Pesach can begin in late March or in the third week of April. Chanukah can start in November or nearly collide with the new year. People describe this as the festivals being “early” or “late,” which quietly assumes the Gregorian calendar is the fixed one. It is not. Both calendars are moving; they simply track different things. What follows is how the Hebrew calendar is built and why the pattern comes out the way it does.
The moon takes about 29 days, 12 hours and 44 minutes to return to the same phase — a synodic month, 29.5306 days. The earth takes about 365.2422 days to complete an orbit. Neither number is a whole number of days, and neither divides neatly into the other. Twelve lunar months come to 354.37 days, roughly eleven days short of a solar year.
Every calendar in history has had to choose which of these to honour.
The Hebrew calendar needs both because its festivals carry both kinds of requirement. Months begin at the new moon: Rosh Chodesh is a lunar event, and the moon visibly matches the date all month, which is why the full moon falls on the fifteenth at Pesach and Sukkot. But Pesach is also commanded to fall in the spring, in the month of Aviv, and Sukkot is an autumn harvest festival. Let the lunar year run free and within fifteen years you would be eating matzah in midwinter.
The solution is intercalation: periodically adding a thirteenth month to a year, so the accumulated drift is repaid in one lump.
The arithmetic behind the schedule is a genuinely elegant coincidence. Take 235 lunar months: that is 6,939.69 days. Take 19 solar years: 6,939.60 days. The two agree to within about two hours. Nineteen years therefore contain almost exactly 235 lunar months, which is twelve months in each of twelve years plus thirteen months in each of seven.
So seven years in every nineteen are leap years, at fixed positions in the cycle: years 3, 6, 8, 11, 14, 17 and 19. The relationship was known to Babylonian astronomers and is named in the West after the Greek astronomer Meton; the Hebrew calendar has used it since the calculated calendar was fixed, a process traditionally associated with Hillel II in the fourth century, replacing the older system in which the Sanhedrin declared each new month on the testimony of witnesses who had seen the new moon.
The extra month is not appended at the end of the year. It is inserted before Adar, the month preceding Nisan and Pesach — placed there precisely because its job is to hold Pesach in the spring.
In a leap year the inserted month is called Adar I, and the original Adar becomes Adar II. The naming misleads almost everyone: it is Adar I that is the addition, and Adar II that is the “real” Adar. That is why Purim is observed in Adar II, keeping its distance from Pesach constant, while the fourteenth of Adar I is marked only as the minor Purim Katan.
The same question arises for a yahrzeit or bar mitzvah that falls in Adar of a common year, and practice varies between communities and cases — a question for your rav rather than for a calendar.
Since the calendar became calculated rather than observed, the anchor is the molad: the mean conjunction of sun and moon, computed rather than sighted. Mean is the operative word — the moon's actual motion is irregular, and the molad deliberately uses a constant average interval, so it can drift from the true new moon by several hours in either direction.
That interval is given as 29 days, 12 hours and 793 chalakim. A chelek is one 1,080th of an hour, or 3⅓ seconds — a unit chosen because 1,080 divides so conveniently. Converted, 793 chalakim is 44 minutes and 3⅓ seconds, giving 29 days 12 hours 44 minutes 3.3 seconds. Modern measurement of the synodic month puts it at 29 days 12 hours 44 minutes 2.9 seconds. The value in use has been accurate to under half a second since antiquity.
The molad of Tishrei sets Rosh Hashanah — but not directly. Four rules, the dechiyot, can push the date back by a day or two.
The first two have transparent reasons. The last two are corrective: without them, the postponements produced by the first two would occasionally leave a year with an impossible length. Their thresholds are the exact points at which that happens, which is why they look so arbitrary. They are the residue of a system being made to close.
Because Rosh Hashanah can be nudged and the following year's cannot be nudged in step, the year has to absorb the difference. Two months are variable in length: Cheshvan and Kislev, each of which can have 29 or 30 days. That yields three shapes of year — deficient, regular and complete — in both common and leap forms:
Combine those six lengths with the four permitted days for Rosh Hashanah and you get fourteen possible year patterns. Every Hebrew year in history and in the future is one of those fourteen, which is what makes a printed calendar for any year computable in advance — and why the weekly parsha schedule differs between Israel and the diaspora in some years but not others.
Now the original question answers itself. A common Hebrew year is about eleven days shorter than a Gregorian one, so each festival appears about eleven days earlier than the year before. After two or three such years the drift has grown to three or four weeks — and then a leap year arrives, adding a month, and the festival jumps roughly nineteen days later again.
Sawtooth, not random. Rosh Hashanah drifts earlier through September for a few years, then springs back into October. Across the whole range, it can fall anywhere from about 5 September to about 5 October — the same one-month window every festival occupies, because they are all governed by the same cycle.
Chanukah is the one people notice most, because its window straddles the Gregorian new year and the difference feels dramatic. It is the identical eleven-day drift as everything else.
One more piece, and it is the one that trips up newcomers to a Jewish calendar app. The Hebrew day runs from evening to evening, following the account in Bereishit in which evening precedes morning.
So the 15th of Nisan begins at nightfall on what a Gregorian calendar still calls the 14th. A festival “on Tuesday” starts on Monday evening. It is the same convention that makes Shabbat begin on Friday at candle lighting, and it is why every Hebrew date on a screen corresponds to two Gregorian dates, depending on the hour.
The fixed calendar is not perfect. Its mean year works out to 365 days, 5 hours, 55 minutes and about 25 seconds — some 6 minutes and 40 seconds longer than the mean tropical year. That surplus accumulates at roughly one day every 216 years.
The effect is that Pesach very gradually moves later relative to the astronomical spring. Over the centuries since the calculated calendar was fixed, it has slipped by well over a week. On a scale of many millennia this becomes a genuine problem, and the literature discussing it is substantial; on the scale of a lifetime it is invisible.
The last familiar feature has a historical rather than astronomical origin. When months were declared by the court in Jerusalem on the testimony of witnesses, the news travelled by signal fires and then by messengers. Distant communities could not know in time whether the preceding month had been given 29 or 30 days, and so could not be certain which day was the festival. Keeping two days resolved the doubt.
The fixed calendar removed the uncertainty, but the practice was retained, and yom tov sheni shel galuyot remains the practice outside Israel — one of the clearer cases of the calendar preserving the shape of a problem it no longer has.
All of this sits behind two lines of text in the Shabbat times panel. The Shabbat Screen dashboard shows the current parsha and upcoming festivals for your location, drawn from the Hebcal API, which implements the whole apparatus above — nineteen-year cycle, molad, postponements and year types included. The companion piece on how candle lighting and havdalah times are calculated covers the other half: not which day it is, but at what minute it starts.