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Leap year starting on Saturday

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Template:Short description 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 obsolete 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.<ref name="math">{{#invoke:citation/CS1|citation |CitationClass=web }} </ref>

Any leap year that starts on Saturday has only one Friday the 13th: the only one in this leap year occurs in October. Common years starting on Sunday share this characteristic, but also have another in January. 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.

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 53 full weekends.

This year has four months (January, April, July and October) which begin on a weekend-day. This is also the only type of leap year in which the first and last day of the calendar year fall on weekend-days.

CalendarsEdit

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any leap year starting on Saturday (dominical letter BA)
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Applicable yearsEdit

Gregorian CalendarEdit

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<ref name=math/>
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

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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 Template:03.75 %
Mon 56 14.00 % Mon G Wed 43 10.75 % Tue GF Thu 13 Template:03.25 %
Tue 58 14.50 % Tue F Thu 44 11.00 % Wed FE Fri 14 Template:03.50 %
Wed 57 14.25 % Wed E Fri 43 10.75 % Thu ED Sat 14 Template:03.50 %
Thu 57 14.25 % Thu D Sat 44 11.00 % Fri DC Sun 13 Template:03.25 %
Fri 58 14.50 % Fri C Sun 43 10.75 % Sat CB Mon 15 Template:03.75 %
Sat 56 14.00 % Sat B Mon 43 10.75 % Sun BA Tue 13 Template:03.25 %
∑ 400 100.0 % 303 75.75 % 97 24.25 %

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Julian CalendarEdit

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

HolidaysEdit

InternationalEdit

Roman Catholic SolemnitiesEdit

Australia and New ZealandEdit

British IslesEdit

CanadaEdit

United StatesEdit

ReferencesEdit

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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 Template:03.75 %
Mon 56 14.00 % Mon G Wed 43 10.75 % Tue GF Thu 13 Template:03.25 %
Tue 58 14.50 % Tue F Thu 44 11.00 % Wed FE Fri 14 Template:03.50 %
Wed 57 14.25 % Wed E Fri 43 10.75 % Thu ED Sat 14 Template:03.50 %
Thu 57 14.25 % Thu D Sat 44 11.00 % Fri DC Sun 13 Template:03.25 %
Fri 58 14.50 % Fri C Sun 43 10.75 % Sat CB Mon 15 Template:03.75 %
Sat 56 14.00 % Sat B Mon 43 10.75 % Sun BA Tue 13 Template:03.25 %
∑ 400 100.0 % 303 75.75 % 97 24.25 %

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