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
January Su Mo Tu We Th Fr Sa 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31	February Su Mo Tu We Th Fr Sa 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29	March Su Mo Tu We Th Fr Sa 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31	April Su Mo Tu We Th Fr Sa 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
May Su Mo Tu We Th Fr Sa 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31	June Su Mo Tu We Th Fr Sa 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30	July Su Mo Tu We Th Fr Sa 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31	August Su Mo Tu We Th Fr Sa 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
September Su Mo Tu We Th Fr Sa 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30	October Su Mo Tu We Th Fr Sa 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31	November Su Mo Tu We Th Fr Sa 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30	December Su Mo Tu We Th Fr Sa 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

ISO 8601-conformant calendar with week numbers for any leap year starting on Sunday (dominical letter AG)
January Wk Mo Tu We Th Fr Sa Su 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	February Wk Mo Tu We Th Fr Sa Su 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	March Wk Mo Tu We Th Fr Sa Su 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	April Wk Mo Tu We Th Fr Sa Su 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
May Wk Mo Tu We Th Fr Sa Su 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	June Wk Mo Tu We Th Fr Sa Su 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	July Wk Mo Tu We Th Fr Sa Su 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	August Wk Mo Tu We Th Fr Sa Su 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
September Wk Mo Tu We Th Fr Sa Su 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	October Wk Mo Tu We Th Fr Sa Su 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	November Wk Mo Tu We Th Fr Sa Su 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	December Wk Mo Tu We Th Fr Sa Su 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	5th	6th	7th	8th	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)

British Isles

• • Saint David's Day falls on a Thursday
  • Mother's Day falls on March 4, March 11, March 18, March 25 or April 1
  • Saint Patrick's Day falls on a Saturday
  • Daylight saving begins on its earliest possible date, March 25
  • Saint George's Day falls on a Monday
  • Father's Day falls on June 17
  • Orangeman's Day falls on a Thursday
  • Daylight saving ends on October 28
  • Guy Fawkes Night falls on a Monday
  • Saint Andrew's Day falls on a Friday

Canada

• • Daylight saving begins on March 11
  • Mother's Day falls on May 13
  • Victoria Day falls on May 21
  • Father's Day falls on June 17
  • Canada Day falls on a Sunday
  • Labour Day falls on September 3
  • Thanksgiving Day falls on its earliest possible date, October 8
  • Daylight saving ends on November 4

United States

• • Martin Luther King Jr. Day falls on January 16
  • President's Day falls on February 20
  • Daylight saving begins on March 11
  • Mother's Day falls on May 13
  • Memorial Day falls on May 28
  • Father's Day falls on June 17
  • Juneteenth falls on a Tuesday
  • Independence Day falls on a Wednesday
  • Labor Day falls on September 3
  • Grandparents' Day falls on September 9
  • Columbus Day falls on its earliest possible date, October 8
  • Daylight saving ends on November 4
  • Thanksgiving Day falls on its earliest possible date, November 22

References

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