Leap year starting on Tuesday

Calendar for any leap year starting on Tuesday

A leap year starting on Tuesday is any year with 366 days (i.e. it includes 29 February) that begins on Tuesday, 1 January, and ends on Wednesday, 31 December. Its dominical letters hence are FE. The most recent year of such kind was 2008 and the next one will be 2036 in the Gregorian calendar[1] or, likewise 2020 and 2048 in the obsolete Julian calendar.

Any leap year that starts on Tuesday, Friday or Saturday has only one Friday the 13th; the only one in this leap year occurs in June. Common years starting on Wednesday share this characteristic.

From August of the common year preceding that year until October in this type of year is also the longest period (14 months) that occurs without a Friday the 17th. Common years starting on Friday share this characteristic, from July of the year that precedes it to September in that type of year.

## Calendars[edit]

Calendar for any leap year starting on Tuesday,
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 Tuesday (dominical letter FE)

|  | January  |

|
|

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

|  | February  |

|
|

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

|  | March  |

|
|

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

|
|

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

|  | May  |

|
|

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

|  | June  |

|
|

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

|
|

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

|  | August  |

|
|

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

|  | September  |

|
|

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

|  | October  |

|
|

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

|  | November  |

|
|

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

|  | December  |

|
|

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

## Applicable years[edit]

### Gregorian Calendar[edit]

Leap years that begin on Tuesday, along with those starting on Wednesday, occur at a rate of approximately 14.43% (14 out of 97) of all total leap years in a 400-year cycle of the Gregorian calendar. Thus, their overall occurrence is 3.5% (14 out of 400).

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

|
|
|
|
|
|
|
|
|
|

17th century | 1608 |  |  | 1636 |  |  | 1664 |  |  | 1692
18th century | 1704 |  |  | 1732 |  | 1760 |  |  | 1788 |
19th century |  |  | 1828 |  |  | 1856 |  |  | 1884 |
20th century |  |  | 1924 |  |  | 1952 |  | 1980 |  |
21st century | 2008 |  |  | 2036 |  |  | 2064 |  |  | 2092
22nd century | 2104 |  |  | 2132 |  | 2160 |  |  | 2188 |
23rd century |  |  | 2228 |  |  | 2256 |  |  | 2284 |
24th century |  |  | 2324 |  |  | 2352 |  | 2380 |  |
25th century | 2408 |  |  | 2436 |  |  | 2464 |  |  | 2492
26th century | 2504 |  |  | 2532 |  | 2560 |  |  | 2588 |
400-year cycle  0–99  | 8 | 36 | 64 | 92

|
|
|
|

100–199  | 104 | 132 | 160 | 188
200–299  | 228 | 256 | 284 |
300–399  | 324 | 352 | 380 |

### Julian Calendar[edit]

Like all leap year types, the one starting with 1 January on a Tuesday 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 Tuesday  Decade  | 1st | 2nd | 3rd | 4th | 5th | 6th | 7th | 8th | 9th | 10th

|
|
|
|
|
|
|
|
|
|

14th century | 1320 |  |  | 1348 |  | 1376 |  |  |  |
15th century | 1404 |  |  | 1432 |  | 1460 |  |  | 1488 |
16th century |  | 1516 |  |  | 1544 |  |  | 1572 |  | 1600
17th century |  |  | 1628 |  |  | 1656 |  |  | 1684 |
18th century  |  | 1712 |  | 1740 |  |  | 1768 |  |  | 1796
19th century  |  |  | 1824 |  |  | 1852 |  | 1880 |  |
20th century  | 1908 |  |  | 1936 |  |  | 1964 |  |  | 1992
21st century  |  | 2020 |  |  | 2048 |  |  | 2076 |  |
22nd century  | 2104 |  |  | 2132 |  | 2160 |  |  | 2188 |

Wikimedia Commons has media related to Leap years starting on Tuesday and ending on Wednesday.

## Holidays[edit]

### International[edit]

*     * Valentine's Day falls on a Thursday
* The leap day (February 29) falls on a Friday
* World Day for Grandparents and the Elderly falls on July 27
* Halloween falls on a Friday
* Christmas Day falls on a Thursday

### Roman Catholic Solemnities[edit]

*     * Epiphany falls on a Sunday
* Candlemas falls on a Saturday
* Saint Joseph's Day falls on a Wednesday
* The Annunciation of Jesus falls on a Tuesday
* The Nativity of John the Baptist falls on a Tuesday
* The Solemnity of Saints Peter and Paul falls on a Sunday
* The Transfiguration of Jesus falls on a Wednesday
* The Assumption of Mary falls on a Friday
* The Exaltation of the Holy Cross falls on a Sunday
* All Saints' Day falls on a Saturday
* All Souls' Day falls on a Sunday
* The Feast of Christ the King falls on November 23 (or on October 26 in versions of the calendar between 1925 and 1962)
* The First Sunday of Advent falls on November 30
* The Immaculate Conception falls on a Monday
* Gaudete Sunday falls on December 14
* Rorate Sunday falls on December 21

### Australia and New Zealand[edit]

*     * Australia Day falls on a Saturday
* Waitangi Day falls on a Wednesday
* Daylight saving ends on April 6
* ANZAC Day falls on a Friday
* Mother's Day falls on May 11
* Father's Day falls on its latest possible date, September 7
* Daylight saving begins on September 28 in New Zealand and October 5 in Australia

### British Isles[edit]

*     * Saint David's Day falls on a Saturday
* Mother's Day falls on March 2, March 9, March 16, March 23 or March 30
* Saint Patrick's Day falls on a Monday
* Daylight saving begins on March 30
* Saint George's Day falls on a Wednesday
* Father's Day falls on its earliest possible date, June 15
* Orangeman's Day falls on a Saturday
* Daylight saving ends on October 26
* Guy Fawkes Night falls on a Wednesday
* Saint Andrew's Day falls on a Sunday

### Canada[edit]

*     * Daylight saving begins on March 9
* Mother's Day falls on May 11
* Victoria Day falls on May 19
* Father's Day falls on its earliest possible date, June 15
* Canada Day falls on a Tuesday
* Labour Day falls on its earliest possible date, September 1
* Thanksgiving Day falls on October 13
* Daylight saving ends on November 2

### United States[edit]

*     * Martin Luther King Jr. Day falls on its latest possible date, January 21. This is the only type of leap year where Columbus Day that precedes this type of year to Martin Luther King Jr. Day in this type of year are 15 weeks apart. They are 14 weeks apart in all other leap years. This is also the only type of leap year where Thanksgiving that precedes this type of year to Martin Luther King Jr. Day in this type of year are 60 days apart. They are 53 days apart in all other leap years
* President's Day falls on February 18
* Daylight saving begins on March 9
* Mother's Day falls on May 11
* Memorial Day falls on May 26
* Father's Day falls on its earliest possible date, June 15. This is the only type of leap year where Martin Luther King Jr. Day and Father’s Day are 146 days apart. They are 153 days apart in all other leap years
* Juneteenth falls on a Thursday
* Independence Day falls on a Friday
* Labor Day falls on its earliest possible date, September 1. This is the only type of leap year where Martin Luther King Jr. Day and Labor Day are 32 weeks apart. They are 33 weeks apart in all other leap years
* Grandparents' Day falls on its earliest possible date, September 7. This is the only type of leap year where Martin Luther King Jr. Day and Grandparent’s Day are 230 days apart. They are 237 days apart in all other leap years.
* Columbus Day falls on October 13
* Daylight saving ends on November 2
* Election Day falls on November 4
* Thanksgiving Day falls on November 27

## 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.

* 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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