Hijri Leap Years Explained: 354 vs 355 Days and the 30-Year Cycle

“Leap year” usually means 29 February. The Hijri calendar has leap years too, but they work differently: there is no extra month and no fixed leap day, and depending on which version of the calendar you use, a different set of years counts as “leap”. This guide clears up what a Hijri leap year is and how to tell whether a given year has 354 or 355 days.

Why a lunar calendar needs leap days

A Hijri month follows the moon, whose average cycle is 29.530589 days. Twelve of those make 354.367 days per year. Since a calendar has to use whole days, a year is either 354 or 355 days. If every year had 354 days, the calendar would fall behind the moon by about 0.367 days a year — roughly one day every three years — and after a few decades the “first of the month” would no longer coincide with the new crescent.

So some years get an extra day to absorb that fraction. Those 355-day years are the Hijri equivalent of leap years, called kabisa (كبيسة) in Arabic. The 354-day years are basita (بسيطة), “simple”.

Note the key difference from the Gregorian calendar: Hijri leap years exist to keep the calendar in step with the moon, not with the sun. The Hijri year still moves about 11 days a year through the seasons either way.

The tabular calendar: a fixed 30-year cycle

The arithmetic (tabular) Islamic calendar uses a simple rule. It treats the year as twelve months that alternate 30 and 29 days — Muharram 30, Safar 29, Rabi’ al-Awwal 30, and so on — giving 354 days. In a leap year, the last month, Dhul-Hijjah, gets a 30th day, making 355.

Over a 30-year cycle, 11 years are leap years. That gives an average year of

(19 × 354 + 11 × 355) ÷ 30 = 354.367 days

which matches the moon almost exactly — the cycle drifts by only about one day in 2,500 years.

Which years are leap years?

In the most widely used version (the one in most software, including this site), the leap years are those that fall at these positions in the 30-year cycle:

2, 5, 7, 10, 13, 16, 18, 21, 24, 26, 29

To find a year’s position, divide the Hijri year by 30 and take the remainder. For example:

Year	Year ÷ 30, remainder	Tabular leap year?
1445 AH	5	Yes — 355 days
1446 AH	6	No — 354 days
1447 AH	7	Yes — 355 days
1448 AH	8	No — 354 days
1449 AH	9	No — 354 days
1450 AH	10	Yes — 355 days

There is a tidy way to express the same rule as a formula: a year y is a tabular leap year when (14 + 11 × y) mod 30 is less than 11. Programmers will recognise this from the standard civil Islamic calendar algorithm.

Other versions of the cycle

Historically, astronomers proposed slightly different patterns. The best-known alternatives place a leap year at position 15 instead of 16, or use other sets entirely. The differences are small — at most a day in particular years — but they explain why two old reference tables can disagree.

Month lengths in a tabular year

Here is how the days are distributed across a tabular year. The only month that changes is Dhul-Hijjah.

Month	Common year	Leap year
Muharram	30	30
Safar	29	29
Rabi’ al-Awwal	30	30
Rabi’ al-Thani	29	29
Jumada al-Ula	30	30
Jumada al-Akhirah	29	29
Rajab	30	30
Sha’ban	29	29
Ramadan	30	30
Shawwal	29	29
Dhul-Qa’dah	30	30
Dhul-Hijjah	29	30
Total	354	355

One consequence: in the tabular calendar, Ramadan always has 30 days. In real life, and on the Umm al-Qura calendar, Ramadan has 29 days about as often as 30 — Ramadan 1448 is expected to have 29 on Umm al-Qura.

Umm al-Qura: leap years without a pattern

Saudi Arabia’s Umm al-Qura calendar does not use a cycle. Instead, each month’s start is fixed by astronomical criteria: broadly, a new month begins if, on the 29th evening, the astronomical new moon has occurred before sunset and the moon sets after the sun as seen from Makkah. Each month comes out as 29 or 30 days depending on the real moon.

The year length is simply whatever the twelve months add up to: sometimes 354, sometimes 355. There is no fixed list of leap years, and the “extra” day can fall in any month, not just Dhul-Hijjah.

The two calendars do not always agree on which years are long:

Year	Umm al-Qura	Tabular
1447 AH	355 days	355 days
1448 AH	355 days	354 days
1449 AH	354 days	354 days

So 1448 AH is a 355-day year on Umm al-Qura, but a 354-day year on the tabular calendar. Both are correct within their own rules.

Leap years in a sighting-based calendar

In communities that start each month by local sighting, there is no such thing as a planned leap year. Each month is 29 days if the crescent is seen on the 29th evening and 30 days if it is not. The year ends up with however many days the twelve months contain — usually 354 or 355, and very occasionally 353 or 356 when an unusual run of sightings occurs.

This is one reason calculated calendars exist: they let you know the length of a year in advance, which matters for contracts, salaries and planning.

Does a Hijri leap year change anything for worship?

Very little. The extra day changes:

• Whether next year’s dates come 10 or 11 days earlier. After a 355-day year, Hijri dates fall 10 days earlier in the next Gregorian year instead of 11.
• The length of one month. In the tabular calendar, Dhul-Hijjah has 30 days in a leap year — which means the 13th of Dhul-Hijjah, the last day of Tashreeq, is not the second-to-last day of the year as it would otherwise be.

It does not change the date of any occasion within the year: Ramadan still begins on 1 Ramadan, Eid al-Adha is still 10 Dhul-Hijjah.

Leap years and anniversaries

What about someone born on 30 Dhul-Hijjah? This is the Hijri equivalent of a 29 February birthday. In years where Dhul-Hijjah has only 29 days, the usual convention is to mark the anniversary on 29 Dhul-Hijjah or 1 Muharram, just as Gregorian leap-day birthdays are marked on 28 February or 1 March. Because month lengths vary in every Hijri calendar, any 30th of a month can fall in a 29-day month in a later year — so this situation is more common than in the Gregorian calendar.

How to check any year quickly

1. For the tabular calendar, divide the year by 30 and check the remainder against the list 2, 5, 7, 10, 13, 16, 18, 21, 24, 26, 29.
2. For Umm al-Qura, add up the month lengths for that year — the Hijri calendar 1448 page lists each month’s start, end and number of days for both methods.
3. For your local calendar, you can only know after the year ends, because each month depends on the sighting.

Summary

• A Hijri leap year has 355 days instead of 354.
• The tabular calendar uses a fixed 30-year cycle with 11 leap years, adding the day to Dhul-Hijjah.
• The Umm al-Qura calendar has no fixed cycle; month lengths follow the real moon.
• 1448 AH is 355 days on Umm al-Qura and 354 on the tabular calendar; 1449 AH is 354 on both.
• Leap years only decide whether Islamic dates shift 10 or 11 days in the next Gregorian year.