Leap year starting on Sunday

A leap year starting on Sunday is any year with 366 days (i.e. it includes 29 February) that begins on Sunday, 1 January, and ends on Monday, 31 December. Its dominical letters hence are AG. The most recent year of such kind was 2012 and the next one will be 2040 in the Gregorian calendar^[1] or, likewise 2024 and 2052 in the obsolete Julian calendar.

This is the only leap year with three occurrences of Friday the 13th: those three in this leap year occur three months (13 weeks) apart: in January, April, and July. Common years starting on Thursday share this characteristic, in the months of February, March, and November.

In this type of year, all dates (except 29 February) fall on their respective weekdays the maximal 58 times in the 400 year Gregorian calendar cycle. Leap years starting on Friday share this characteristic. Additionally, these types of years are the only ones which contain 54 different calendar weeks (2 partial, 52 in full) in areas of the world where Monday is considered the first day of the week.

Calendars

Calendar for any leap year starting on Sunday,
presented as common in many English-speaking areas

ISO 8601-conformant calendar with week numbers for
any leap year starting on Sunday (dominical letter AG)

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	January
52							01
01	02	03	04	05	06	07	08
02	09	10	11	12	13	14	15
03	16	17	18	19	20	21	22
04	23	24	25	26	27	28	29
05	30	31

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	February
05			01	02	03	04	05
06	06	07	08	09	10	11	12
07	13	14	15	16	17	18	19
08	20	21	22	23	24	25	26
09	27	28	29

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	March
09				01	02	03	04
10	05	06	07	08	09	10	11
11	12	13	14	15	16	17	18
12	19	20	21	22	23	24	25
13	26	27	28	29	30	31

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	April
13							01
14	02	03	04	05	06	07	08
15	09	10	11	12	13	14	15
16	16	17	18	19	20	21	22
17	23	24	25	26	27	28	29
18	30

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	May
18		01	02	03	04	05	06
19	07	08	09	10	11	12	13
20	14	15	16	17	18	19	20
21	21	22	23	24	25	26	27
22	28	29	30	31

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	June
22					01	02	03
23	04	05	06	07	08	09	10
24	11	12	13	14	15	16	17
25	18	19	20	21	22	23	24
26	25	26	27	28	29	30

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	July
26							01
27	02	03	04	05	06	07	08
28	09	10	11	12	13	14	15
29	16	17	18	19	20	21	22
30	23	24	25	26	27	28	29
31	30	31

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	August
31			01	02	03	04	05
32	06	07	08	09	10	11	12
33	13	14	15	16	17	18	19
34	20	21	22	23	24	25	26
35	27	28	29	30	31

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	September
35						01	02
36	03	04	05	06	07	08	09
37	10	11	12	13	14	15	16
38	17	18	19	20	21	22	23
39	24	25	26	27	28	29	30

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	October
40	01	02	03	04	05	06	07
41	08	09	10	11	12	13	14
42	15	16	17	18	19	20	21
43	22	23	24	25	26	27	28
44	29	30	31

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	November
44				01	02	03	04
45	05	06	07	08	09	10	11
46	12	13	14	15	16	17	18
47	19	20	21	22	23	24	25
48	26	27	28	29	30

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	December
48						01	02
49	03	04	05	06	07	08	09
50	10	11	12	13	14	15	16
51	17	18	19	20	21	22	23
52	24	25	26	27	28	29	30
01	31

Applicable years

Gregorian Calendar

Leap years that begin on Sunday, along with those starting on Friday, occur most frequently: 15 of the 97 (≈ 15.46%) total leap years in a 400-year cycle of the Gregorian calendar. Thus, their overall occurrence is 3.75% (15 out of 400).

Gregorian leap years starting on Sunday^[1]
Decade	1st	2nd	3rd	4th	6th	7th	9th	10th
16th century	prior to first adoption (proleptic)						1584
17th century		1612		1640		1668		1696
18th century	1708			1736		1764		1792
19th century	1804			1832	1860		1888
20th century			1928		1956		1984
21st century		2012		2040		2068		2096
22nd century	2108			2136		2164		2192
23rd century	2204			2232	2260		2288
24th century			2328		2356		2384
25th century		2412		2440		2468		2496
26th century	2508			2536		2564		2592
27th century	2604			2632	2660		2688

400-year cycle
0–99	12	40	68	96
100–199	108	136	164	192
200–299	204	232	260	288
300–399	328	356	384

Julian Calendar

Like all leap year types, the one starting with 1 January on a Sunday occurs exactly once in a 28-year cycle in the Julian calendar, i.e., in 3.57% of years. As the Julian calendar repeats after 28 years, it will also repeat after 700 years, i.e., 25 cycles. The formula gives the year's position in the cycle ((year + 8) mod 28) + 1).

Julian leap years starting on Sunday
Decade	1st	2nd	3rd	4th	5th	6th	7th	8th	9th	10th
15th century	1408			1436			1464			1492
16th century		1520			1548			1576
17th century	1604			1632		1660			1688
18th century		1716			1744			1772		1800
19th century			1828			1856			1884
20th century		1912		1940			1968			1996
21st century			2024			2052		2080
22nd century	2108			2136			2164			2192

Holidays

International

- Valentine's Day falls on a Tuesday
- The leap day (February 29) falls on a Wednesday
- World Day for Grandparents and the Elderly falls on its earliest possible date, July 22
- Halloween falls on a Wednesday
- Christmas Day falls on a Tuesday

Roman Catholic Solemnities

- Epiphany falls on a Friday
- Candlemas falls on a Thursday
- Saint Joseph's Day falls on a Monday
- The Annunciation of Jesus falls on a Sunday
- The Nativity of John the Baptist falls on a Sunday
- The Solemnity of Saints Peter and Paul falls on a Friday
- The Transfiguration of Jesus falls on a Monday
- The Assumption of Mary falls on a Wednesday
- The Exaltation of the Holy Cross falls on a Friday
- All Saints' Day falls on a Thursday
- All Souls' Day falls on a Friday
- The Feast of Christ the King falls on November 25 (or on October 28 in versions of the calendar between 1925 and 1962)
- The First Sunday of Advent falls on December 2
- The Immaculate Conception falls on a Saturday
- Gaudete Sunday falls on December 16
- Rorate Sunday falls on December 23

Australia and New Zealand

- Australia Day falls on a Thursday
- Waitangi Day falls on a Monday
- Daylight saving ends on its earliest possible date, April 1
- ANZAC Day falls on a Wednesday
- Mother's Day falls on May 13
- Father's Day falls on September 2
- Daylight saving begins on its latest possible date, September 30 in New Zealand and October 7 in Australia – this is the only leap year where the period of standard time over the winter months lasts 26 weeks in New Zealand and 27 weeks in Australia (in all other leap years, it lasts only 25 weeks in New Zealand and 26 weeks in Australia)

References

^ ^a ^b Robert van Gent (2017). "The Mathematics of the ISO 8601 Calendar". Utrecht University, Department of Mathematics. Retrieved 20 July 2017.

[math-1] Robert van Gent (2017). "The Mathematics of the ISO 8601 Calendar". Utrecht University, Department of Mathematics. Retrieved 20 July 2017.

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