Leap year starting on Thursday

Type of year DC on a solar calendar

A leap year starting on Thursday is any year with 366 days (i.e. it includes 29 February) that begins on Thursday 1 January, and ends on Friday 31 December. Its dominical letters hence are DC. The most recent year of such kind was 2004 and the next one will be 2032 in the Gregorian calendar[1] or, likewise, 2016 and 2044 in the obsolete Julian calendar.

This is the only year in which February has five Sundays, as the leap day adds that extra Sunday.

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

Any leap year that starts on Monday, Wednesday or Thursday has two Friday the 13ths: those two in this leap year occur in February and August.

## Calendars

[edit]

Calendar for any leap year starting on Thursday,
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 Thursday (dominical letter DC)

|  | January  |

|
|

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

|  | February  |

|
|

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

|  | March  |

|
|

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

|  | April  |

|
|

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

|  | May  |

|
|

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

|
|

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

|  | July  |

|
|

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

|  | August  |

|
|

Wk  | Mo  | Tu  | We  | Th  | Fr  | Sa  | Su
31  |  |  |  |  |  |  | 01
32  | 02 | 03 | 04 | 05 | 06 | 07 | 08
33  | 09 | 10 | 11 | 12 | 13 | 14 | 15
34  | 16 | 17 | 18 | 19 | 20 | 21 | 22
35  | 23 | 24 | 25 | 26 | 27 | 28 | 29
36  | 30 | 31  |
|  | September  |

|
|

Wk  | Mo  | Tu  | We  | Th  | Fr  | Sa  | Su
36  |  |  | 01 | 02 | 03 | 04 | 05
37  | 06 | 07 | 08 | 09 | 10 | 11 | 12
38  | 13 | 14 | 15 | 16 | 17 | 18 | 19
39  | 20 | 21 | 22 | 23 | 24 | 25 | 26
40  | 27 | 28 | 29 | 30 |  |

|  | October  |

|
|

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

|  | November  |

|
|

Wk  | Mo  | Tu  | We  | Th  | Fr  | Sa  | Su
45  | 01 | 02 | 03 | 04 | 05 | 06 | 07
46  | 08 | 09 | 10 | 11 | 12 | 13 | 14
47  | 15 | 16 | 17 | 18 | 19 | 20 | 21
48  | 22 | 23 | 24 | 25 | 26 | 27 | 28
49  | 29 | 30 |  |

|  | December  |

|
|

Wk  | Mo  | Tu  | We  | Th  | Fr  | Sa  | Su
49  |  |  | 01 | 02 | 03 | 04 | 05
50  | 06 | 07 | 08 | 09 | 10 | 11 | 12
51  | 13 | 14 | 15 | 16 | 17 | 18 | 19
52  | 20 | 21 | 22 | 23 | 24 | 25 | 26
53  | 27 | 28 | 29 | 30 | 31  |

## Applicable years

[edit]

### Gregorian Calendar

[edit]

Leap years that begin on Thursday, along with those starting on Monday and Saturday, occur least frequently: 13 out of 97 (≈ 13.402%) total leap years in a 400-year cycle of the Gregorian calendar. Their overall occurrence is thus 3.25% (13 out of 400).

For this kind of year, the corresponding ISO year has 53 weeks, and the ISO week 10 (which begins March 1) and all subsequent ISO weeks occur earlier than in all other years, and exactly one week earlier than common years starting on Friday, for example, June 20 falls on week 24 in common years starting on Friday, but on week 25 in leap years starting on Thursday, despite falling on Sunday in both types of year. That means that moveable holidays may occur one calendar week later than otherwise possible, e.g. Gregorian Easter Sunday in week 17 in years when it falls on April 25 and which are also leap years, falling on week 16 in common years.[2]

Gregorian leap years starting on Thursday[1] Decade  | 1st | 2nd | 3rd | 4th | 5th | 6th | 7th | 8th | 9th | 10th

|
|
|
|
|
|
|
|
|
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17th century | 1604 |  |  | 1632 |  | 1660 |  |  | 1688 |
18th century |  |  | 1728 |  |  | 1756 |  |  | 1784 |
19th century |  |  | 1824 |  |  | 1852 |  | 1880 |  |
20th century |  | 1920 |  |  | 1948 |  |  | 1976 |  |
21st century | 2004 |  |  | 2032 |  | 2060 |  |  | 2088 |
22nd century |  |  | 2128 |  |  | 2156 |  |  | 2184 |
23rd century |  |  | 2224 |  |  | 2252 |  | 2280 |  |
24th century |  | 2320 |  |  | 2348 |  |  | 2376 |  |
25th century | 2404 |  |  | 2432 |  | 2460 |  |  | 2488 |
26th century |  |  | 2528 |  |  | 2556 |  |  | 2584 |
27th century |  |  | 2624 |  |  | 2652 |  | 2680 |  |
400-year cycle  0–99  | 4 | 32 | 60 | 88

|
|
|
|

100–199  | 128 | 156 | 184 |
200–299  | 224 | 252 | 280 |
300–399  | 320 | 348 | 376 |

