Leap year

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A leap year is any year that has exactly 366 days, including February 29 (known as Leap Day). For example, the years 2016, 2020, and 2024 are leap years. Years that are not leap years are known as common years.

In the Julian calendar, leap years occur every 4 years without exception. On the other hand, in the Gregorian calendar, leap years usually still occur every 4 years, except that century years (those that end with "00") are not leap years unless divisible by 400. So, the years 2000 and 2400 are leap years, while the years 1800, 1900, 2100, and 2200 are not leap years.

Types of leap years[edit source]

There are 7 types of leap years, one for each day of the week.

Starting on Sunday[edit source]

Leap year with dominical letter AG
January February March April
Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat
1 2 3 4 5 6 7 1 2 3 4 1 2 3 1 2 3 4 5 6 7
8 9 10 11 12 13 14 5 6 7 8 9 10 11 4 5 6 7 8 9 10 8 9 10 11 12 13 14
15 16 17 18 19 20 21 12 13 14 15 16 17 18 11 12 13 14 15 16 17 15 16 17 18 19 20 21
22 23 24 25 26 27 28 19 20 21 22 23 24 25 18 19 20 21 22 23 24 22 23 24 25 26 27 28
29 30 31 26 27 28 29 25 26 27 28 29 30 31 29 30
May June July August
Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat
1 2 3 4 5 1 2 1 2 3 4 5 6 7 1 2 3 4
6 7 8 9 10 11 12 3 4 5 6 7 8 9 8 9 10 11 12 13 14 5 6 7 8 9 10 11
13 14 15 16 17 18 19 10 11 12 13 14 15 16 15 16 17 18 19 20 21 12 13 14 15 16 17 18
20 21 22 23 24 25 26 17 18 19 20 21 22 23 22 23 24 25 26 27 28 19 20 21 22 23 24 25
27 28 29 30 31 24 25 26 27 28 29 30 29 30 31 26 27 28 29 30 31
September October November December
Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat
1 1 2 3 4 5 6 1 2 3 1
2 3 4 5 6 7 8 7 8 9 10 11 12 13 4 5 6 7 8 9 10 2 3 4 5 6 7 8
9 10 11 12 13 14 15 14 15 16 17 18 19 20 11 12 13 14 15 16 17 9 10 11 12 13 14 15
16 17 18 19 20 21 22 21 22 23 24 25 26 27 18 19 20 21 22 23 24 16 17 18 19 20 21 22
23 24 25 26 27 28 29 28 29 30 31 25 26 27 28 29 30 23 24 25 26 27 28 29
30 30 31

For such a year, the dominical letter is AG, February 29 is on a Wednesday, and Friday the 13ths occur on January 13, April 13, and July 13. Such years occur 15 times in the 400-year cycle of the Gregorian calendar and once in the 28-year cycle of the Julian calendar.

Occurrences in the Gregorian cycle (mod 400)
12 40 68 96
108 136 164 192
204 232 260 288
328 356 384

In the Julian calendar, such years occur when the year reduces to 8 mod 28.

Starting on Monday[edit source]

