The Short Answer

Every so often a Gregorian year contains the same Eid twice. The most recent examples were 2000 (two Eid al-Fitr) and 2006 (two Eid al-Adha). The next are:

Eid al-Fitr twice: 2033, then 2065.
Eid al-Adha twice: 2039, then 2071.

These dates come from the Umm al-Qura calendar table, the same one that powers the calendar page. They are calendar dates, not announcements. Real Eids are set by sighting or by each country's rule and can differ by a day, so a few of the years below sit close enough to the edge that one country could have two while its neighbour has one. The table later in the post says which.

Why It Happens

A Hijri year is 12 lunar months, which adds up to 354 or 355 days. Over 1420 to 1500 AH the Umm al-Qura years average 354.36 days. A Gregorian year is 365.2425 days on average. Each Hijri date therefore lands about 11 days earlier (10.9 on average) in the Gregorian calendar than it did the year before. For the background on why the lunar year is shorter, see how the Islamic lunar calendar works.

Now follow one date, say 1 Shawwal, down the years. It slides earlier by about 11 days each time. Eventually it falls in the first days of January. The next occurrence is 354 or 355 days later, and a Gregorian year has 365 days (366 in a leap year). If the first one fell on 1 to 11 January, the next one is still inside the same year. A date on 11 January plus 354 days is 31 December. That is the window: about the first 11 days of January.

After that the date wraps around to the end of the previous December and starts sliding earlier through the year again. The cycle takes 365.2425 / 10.876 = 33.6 Hijri years, which is about 32.6 Gregorian years. In practice the double years for any one date are 32 or 33 years apart. We checked this on the tabular Hijri calendar over 1,501 Gregorian years (700 to 2200): every date has 46 double years, and the gaps are always 32 or 33.

The Drift, Drawn

The chart below follows Eid al-Fitr and Eid al-Adha for Hijri years 1420 to 1500 (2000 to 2077). The vertical position is the date inside the Gregorian year. Each Eid slides up the chart by about 11 days a year, then jumps from the top (early January) to the bottom (late December) and starts again. The ringed points are the double years.

The Full Table

Date	Year	First date	Second date	Source
Eid al-Fitr (1 Shawwal)	2000	8 January	27 December	Umm al-Qura
	2033	2 January	23 December	Umm al-Qura
	2065	8 January	28 December	Umm al-Qura
	2098	4 January	25 December	Tabular model
Eid al-Adha (10 Dhul-Hijjah)	2006	10 January	31 December	Umm al-Qura
	2039	5 January	26 December	Umm al-Qura
	2071	11 January	31 December	Umm al-Qura
	2104	9 January	28 December	Tabular model
1 Ramadan	1997	10 January	30 December	Umm al-Qura
	2030	5 January	26 December	Umm al-Qura
	2063	1 January	21 December	Umm al-Qura
	2095	7 January	28 December	Tabular model
1 Muharram (Hijri New Year)	2008	10 January	29 December	Umm al-Qura
	2041	4 January	24 December	Umm al-Qura
	2073	9 January	30 December	Umm al-Qura
	2106	7 January	27 December	Tabular model

Two cautions on reading it.

Dates after 2077 are a model. The Umm al-Qura table we use ends at 1500 AH (2077). Later rows come from the arithmetic (tabular) Hijri calendar, which repeats a fixed 30-year cycle. Over 1400 to 1500 AH it differs from Umm al-Qura by up to 2 days on these four dates, and it can differ from a real sighting by a day or two as well. Treat 2095 to 2106 as "roughly then", not as a forecast.

Borderline years can flip. A year only counts if both dates fall inside it. 2006 (10 January and 31 December) and 2071 (11 January and 31 December) sit right at the edge: one day later at the end, and the second Eid is on 1 January of the next year. We saw this when we cross-checked with a second implementation, the Islamic Umm al-Qura calendar built into JavaScript's Intl.DateTimeFormat. It agrees with the table for every date in 1420 to 1451 AH (to 2030), including 2000 and 2006. From 1452 AH on it is one day later on many dates, including 2033 Eid al-Fitr (3 January instead of 2 January), 2065 Eid al-Fitr (29 December instead of 28) and 2071 Eid al-Adha (12 January and 1 January 2072, which moves that double year to 2072). The years 2033, 2039 and 2065 are double in both, so they are the safer ones. 2071 is the one to hold loosely.

Never Zero, Never Three

Look down the table and you will notice something: in every Gregorian year the number of Eid al-Fitr (or of any other Hijri date) is one or two. It is never none and never three.

