Leap year starting on Saturday

A leap year starting on Saturday is any year with 366 days (i.e. it includes 29 February) that begins on Saturday, 1 January, and ends on Sunday, 31 December. Its dominical letters hence are BA. The most recent year of such kind was 2000 and the next one will be 2028 in the Gregorian calendar or, likewise 2012 and 2040 in the obsolescent Julian calendar. In the Gregorian calendar, years divisible by 400 are always leap years starting on Saturday. The most recent such occurrence was 2000 and the next one will be 2400, see below for more.[1]

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 October. 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 13th. Common years starting on Tuesday share this characteristic, from July of the year that precedes it to September in that type of year.

This is the only type of year in which all dates (except 29 February) fall on their respective weekdays the minimal 56 times in the 400 year Gregorian Calendar cycle. 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 Sunday is considered the first day of the week, and also the only type of year to contain both 53 Saturdays and Sundays.

## Calendars

[edit]

Calendar for any leap year starting on Saturday,
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 Saturday (dominical letter BA)

|  | January  |

|
|

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

|
|

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

|  | March  |

|
|

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

|  | April  |

|
|

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

|  | May  |

|
|

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

|  | June  |

|
|

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

|  | July  |

|
|

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

|
|

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

|  | September  |

|
|

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

|  | October  |

|
|

Wk  | Mo  | Tu  | We  | Th  | Fr  | Sa  | Su
39  |  |  |  |  |  |  | 01
40  | 02 | 03 | 04 | 05 | 06 | 07 | 08
41  | 09 | 10 | 11 | 12 | 13 | 14 | 15
42  | 16 | 17 | 18 | 19 | 20 | 21 | 22
43  | 23 | 24 | 25 | 26 | 27 | 28 | 29
44  | 30 | 31  |
|  | November  |

|
|

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

|  | December  |

|
|

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

## Applicable years

[edit]

### Gregorian Calendar

[edit]

Leap years that begin on Saturday, along with those starting on Monday and Thursday, 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).

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

|
|
|
|
|
|
|
|
|
|

16th century | prior to first adoption (proleptic) | 1600
17th century |  |  | 1628 |  |  | 1656 |  |  | 1684 |
18th century |  |  | 1724 |  |  | 1752 |  | 1780 |  |
19th century |  | 1820 |  |  | 1848 |  |  | 1876 |  |
20th century |  | 1916 |  |  | 1944 |  |  | 1972 |  | 2000
21st century |  |  | 2028 |  |  | 2056 |  |  | 2084 |
22nd century |  |  | 2124 |  |  | 2152 |  | 2180 |  |
23rd century |  | 2220 |  |  | 2248 |  |  | 2276 |  |
24th century |  | 2316 |  |  | 2344 |  |  | 2372 |  | 2400
25th century |  |  | 2428 |  |  | 2456 |  |  | 2484 |
400-year cycle  0–99  | 0 | 28 | 56 | 84

|
|
|
|

100–199  | 124 | 152 | 180 |
200–299  | 220 | 248 | 276 |
300–399  | 316 | 344 | 372 |

* 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.

### Julian Calendar

[edit]

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

|
|
|
|
|
|
|
|
|
|

15th century |  |  | 1424 |  |  | 1452 |  | 1480 |  |
16th century | 1508 |  |  | 1536 |  |  | 1564 |  |  | 1592
17th century |  | 1620 |  |  | 1648 |  |  | 1676 |  |
18th century  | 1704 |  |  | 1732 |  | 1760 |  |  | 1788 |
19th century  |  | 1816 |  |  | 1844 |  |  | 1872 |  | 1900
20th century  |  |  | 1928 |  |  | 1956 |  |  | 1984 |
21st century  |  | 2012 |  | 2040 |  |  | 2068 |  |  | 2096
22nd century  |  |  | 2124 |  |  | 2152 |  | 2180 |  |

## Holidays

[edit]

### International

[edit]

*     * Valentine's Day falls on a Monday
* The leap day (February 29) falls on a Tuesday
* World Day for Grandparents and the Elderly falls on July 23
* Halloween falls on a Tuesday
* Christmas Day falls on a Monday

### Roman Catholic Solemnities

[edit]

*     * Epiphany falls on a Thursday
* Candlemas falls on a Wednesday
* Saint Joseph's Day falls on a Sunday
* The Annunciation of Jesus falls on a Saturday
* The Nativity of John the Baptist falls on a Saturday
* The Solemnity of Saints Peter and Paul falls on a Thursday
* The Transfiguration of Jesus falls on a Sunday
* The Assumption of Mary falls on a Tuesday
* The Exaltation of the Holy Cross falls on a Thursday
* All Saints' Day falls on a Wednesday
* All Souls' Day falls on a Thursday
* The Feast of Christ the King falls on its latest possible date, November 26 (or on October 29 in versions of the calendar between 1925 and 1962)
* The First Sunday of Advent falls on its latest possible date, December 3
* The Immaculate Conception falls on a Friday
* Gaudete Sunday falls on its latest possible date, December 17
* Rorate Sunday falls on its latest possible date, December 24

### Australia and New Zealand

[edit]

*     * Australia Day falls on a Wednesday
* Waitangi Day falls on a Sunday
* Daylight saving ends on April 2
* ANZAC Day falls on a Tuesday
* Mother's Day falls on its latest possible date, May 14
* Father's Day falls on September 3
* Daylight saving begins on its earliest possible date, September 24 in New Zealand and October 1 in Australia

### British Isles

[edit]

*     * Saint David's Day falls on a Wednesday
* Mother's Day falls on March 5, March 12, March 19, March 26 or April 2
* Daylight saving begins on March 26
* Saint Patrick's Day falls on a Friday
* Saint George's Day falls on a Sunday
* Father's Day falls on June 18
* Orangeman's Day falls on a Wednesday
* Daylight saving ends on October 29
* Guy Fawkes Night falls on a Sunday
* Saint Andrew's Day falls on a Thursday

### Canada

[edit]

*     * Daylight saving begins on March 12
* Mother's Day falls on its latest possible date, May 14
* Victoria Day falls on May 22
* Father's Day falls on June 18
* Canada Day falls on a Saturday
* Labour Day falls on September 4
* Thanksgiving Day falls on October 9
* Daylight saving ends on November 5

### United States

[edit]

*     * Martin Luther King Jr. Day falls on January 17
* President's Day falls on its latest possible date, February 21
* Daylight saving begins on March 12
* Mother's Day falls on its latest possible date, May 14
* Memorial Day falls on May 29
* Father's Day falls on June 18
* Juneteenth falls on a Monday
* Independence Day falls on a Tuesday
* Labor Day falls on September 4
* Grandparents' Day falls on September 10
* Columbus Day falls on October 9
* Daylight saving ends on November 5
* Election Day falls on November 7
* Thanksgiving Day falls on November 23

## References

[edit]

Wikimedia Commons has media related to Leap years starting on Saturday and ending on Sunday.

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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