### Julian Calendar

[edit]

Like all leap year types, the one starting with 1 January on a Thursday 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 that means it will also repeat after 700 years, i.e. 25 cycles. The year's position in the cycle is given by the formula (((year + 8) mod 28) + 1).

Julian leap years starting on Thursday  Decade  | 1st | 2nd | 3rd | 4th | 5th | 6th | 7th | 8th | 9th | 10th

|
|
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|
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15th century |  |  | 1428 |  |  | 1456 |  |  | 1484 |
16th century |  | 1512 |  | 1540 |  |  | 1568 |  |  | 1596
17th century |  |  | 1624 |  |  | 1652 |  | 1680 |  |
18th century  | 1708 |  |  | 1736 |  |  | 1764 |  |  | 1792
19th century  |  | 1820 |  |  | 1848 |  |  | 1876 |  |
20th century  | 1904 |  |  | 1932 |  | 1960 |  |  | 1988 |
21st century  |  | 2016 |  |  | 2044 |  |  | 2072 |  | 2100
22nd century  |  |  | 2128 |  |  | 2156 |  |  | 2184 |

Wikimedia Commons has media related to Leap years starting on Thursday and ending on Friday.

## Holidays

[edit]

### International

[edit]

*     * Valentine's Day falls on a Saturday
* World Day for Grandparents and the Elderly falls on July 25
* Halloween falls on a Sunday
* Christmas Day falls on a Saturday

### Roman Catholic Solemnities

[edit]

*     * Epiphany falls on a Tuesday
* Candlemas falls on a Monday
* Saint Joseph's Day falls on a Friday
* The Annunciation of Jesus falls on a Thursday
* The Nativity of John the Baptist falls on a Thursday
* The Solemnity of Saints Peter and Paul falls on a Tuesday
* The Transfiguration of Jesus falls on a Friday
* The Assumption of Mary falls on a Sunday
* The Exaltation of the Holy Cross falls on a Tuesday
* All Saints' Day falls on a Monday. This is the only year when All Saints Day falls in ISO week 45. They fall in ISO week 44 in all other years.
* All Souls' Day falls on a Tuesday
* The Feast of Christ the King falls on November 21 (or on its latest possible date of October 31 in versions of the calendar between 1925 and 1962)
* The First Sunday of Advent falls on November 28
* The Immaculate Conception falls on a Wednesday
* Gaudete Sunday falls on December 12
* Rorate Sunday falls on December 19

### Australia and New Zealand

[edit]

*     * Australia Day falls on a Monday
* Waitangi Day falls on a Friday
* Daylight saving ends on April 4
* ANZAC Day falls on a Sunday, and in some years coincides with Easter Sunday falling on its latest possible date
* Mother's Day falls on May 9
* Father's Day falls on September 5
* Daylight saving begins on September 26 in New Zealand and October 3 in Australia

### British Isles

[edit]

*     * Saint David's Day falls on a Monday. This is the only year when Saint David's Day falls in ISO week 10. They fall in ISO week 9 in all other years
* Mother's Day falls on March 7, March 14, March 21, March 28 or on its latest possible date of April 4
* Daylight saving begins on March 28
* Saint Patrick's Day falls on a Wednesday
* Saint George's Day falls on a Friday, and in some years coincides with Good Friday falling on its latest possible date
* Father's Day falls on June 20
* Orangeman's Day falls on a Monday. This is the only year when Orangeman's Day falls in ISO week 29. They fall in ISO week 28 in all other years
* Daylight saving ends on its latest possible date, October 31. This is the only year when Daylight Saving Time ends in ISO week 44. They end in ISO week 43 in all other years
* Guy Fawkes Night falls on a Friday
* Saint Andrew's Day falls on a Tuesday

### Canada

[edit]

