Leap year starting on Wednesday

A leap year starting on Wednesday is any year with 366 days (i.e. it includes 29 February) that begins on Wednesday 1 January and ends on Thursday 31 December. Its dominical letters hence are ED. The most recent year of such kind was 2020 and the next one will be 2048 in the Gregorian calendar, or likewise, 2004 and 2032 in the obsolete Julian calendar, see below for more.[1]

Any leap year that starts on Monday, Wednesday or Thursday has two Friday the 13ths: those two in this leap year occur in March and November. Common years starting on Thursday share this characteristic, but also have another in February.

In this leap year, Martin Luther King Jr. Day is on January 20, Valentine’s Day is on a Friday, President's Day is on February 17, the leap day is on a Saturday, Saint Patrick’s Day is on a Tuesday, Memorial Day is on its earliest possible date, May 25, Juneteenth is on a Friday, U.S. Independence Day is on a Saturday, Labor Day is on its latest possible date, September 7, Halloween is on a Saturday, Veterans Day is on a Wednesday, Thanksgiving is on November 26, and Christmas is on a Friday. Also like a common year starting on Thursday, this leap year is the only one where Memorial Day and Labor Day are not 14 weeks (98 days) apart: they are 15 weeks (105 days) apart in this leap year.

CalendarsEdit

Calendar for any leap year starting on Wednesday,
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 Wednesday (dominical letter ED)
January
Wk Mo Tu We Th Fr Sa Su
01 01 02 03 04 05
02 06 07 08 09 10 11 12
03 13 14 15 16 17 18 19
04 20 21 22 23 24 25 26
05 27 28 29 30 31  
   
February
Wk Mo Tu We Th Fr Sa Su
05 01 02
06 03 04 05 06 07 08 09
07 10 11 12 13 14 15 16
08 17 18 19 20 21 22 23
09 24 25 26 27 28 29
   
March
Wk Mo Tu We Th Fr Sa Su
09 01
10 02 03 04 05 06 07 08
11 09 10 11 12 13 14 15
12 16 17 18 19 20 21 22
13 23 24 25 26 27 28 29
14 30 31  
April
Wk Mo Tu We Th Fr Sa Su
14 01 02 03 04 05
15 06 07 08 09 10 11 12
16 13 14 15 16 17 18 19
17 20 21 22 23 24 25 26
18 27 28 29 30  
   
May
Wk Mo Tu We Th Fr Sa Su
18 01 02 03
19 04 05 06 07 08 09 10
20 11 12 13 14 15 16 17
21 18 19 20 21 22 23 24
22 25 26 27 28 29 30 31
   
June
Wk Mo Tu We Th Fr Sa Su
23 01 02 03 04 05 06 07
24 08 09 10 11 12 13 14
25 15 16 17 18 19 20 21
26 22 23 24 25 26 27 28
27 29 30  
   
July
Wk Mo Tu We Th Fr Sa Su
27 01 02 03 04 05
28 06 07 08 09 10 11 12
29 13 14 15 16 17 18 19
30 20 21 22 23 24 25 26
31 27 28 29 30 31  
   
August
Wk Mo Tu We Th Fr Sa Su
31 01 02
32 03 04 05 06 07 08 09
33 10 11 12 13 14 15 16
34 17 18 19 20 21 22 23
35 24 25 26 27 28 29 30
36 31  
September
Wk Mo Tu We Th Fr Sa Su
36 01 02 03 04 05 06
37 07 08 09 10 11 12 13
38 14 15 16 17 18 19 20
39 21 22 23 24 25 26 27
40 28 29 30  
   
October
Wk Mo Tu We Th Fr Sa Su
40 01 02 03 04
41 05 06 07 08 09 10 11
42 12 13 14 15 16 17 18
43 19 20 21 22 23 24 25
44 26 27 28 29 30 31  
   
November
Wk Mo Tu We Th Fr Sa Su
44 01
45 02 03 04 05 06 07 08
46 09 10 11 12 13 14 15
47 16 17 18 19 20 21 22
48 23 24 25 26 27 28 29
49 30  
December
Wk Mo Tu We Th Fr Sa Su
49 01 02 03 04 05 06
50 07 08 09 10 11 12 13
51 14 15 16 17 18 19 20
52 21 22 23 24 25 26 27
53 28 29 30 31  
   

Applicable yearsEdit

Gregorian CalendarEdit

Leap years that begin on Wednesday, like those that start on Tuesday, 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. Their overall occurrence is thus 3.5% (14 out of 400).

For this kind of year, the corresponding ISO year has 53 weeks.

Gregorian leap years starting on Wednesday[1]
Decade 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th
17th century 1620 1648 1676
18th century 1716 1744 1772
19th century 1812 1840 1868 1896
20th century 1908 1936 1964 1992
21st century 2020 2048 2076
22nd century 2116 2144 2172
23rd century 2212 2240 2268 2296
24th century 2308 2336 2364 2392
25th century 2420 2448 2476
26th century 2516 2544 2572
27th century 2612 2640 2668 2696

400 year cycle

century 1: 20, 48, 76

century 2: 116, 144, 172

century 3: 212, 240, 268, 296

century 4: 308, 336, 364, 392

Julian CalendarEdit

Like all leap year types, the one starting with 1 January on a Wednesday 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 Wednesday
Decade 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th
15th century 1416 1444 1472 1500
16th century 1528 1556 1584
17th century 1612 1640 1668 1696
18th century 1724 1752 1780
19th century 1808 1836 1864 1892
20th century 1920 1948 1976
21st century 2004 2032 2060 2088
22nd century 2116 2144 2172 2200

ReferencesEdit

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