 days the yahrzeit is observed on Rosh Chodesh (1 Kislev or 1 Tevet respectively) — same as the birthday rule.
  • If that year did not have a 30th (the month was deficient), the yahrzeit is observed on the last day of that month every year — 29 in deficient years, 30 when the month is full.
  See also Kitzur Shulchan Aruch 221².

Other recurring events

Bar / Bat mitzvah, wedding anniversaries and other recurring Hebrew-date events follow the birthday rule above.

The 19-year cycle

The Hebrew calendar reconciles the lunar month with the solar year by inserting a leap month (Adar I) in 7 of every 19 years. Over the full cycle, 19 solar years equal almost exactly 235 lunar months (12 × 12 + 7 × 13), so months and seasons stay aligned.

Within each 19-year cycle, the leap years are years 3, 6, 8, 11, 14, 17 and 19. This is remembered by the mnemonic גו״ח אדז״ט, where each Hebrew letter is its numeric position modulo 10.

The current Hebrew year's position in the cycle is:

((year − 1) mod 19) + 1

See Rambam, Hilchot Kiddush HaChodesh 6:11³.

Computing the day of Rosh Hashana

The molad (new moon) of Rosh Hashana is computed from the traditional constants: the mean synodic month is 29 days 12 hours 793 chalakim (1 chelek = 1/1080 hour ≈ 3⅓ seconds). Molad Tishrei of any year is projected from Molad Beharad — the reference molad of Nisan year 1, which fell on Monday at 5 hours 204 chalakim after 6 PM Sunday. Note that this molad (and almost the entire year 1) is before creation according to the tradition that the world was created in Tishrei (Rabbi Eliezer in Rosh Hashana 10b⁴), and is sometimes called molad tohu.

Once the molad is known, Rosh Hashana can be postponed by up to two days via the four dechiyot (postponement rules):

1. Molad zaken (מולד זקן) — if the molad falls at noon or later, Rosh Hashana is pushed to the next day.
2. Lo ADU rosh (לא אד״ו ראש) — Rosh Hashana never falls on Sunday, Wednesday or Friday. If the molad (or the day after molad zaken) lands on one of these, push forward one day.
3. Gatarad (גטר״ד — ג=Tue, ט=9h, ר״ד=204ch) — in a non-leap year, if the molad falls on Tuesday at 9 hours 204 chalakim or later, Rosh Hashana is pushed to Thursday (via lo ADU rosh).
4. Betutakpat (בט״ו תקפ״ט — ב=Mon, ט״ו=15h, תקפ״ט=589ch) — in the year immediately after a leap year, if the molad falls on Monday at 15 hours 589 chalakim or later, Rosh Hashana is pushed to Tuesday.

See Mishneh Torah — Hilchot Kiddush HaChodesh, chapters 6–8³.

Parshiyot

The schedule of weekly Torah readings is governed by the rules set out in Tur, Orach Chaim 428⁵. There are 14 year types, determined by: (1) the day of the week of Rosh Hashana, (2) whether Cheshvan and Kislev have their standard number of days, and (3) the day of the week of the first day of Pesach. The rules for merging and splitting certain parsha pairs were codified by R. Chaim Mordechai haCohen Brecher and are printed in the back of some Chumash editions (see table⁶).

Each year type is encoded with three Hebrew letters: the day of Rosh Hashana (ב Mon · ג Tue · ה Thu · ז Sat), the year length (ח deficient · כ regular · ש complete), and the day of the first day of Pesach. This code appears in Chumashim and Tikun Korim.

In some years certain readings in Eretz Israel differ from the Diaspora because a second day of Yom Tov displaces a reading in the Diaspora. The Parshiot page shows both readings.

Tekufot and Birkat HaChama

Tekufot are the four astronomical seasons: Tekufat Nisan (spring equinox), Tekufat Tammuz (summer solstice), Tekufat Tishrei (autumnal equinox) and Tekufat Tevet (winter solstice). Two calculations are traditional:

• Tekufat Shmuel — a simple year of exactly 365¼ days, giving 91⅜ days per season. This is what governs practical halachic reckoning today (Tal uMatar in the Diaspora, Birkat HaChama). See Eruvin 56a⁷; Rambam, Kiddush HaChodesh 9:4³.
• Tekufat Rav Ada — matches the mean solar year underlying the molad calculation (365 days, 5h, 55m, 25 25⁄57 sec); more accurate but retained mostly for theoretical reference. See Rambam, Kiddush HaChodesh 10:1³.

Birkat HaChama (blessing on the sun) is recited every 28 years, on the morning after Tekufat Nisan (per Shmuel) falls on Tuesday evening / Wednesday sunrise. The last occurrence was Wednesday 8 April 2009; the next is 8 April 2037.

This is because, according to Shmuel, Tekufat Nisan advances by 1¼ days in the weekly cycle every year, so once in 28 years it falls on Tuesday at 6 AM — the hour the sun was traditionally created. There is no associated astronomical event; it is the halachically accepted tradition.

See Mishneh Torah — Hilchot Kiddush HaChodesh, chapter 10³.

References

1. Shulchan Aruch OC 568:7 — yahrzeit for one who died in Adar (with Rama gloss, Magen Avraham and Kaf HaChaim) — sefaria.org
2. Kitzur Shulchan Aruch 221 on Yahrzeit — sefaria.org
3. Mishneh Torah — Hilchot Kiddush HaChodesh — sefaria.org
4. Rosh Hashana 10b — Rabbi Eliezer: the world was created in Tishrei — sefaria.org
5. Tur, Orach Chaim 428 — R. Yaakov ben Asher, summarizing the rulings of his father R. Asher ben Yechiel (the Rosh) — sefaria.org  |  traditional print edition — hebrewbooks.org
6. R. Chaim Mordechai haCohen Brecher — Parsha pairing/splitting table — hebrewbooks.org
7. Eruvin 56a — Shmuel's astronomical year of 365¼ days — sefaria.org