Leap year with dominical letter GF
January February March April
Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat
1 2 3 4 5 6 1 2 3 1 2 1 2 3 4 5 6
7 8 9 10 11 12 13 4 5 6 7 8 9 10 3 4 5 6 7 8 9 7 8 9 10 11 12 13
14 15 16 17 18 19 20 11 12 13 14 15 16 17 10 11 12 13 14 15 16 14 15 16 17 18 19 20
21 22 23 24 25 26 27 18 19 20 21 22 23 24 17 18 19 20 21 22 23 21 22 23 24 25 26 27
28 29 30 31 25 26 27 28 29 24 25 26 27 28 29 30 28 29 30
31
May June July August
Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat
1 2 3 4 1 1 2 3 4 5 6 1 2 3
5 6 7 8 9 10 11 2 3 4 5 6 7 8 7 8 9 10 11 12 13 4 5 6 7 8 9 10
12 13 14 15 16 17 18 9 10 11 12 13 14 15 14 15 16 17 18 19 20 11 12 13 14 15 16 17
19 20 21 22 23 24 25 16 17 18 19 20 21 22 21 22 23 24 25 26 27 18 19 20 21 22 23 24
26 27 28 29 30 31 23 24 25 26 27 28 29 28 29 30 31 25 26 27 28 29 30 31
30
September October November December
Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat
1 2 3 4 5 6 7 1 2 3 4 5 1 2 1 2 3 4 5 6 7
8 9 10 11 12 13 14 6 7 8 9 10 11 12 3 4 5 6 7 8 9 8 9 10 11 12 13 14
15 16 17 18 19 20 21 13 14 15 16 17 18 19 10 11 12 13 14 15 16 15 16 17 18 19 20 21
22 23 24 25 26 27 28 20 21 22 23 24 25 26 17 18 19 20 21 22 23 22 23 24 25 26 27 28
29 30 27 28 29 30 31 24 25 26 27 28 29 30 29 30 31

For such a year, the dominical letter is GF, February 29 is on a Thursday, and Friday the 13ths occur on September 13 and December 13. Such years occur 13 times in the 400-year cycle of the Gregorian calendar and once in the 28-year cycle of the Julian calendar.

Occurrences in the Gregorian cycle (mod 400)
24 52 80
120 148 176
216 244 272
312 340 368 396

In the Julian calendar, such years occur when the year reduces to 20 mod 28.

Starting on Tuesday[edit source]

Leap year with dominical letter FE
January February March April
Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat
1 2 3 4 5 1 2 1 1 2 3 4 5
6 7 8 9 10 11 12 3 4 5 6 7 8 9 2 3 4 5 6 7 8 6 7 8 9 10 11 12
13 14 15 16 17 18 19 10 11 12 13 14 15 16 9 10 11 12 13 14 15 13 14 15 16 17 18 19
20 21 22 23 24 25 26 17 18 19 20 21 22 23 16 17 18 19 20 21 22 20 21 22 23 24 25 26
27 28 29 30 31 24 25 26 27 28 29 23 24 25 26 27 28 29 27 28 29 30
30 31
May June July August
Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat
1 2 3 1 2 3 4 5 6 7 1 2 3 4 5 1 2
4 5 6 7 8 9 10 8 9 10 11 12 13 14 6 7 8 9 10 11 12 3 4 5 6 7 8 9
11 12 13 14 15 16 17 15 16 17 18 19 20 21 13 14 15 16 17 18 19 10 11 12 13 14 15 16
18 19 20 21 22 23 24 22 23 24 25 26 27 28 20 21 22 23 24 25 26 17 18 19 20 21 22 23
25 26 27 28 29 30 31 29 30 27 28 29 30 31 24 25 26 27 28 29 30
31
September October November December
Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat
1 2 3 4 5 6 1 2 3 4 1 1 2 3 4 5 6
7 8 9 10 11 12 13 5 6 7 8 9 10 11 2 3 4 5 6 7 8 7 8 9 10 11 12 13
14 15 16 17 18 19 20 12 13 14 15 16 17 18 9 10 11 12 13 14 15 14 15 16 17 18 19 20
21 22 23 24 25 26 27 19 20 21 22 23 24 25 16 17 18 19 20 21 22 21 22 23 24 25 26 27
28 29 30 26 27 28 29 30 31 23 24 25 26 27 28 29 28 29 30 31
30

For such a year, the dominical letter is FE, February 29 is on a Friday, and a Friday the 13th occurs on June 13. Such years occur 14 times in the 400-year cycle of the Gregorian calendar and once in the 28-year cycle of the Julian calendar.

Occurrences in the Gregorian cycle (mod 400)
8 36 64 92
104 132 160 188
228 256 284
324 352 380

In the Julian calendar, such years occur when the year reduces to 4 mod 28.

