The year that wanders

Twelve moons, 354 days, no seasons — the Islamic calendar refuses every fix. ← Calendar Contraptions

Most calendars have a trick for reconciling the moon and the sun: extra days, extra months, fudged weeks. The Islamic (Hijri) calendar has no trick. It runs twelve real lunar months — 354 or 355 days — and lets the year slide backwards through the seasons, about eleven days each year, a full circuit in about 33½. Summer Ramadan becomes winter Ramadan with nothing done about it, on purpose. It is one of the very few calendars in wide use that never intercalates at all — and it is still the machine that sets the fasting month and the pilgrimage for nearly two billion people. Below: the working arithmetic, the official Saudi table, and the story of an era that was started two months late, by committee.

Read a date

Where 1 Ramadan walks

The fast month makes the wander visible. Pick a month, a day and a stretch of years — the table shows the same Islamic date in each Hijri year, and how far the official Saudi table sits from the pure arithmetic.

Any Hijri year, taken apart

The tabular year is strict arithmetic: odd months get 30 days, even months 29, and eleven years in thirty give the twelfth month a 30th day. Type a year and the machine takes it apart.

From Hijri back to Gregorian

Why the year wanders

The mean lunar month — new moon to new moon — is 29.530587981 days. Twelve of them come to 354.367 days. The solar year is 365.242 days. Nothing can reconcile those two numbers with a whole day, and every other calendar in this corner quietly pays the difference somewhere. This one refuses to pay at all: it keeps the months honest and lets the year carry the debt, eleven days further back each year. After about 33.58 solar years — the debt is one full circuit of the seasons — the same month-name is back where it started. The folk rule says "34 Hijri years fit in 33 solar ones"; precisely, 34 Hijri years are 12,048.5 days against 12,053.0 days of 33 solar years, so 34 new years squeeze in with four and a half days to spare.

The wander shows in the month names themselves, which are pre-Islamic weather words. Rabīʿ means spring, the two Jumādā are named for frozen water, Ramaḍān for burning heat — names that only made sense while the months stayed in their seasons. Before Islam, the calendar was lunisolar: an intercalary month (the practice called nasīʾ, "postponement") was inserted now and then to pull the pilgrimage back into its season. The Qur'an forbids exactly that (9:36–37), in terms that read like a calendar reform written as theology: twelve months is the count "since the day He created the heavens and the earth", and shifting the sacred months around "is an increase in disbelief". Whether nasīʾ really was intercalation or just the postponement of ritual dates within the year is argued in the literature; either way, the prohibition froze the calendar to the moon and set the year wandering. A month-name has not meant weather since.

The arithmetic moon

What most converters compute — including every "today is 21 Rabīʿ al-ʾAwwal" box on the web — is not the sky. It is the tabular Islamic calendar: months strictly 30/29/30/29… with the leap day dropped onto the twelfth month in eleven years of every thirty. Where those eleven go is a rounding decision, and it has been argued for twelve centuries. The natural rule: each common year leaves a remainder of 11/30 of a day, and whenever the accumulated remainder exceeds half a day, take a leap day — that puts leap years at 2, 5, 7, 10, 13, 16, 18, 21, 24, 26 and 29 of each cycle. Let "half a day or more" be enough and 15 replaces 16; other schools moved it to 8, or 19, or 27. The variant matters for exactly one year in every thirty and one day in every 10,631 — but it matters.

The arithmetic is old and good: the 30-year cycle holds 10,631 days, a mean month of 29.530556 days — 29 d 12 h 44 m. The real mean month is 29.530587981. The machine loses 2.8 seconds a month, so it falls a full day behind the sky about once in 2,500 solar years. A cruder contraption, the 8-year cycle with leaps at 2, 5 and 8, was used in the Ottoman Empire and Southeast Asia: 2,835 days = exactly 405 weeks, so weekdays land on the same dates each cycle — convenient, and worth the extra inaccuracy. In the Dutch East Indies it was reset every 120 years to recover the better mean. And when Microsoft needed a "Kuwaiti algorithm" for Windows in the 1990s, described as derived from statistical analysis of Kuwaiti historical data, researchers promptly showed it was this same 8th-century tabular scheme — type IIa in the classifications — that Islamic astronomical tables have used since the 800s.

One more fork: the epoch. The classic back-computation puts 1 Muḥarram 1 on Friday 16 July 622 (Julian) — that is the civil epoch, the one this page defaults to. Some tables and software run the whole machine from Thursday 15 July 622 instead, one day earlier, and every date they output is one day later. The tidy historical check: the Farewell Sermon fell on 9 Dhū l-Ḥijja 10 AH, and the sources record it as a Friday, 6 March 632. Run the sermon date through the 15-July epoch and you get Friday, 6 March — the weekday the record asks for. Through the 16-July epoch you get Saturday. Nobody is wrong; the two machines are one day apart by construction, and they have been for 1,400 years.