We checked this by scanning the tabular calendar across 1,501 Gregorian years (700 to 2200). For each of the four dates, no year had zero and no year had three or more. The reason is short:

Never zero. Two consecutive occurrences of a date are one Hijri year apart: 354 or 355 days. To skip a whole Gregorian year, one occurrence would have to fall on 31 December and the next on 1 January of the year after, a gap of more than 365 days. A Hijri year is always shorter than that, so every Gregorian year catches at least one.
Never three. Three occurrences need two gaps in a row inside one year, at least 708 days. A Gregorian year has 365 or 366.

So the count per year is simply 1 almost always, and 2 in the rare years when the date is parked in the first 11 days of January.

Eid al-Fitr and Eid al-Adha Are Six Years Apart

The double Eid al-Adha always follows the double Eid al-Fitr by six years in the table: 2000 then 2006, 2033 then 2039, 2065 then 2071 (and in the model, 2098 then 2104). The reason is the gap inside one Hijri year. Eid al-Fitr is 1 Shawwal; Eid al-Adha is 10 Dhul-Hijjah, 68 days later in the Umm al-Qura table for 1420, 1454 and 1487 AH. At 10.9 days a year, the date needs about six years of drift to slide back by that much (6 x 10.9 = 65 days), and the 11-day window absorbs the remaining 3.

What This Means in Practice

Fasting Ramadan twice in one Gregorian year. 1 Ramadan has its own double years: 2030 (5 January and 26 December) and 2063 (1 January and 21 December). In those years Ramadan begins twice on the Gregorian calendar.

Two Hijri New Years. 1 Muharram is double in 2008 (10 January and 29 December) and 2041 (4 January and 24 December).

What 2000 and 2006 looked like. In the Umm al-Qura table, Eid al-Fitr 1420 AH was 8 January 2000 and Eid al-Fitr 1421 AH was 27 December 2000. Eid al-Adha 1426 AH was 10 January 2006 and Eid al-Adha 1427 AH was 31 December 2006. Public listings agree on the 2006 dates: Calendarific's Saudi Arabia page for 2006 shows Eid al-Adha on 10 January and 31 December. For Eid al-Fitr in January 2000 the date was not the same everywhere: a Bangladeshi newspaper preview expected 9 January, while another listing gave 8 January for Oman. That is the normal pattern. Countries announce their own dates, and a year that is double in one place may be a day away from double in another.

Edge cases. In the Umm al-Qura table, 1 Ramadan 2063 falls on 1 January itself, and Eid al-Adha 2071 falls on 31 December. The Intl calendar puts that Eid al-Adha on 1 January 2072 instead. In borderline years like these, one country's Eid can be on 31 December while another's is on 1 January.

Frequently Asked Questions

Is this a leap-year thing?

No. A leap year in the Gregorian calendar adds one day to February, which only changes where the window sits by a day. The cause is that 12 lunar months are about 11 days shorter than a solar year. The Hijri calendar has its own leap years (a 355-day year in the tabular model), but they are a small correction to the same drift.

Will Eid fall on 1 January someday?

Yes, sometimes. Each Hijri date visits every day of the Gregorian year over the centuries. In the Umm al-Qura table, 1 Ramadan falls on 1 January in 2063. Whether an Eid does depends on the date and on how each country announces it, so there is no single year to name.

Why not 2032 or 2038?

Because the first date of the year is just outside the window. Eid al-Fitr 2032 is on 14 January in the Umm al-Qura table, three days past the 11 January edge, and the next one is on 2 January 2033. Likewise Eid al-Adha is on 16 January 2038 and then 5 January 2039. Only if the January 2033 date were two days earlier (31 December 2032) would 2032 have two, which is why the early edge matters too.

How rare is it?

For any one of the four dates, about once every 32 to 33 years. The four dates cluster: in the Umm al-Qura table the double years are 1997, 2000, 2006 and 2008, then 2030, 2033, 2039 and 2041, then 2063, 2065, 2071 and 2073. Each cluster spans about 11 years, followed by about 20 quiet years.

Do all countries get two?

Not always. Countries' own dates differ by a day or so, and a year only counts as double for a country whose two dates both fall inside it. Countries that follow Umm al-Qura get exactly the dates above. Countries that announce Eid after a local sighting can be a day later, and in a borderline year (2006, 2071) that can push the second Eid into the following January.

References

Umm al-Qura dates: the @umalqura/core table for 1300 to 1500 AH, cross-checked against the Islamic Umm al-Qura calendar in JavaScript's Intl.DateTimeFormat (they agree to 1451 AH and differ by one day on many dates afterwards).
Calendarific. Saudi Arabia public holidays 2006. https://calendarific.com/holidays/2006/sa
Calendarific. Oman public holidays 2000. https://calendarific.com/holidays/2000/om
The Daily Star (Bangladesh). Viva 2000. https://www.thedailystar.net/news/viva-2000

Which Year Will Have Two Eid al-Fitr or Two Eid al-Adha?