Guide · 7 min read
Leap years in the Hijri calendar
In the Gregorian calendar a leap year means one thing: a 29th of February. The Hijri calendar has leap years too, but they look nothing like that. A Hijri leap year is simply a year of 355 days instead of 354 - one more day across the whole year, no extra month, and no attempt to catch up with the seasons. And unlike the Gregorian rule, which everyone shares, the two calendar systems this site implements do not even agree on which years are the long ones.
This guide explains what the extra day is for, the exact 30-year rule the tabular calendar uses to place it, why the Umm al-Qura calendar follows no rule at all, and what the disagreement between them means when you convert a date. The worked dates below come from the Umm al-Qura calendar, the same engine behind the converter on this site; they are civil calculations and can differ by about a day from a locally sighted date.
A leap year with no leap day in February
A common Hijri year is 354 days and a leap year is 355. That is the entire difference. There is no intercalary month, ever: the Hijri year is always exactly twelve lunar months, and the leap arrangements only decide whether one of those months runs to 30 days instead of 29.
The Umm al-Qura calendar shows what a long year looks like in practice. 1447 AH began on 26 June 2025 and ended on 15 June 2026, a span of 355 days, while 1446 AH before it ran 354 days, from 7 July 2024 to 25 June 2025. Every Hijri year page on this site states which kind of year it is and lists the length of each month, so the extra day is easy to find.
Crucially, the leap year does not stop the calendar drifting against the seasons, and it is not meant to. Even a 355-day year is about ten days short of a solar year, which is why every Hijri date arrives earlier each Gregorian year. The leap day serves the Moon, not the Sun.
Why the calendar needs a leap day at all
A lunar month - one full cycle of the Moon's phases - lasts about 29.53 days. Since calendar months need whole days, the natural scheme is to alternate 30-day and 29-day months, which averages 29.5 days per month and gives a year of exactly 354 days.
But 29.5 is slightly too small. Twelve true lunar months come to about 354.37 days, so a calendar of permanent 354-day years would slip behind the Moon by about a third of a day every year - roughly eleven days per thirty years. After a century the calendar months would visibly disagree with the sky.
The fix is the same trick the Gregorian calendar uses for the Sun, applied to the Moon: add a day every so often. Eleven extra days spread over each thirty-year span cancel the drift almost perfectly. That is the origin of the number that defines the arithmetic calendar: 11 leap years in every 30.
The tabular rule: 11 long years in every 30
The tabular (arithmetic) Islamic calendar makes the fix a fixed rule. Years are grouped into repeating 30-year cycles of 10,631 days, and within each cycle the years in positions 2, 5, 7, 10, 13, 16, 18, 21, 24, 26 and 29 are leap years. In code the test is a one-liner, the same one this site's engine uses: a year is a leap year when (11 x year + 14) mod 30 is less than 11.
To place a year, divide by 30 and keep the remainder. 1447 AH is 48 whole cycles plus 7, and position 7 is on the list, so tabular 1447 is a 355-day year. 1448 leaves remainder 8, which is not on the list, so it is a common year.
In the tabular calendar the extra day always lands in the same place: Dhu al-Hijjah, the twelfth and final month, runs to 30 days in a leap year instead of 29. And because the cycle positions are spaced two or three years apart, the tabular calendar never has two leap years in a row.
The appeal of all this is that it needs no data and no observation. The rule reaches any year, past or future, which is why this site uses the tabular engine wherever its Umm al-Qura table ends.
Umm al-Qura has no leap rule at all
The Umm al-Qura calendar - the official civil calendar of Saudi Arabia and the default engine on this site - does not decide leap years by formula. Its month lengths are published in official tables, and a year is long or short simply because its twelve published months add up to 355 days or 354. A common year has six 30-day months; a long year has seven.