The moon you have to see

Now the part no arithmetic can do. Religious months don't start when the arithmetic says; they start when a trustworthy witness sees the thin crescent (hilal) after sunset. Seen it? The new month starts that evening. Not seen — clouds, a sky still too bright, the moon setting before the sun gets far enough below the horizon? The old month runs to 30 days. The observational calendar therefore has month lengths with no pattern at all, and never strays more than about three days from the astronomical moon. The crescent only becomes visible some 17 hours after conjunction, and it favors the west — the moon sets later than the sun as you go westward, so Morocco can see tomorrow's moon tonight and announce a day before Mecca does. Countries disagree, by one and two days, routinely.

Most states run some official machinery on top. Saudi Arabia's administrative calendar, Umm al-Qura, is a precomputed table: before 1420 AH (1999) it asked only that the moon be 12 hours old at Riyadh's sunset; from 1420 to 1422, that moonset at Mecca came after sunset; since 1 Muḥarram 1423 (16 March 2002) it also requires the conjunction to happen before sunset — the moon must have passed the sun by then, even if the sky is still too bright to show the crescent. (In 2016 the Kingdom moved state salaries to the Gregorian calendar; the Hijri calendar stayed for the religious year.) Turkey's Diyanet precomputes its own calendar years ahead; its current rule wants the computed crescent above Ankara's horizon at sunset. Malaysia and Indonesia use moonset-after-sunset. Egypt asks for five minutes. A detailed analysis by calendar watchers concludes that what several countries say they do is impossible, and what they do is not what they say.

Whether calculation is even allowed is a live theological question: the majority position holds that seeing the moon is the point, while jurists like Aḥmad Muḥammad Shākir (1939) and Yūsuf al-Qaraḍāwī (2004), the Fiqh Council of North America (2006) and the European Council for Fatwa and Research (2007) have endorsed calculated calendars. France's council adopted a calculated calendar in 2013 — then followed the Saudi announcement anyway, dividing its own community. The machines on this page are the arithmetic; the sky keeps the final say.

Umar invents an era

The calendar counts from the Hijra, Muhammad's move from Mecca to Medina — but it was never counted at the time. For its first decade the community simply didn't number years; each had a name. The year of permission, the year of the order of fighting, the year of the trial, the year of congratulation on marriage, the year of the earthquake, the year of enquiring, the year of gaining victory, the year of equality, the year of exemption, the year of farewell. Around 17 AH (638 CE), the governor's official Abū Mūsā al-Ashʿarī wrote from Basra that letters from Umar carried no date at all, and he couldn't tell which instruction was newest. Umar convened his counsellors and invented an era: year one would be the year of the arrival in Medina. ʿUthmān then decided the year should start with Muḥarram — which quietly began the era two months before the migration itself, in Safar and Rabīʿ I. That is why "1 AH" begins in July 622 while the Hijra happened in September.

Where does "16 July 622" come from, then? Not from observation. Medieval Muslim astronomers ran the tabular machine backwards and let it print the epoch; al-Bīrūnī quotes the same date around the year 1000. The first surviving document actually dated in both Hijri and another calendar is a papyrus from Egypt, PERF 558, in AH 22 (643 CE) next to a Coptic date. (A coin cited from AH 17 is disputed.) Even the month order is argued: Twelver Shia tradition starts the year at Rabīʿ al-Awwal, the month of the migration, which shifts event years by one — the massacre of Karbala falls in 61 AH by the Sunni count and 60 by the Shia. And Libya under Gaddafi demonstrated in the 1970s that you can also just move the epoch to the Prophet's death and rename the summer months after Nasser and Hannibal; visitors reported people unsure what year it was.

Days that start at sunset

The Islamic day begins at sunset, not midnight — the evening comes first, as it does in the Jewish calendar. The weekday names are mostly ordinals: first (Sunday) through fifth (Thursday), then two exceptions — al-jumʿa, "the gathering", for the Friday prayer, and as-sabt, "the rest", for Saturday. Weekends follow suit unevenly: Friday–Saturday in Egypt and Saudi Arabia, Friday alone in Iran, Saturday–Sunday with a long Friday lunch break in Indonesia, Turkey, Pakistan and Morocco. When Umar's era began, the committee also had to pick which of the four sacred months — Muḥarram, Rajab, Dhū l-Qaʿda, Dhū l-Ḥijja — should open the year; the sacred four are marked below.

What this page doesn't do

Everything above is the tabular machine — pure arithmetic, exact, and up to two days off any real religious calendar. The Saudi table shown beside it is the official Umm al-Qura sequence (valid 1343–1500 AH, i.e. 1924–2077), where the months are astronomically fixed rather than 30/29 alternated; its year lengths drift between 353 and 356 days — only 95 of its 157 years here are the 354 the arithmetic promises — and it still isn't the announcement your mosque heard, which depends on sighting committees and weather. This page shows dates, not times: nothing here knows when the sun sets where you are, and days "beginning at sunset" are shown as whole days. Dates before the era are computed on the proleptic machine without ceremony, the same as the other pages here, and "today" means your device's own date. For when Ramadan actually starts where you live, the honest answer is: ask locally, in late Shaʿbān.