*     * Daylight saving begins on its latest possible date, March 14. This is the only year when Daylight Saving Time begins in ISO week 11. They begin in ISO week 10 in all other years.
* Mother's Day falls on May 9
* Victoria Day falls on its latest possible date, May 24. This is the only year when Victoria Day falls in ISO week 22. They fall in ISO week 21 in all other years. This is also the only year when Labour Day that precedes this type of year to Victoria Day in this type of year are 38 weeks apart. They are 37 weeks apart in all other years. This is also the only year when Father's Day that precedes this type of year to Victoria Day in this type of year are 344 days apart. They are 337 days apart in all other years.
* Father's Day falls on June 20
* Canada Day falls on a Thursday
* Labour Day falls on September 6
* Thanksgiving Day falls on October 11
* Daylight saving ends on its latest possible date, November 7. This is the only year when Daylight Saving Time ends in ISO week 45. They end in ISO week 44 in all other years.

### United States

[edit]

*     * Martin Luther King Jr. Day falls on January 19
* President's Day falls on February 16
* Daylight saving begins on its latest possible date, March 14. This is the only year when Daylight Saving Time begins in ISO week 11. They begin in ISO week 10 in all other years. This is also the only type of year where Labor Day that precedes this type of year to start of Daylight Saving Time is 195 days apart. They are 188 days apart in all other years. This is also the only type of year where Grandparent's Day that precedes this type of year to start of Daylight Saving Time is 27 weeks apart. They are 26 weeks apart in all other years. This is also the only type of year where Father's Day that precedes this type of year to start of Daylight Saving Time is 39 weeks apart. They are 38 weeks apart in all other years.
* Mother's Day falls on May 9
* Memorial Day falls on its latest possible date, May 31. This is the only year when Memorial Day falls in ISO week 23. They fall in ISO week 22 in all other years. This is also the only type of year where Labor Day that precedes this type of year to Memorial Day in this type of year are 39 weeks apart. They are 38 weeks apart in all other years. This is also the only type of year where Grandparent's Day that precedes this type of year to Memorial Day in this type of year are 267 days apart. They are 260 days apart in all other years. This is also the only type of year where Father's Day that precedes this type of year to Memorial Day in this type of year is 351 days apart. They are 344 days apart in all other years.
* Juneteenth falls on a Saturday
* Father's Day falls on June 20
* Independence Day falls on a Sunday
* Labor Day falls on September 6
* Grandparents' Day falls on September 12
* Columbus Day falls on October 11
* Election Day falls on its earliest possible date, November 2. This is the only leap year to have Election Day fall during Daylight Saving Time.
* Daylight saving ends on its latest possible date, November 7. This is the only year when Daylight Saving Time ends in ISO week 45. They end in ISO week 44 in all other years
* Thanksgiving Day falls on November 25

## References

[edit]

1. ^ a b Robert van Gent (2017). "The Mathematics of the ISO 8601 Calendar". Utrecht University, Department of Mathematics. Retrieved 20 July 2017.
2. ^ Leap years when Easter Sunday falls on April 25 are only possible years when Easter Sunday can fall on week 17.

* v
* t
* e

Gregorian year types per leap cycle by Dominical letter (DL) and Doomsday (DD)

| Year starts  |  | Common years |  | Leap years

|
|
|
|

1 Jan | Count | Ratio  | 31 Dec | DL | DD | Count | Ratio  | 31 Dec | DL | DD | Count | Ratio
Sun | 58 | 14.50 %  | Sun | A | Tue | 43 | 10.75 %  | Mon | AG | Wed | 15 | 03.75 %
Sat | 56 | 14.00 %  | Sat | B | Mon | 43 | 10.75 %  | Sun | BA | Tue | 13 | 03.25 %
Fri | 58 | 14.50 %  | Fri | C | Sun | 43 | 10.75 %  | Sat | CB | Mon | 15 | 03.75 %
Thu | 57 | 14.25 %  | Thu | D | Sat | 44 | 11.00 %  | Fri | DC | Sun | 13 | 03.25 %
Wed | 57 | 14.25 %  | Wed | E | Fri | 43 | 10.75 %  | Thu | ED | Sat | 14 | 03.50 %
Tue | 58 | 14.50 %  | Tue | F | Thu | 44 | 11.00 %  | Wed | FE | Fri | 14 | 03.50 %
Mon | 56 | 14.00 %  | Mon | G | Wed | 43 | 10.75 %  | Tue | GF | Thu | 13 | 03.25 %
∑  | 400 | 100.0 %  |  | 303 | 75.75 %  |  | 97 | 24.25 %

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