That produces patterns the tabular rule can never make. In the Umm al-Qura table, 1447 and 1448 AH are both 355-day years, back to back, which is impossible under the 30-year cycle. Stranger still, Umm al-Qura 1447 is a long year whose Dhu al-Hijjah has only 29 days - its seventh 30-day month sits earlier in the year - while 1445 has a 30-day Dhu al-Hijjah inside an ordinary 354-day year. In Umm al-Qura the extra day is wherever the table puts it.
Put the two systems side by side and the disagreement is constant. Over 1444 to 1451 they agree on just one leap year:
| Hijri year | Umm al-Qura | Tabular rule |
|---|---|---|
| 1444 AH | 354 days | 354 days |
| 1445 AH | 354 days | 355 days (leap) |
| 1446 AH | 354 days | 354 days |
| 1447 AH | 355 days (leap) | 355 days (leap) |
| 1448 AH | 355 days (leap) | 354 days |
| 1449 AH | 354 days | 354 days |
| 1450 AH | 354 days | 355 days (leap) |
| 1451 AH | 354 days | 354 days |
What the disagreement means in practice
The two systems track the same Moon, so they cannot drift apart for long: across 1440-1469 AH each has exactly 11 long years. But they hand out the extra days in different years and different months, and that is a large part of why the same Gregorian date can convert to two Hijri dates a day apart, and why the same Hijri date can land on two different Gregorian days. A Hijri date quoted without naming its calendar is ambiguous by about a day.
The stakes are not academic, because Dhu al-Hijjah - the month whose length the systems argue over - contains the Hajj season, the Day of Arafah on the 9th and Eid al-Adha on the 10th. Any date this site computes for those days is a civil calculation, not an announcement: it can differ by about a day from a local crescent sighting, and the day a community observes follows its local religious authority.
The guide on Umm al-Qura, tabular and moon-sighting calendars covers the wider comparison; the point here is narrower. When two sources disagree about a Hijri date, checking which years each treats as long is very often the whole explanation.
Where to look a year up
You never need to run the cycle arithmetic yourself. Every Hijri year page on this site states whether the year has 354 or 355 days, when it begins and ends in the Gregorian calendar, and how long each of its twelve months is - compare the page for 1447 AH, a long year, with the page for 1446 AH, a common one.
The converter shows any single date under Umm al-Qura and both tabular variants side by side, which makes a one-day disagreement visible instead of mysterious. And for the bigger picture of why the whole calendar slides through the Gregorian year, start with the guide on how the Islamic calendar works.
Frequently asked questions
Does the Islamic calendar have leap years?
Yes, but not with an extra day in February. A Hijri leap year is a year of 355 days instead of the usual 354; the year still has exactly twelve lunar months, and the extra day simply makes one more of those months 30 days long. Its purpose is to keep the calendar months aligned with the Moon's actual cycle of about 29.53 days, not to correct for the seasons.
Which years are leap years in the tabular Islamic calendar?
The tabular calendar repeats a 30-year cycle in which years at positions 2, 5, 7, 10, 13, 16, 18, 21, 24, 26 and 29 are leap years - 11 long years per cycle. Equivalently, a year is a leap year when (11 x year + 14) mod 30 is less than 11. For example, 1447 AH falls at position 7 of its cycle, so it is a 355-day year under the tabular rule.
Where does the extra day go in a Hijri leap year?
In the tabular calendar it always goes to Dhu al-Hijjah, the twelfth month, which runs 30 days instead of 29. The Umm al-Qura calendar has no fixed slot: a year is long because its published month lengths add up to 355, and the seventh 30-day month can sit anywhere in the year. Umm al-Qura 1447 AH is a 355-day year whose Dhu al-Hijjah still has only 29 days.
Why do Umm al-Qura and the tabular calendar disagree about which years are leap years?
Because they answer the question differently. The tabular calendar applies one arithmetic rule forever, while Umm al-Qura publishes each year's month lengths in official tables, so its long years follow no formula - it can even have two 355-day years in a row, as it does in 1447 and 1448 AH. Both average 11 long years per 30, but rarely in the same years, which is a major reason the two systems can sit a day apart.