Starting on Wednesday[edit source]

Leap year with dominical letter ED
January February March April
Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat
1 2 3 4 1 1 2 3 4 5 6 7 1 2 3 4
5 6 7 8 9 10 11 2 3 4 5 6 7 8 8 9 10 11 12 13 14 5 6 7 8 9 10 11
12 13 14 15 16 17 18 9 10 11 12 13 14 15 15 16 17 18 19 20 21 12 13 14 15 16 17 18
19 20 21 22 23 24 25 16 17 18 19 20 21 22 22 23 24 25 26 27 28 19 20 21 22 23 24 25
26 27 28 29 30 31 23 24 25 26 27 28 29 29 30 31 26 27 28 29 30
May June July August
Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat
1 2 1 2 3 4 5 6 1 2 3 4 1
3 4 5 6 7 8 9 7 8 9 10 11 12 13 5 6 7 8 9 10 11 2 3 4 5 6 7 8
10 11 12 13 14 15 16 14 15 16 17 18 19 20 12 13 14 15 16 17 18 9 10 11 12 13 14 15
17 18 19 20 21 22 23 21 22 23 24 25 26 27 19 20 21 22 23 24 25 16 17 18 19 20 21 22
24 25 26 27 28 29 30 28 29 30 26 27 28 29 30 31 23 24 25 26 27 28 29
31 30 31
September October November December
Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat
1 2 3 4 5 1 2 3 1 2 3 4 5 6 7 1 2 3 4 5
6 7 8 9 10 11 12 4 5 6 7 8 9 10 8 9 10 11 12 13 14 6 7 8 9 10 11 12
13 14 15 16 17 18 19 11 12 13 14 15 16 17 15 16 17 18 19 20 21 13 14 15 16 17 18 19
20 21 22 23 24 25 26 18 19 20 21 22 23 24 22 23 24 25 26 27 28 20 21 22 23 24 25 26
27 28 29 30 25 26 27 28 29 30 31 29 30 27 28 29 30 31

For such a year, the dominical letter is ED, February 29 is on a Saturday, and Friday the 13ths occur on March 13 and November 13. Such years occur 14 times in the 400-year cycle of the Gregorian calendar and once in the 28-year cycle of the Julian calendar.

Occurrences in the Gregorian cycle (mod 400)
20 48 76
116 144 172
212 240 268 296
308 336 364 392

In the Julian calendar, such years occur when the year reduces to 16 mod 28.

Starting on Thursday[edit source]

Leap year with dominical letter DC
January February March April
Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat
1 2 3 1 2 3 4 5 6 7 1 2 3 4 5 6 1 2 3
4 5 6 7 8 9 10 8 9 10 11 12 13 14 7 8 9 10 11 12 13 4 5 6 7 8 9 10
11 12 13 14 15 16 17 15 16 17 18 19 20 21 14 15 16 17 18 19 20 11 12 13 14 15 16 17
18 19 20 21 22 23 24 22 23 24 25 26 27 28 21 22 23 24 25 26 27 18 19 20 21 22 23 24
25 26 27 28 29 30 31 29 28 29 30 31 25 26 27 28 29 30
May June July August
Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat
1 1 2 3 4 5 1 2 3 1 2 3 4 5 6 7
2 3 4 5 6 7 8 6 7 8 9 10 11 12 4 5 6 7 8 9 10 8 9 10 11 12 13 14
9 10 11 12 13 14 15 13 14 15 16 17 18 19 11 12 13 14 15 16 17 15 16 17 18 19 20 21
16 17 18 19 20 21 22 20 21 22 23 24 25 26 18 19 20 21 22 23 24 22 23 24 25 26 27 28
23 24 25 26 27 28 29 27 28 29 30 25 26 27 28 29 30 31 29 30 31
30 31
September October November December
Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat
1 2 3 4 1 2 1 2 3 4 5 6 1 2 3 4
5 6 7 8 9 10 11 3 4 5 6 7 8 9 7 8 9 10 11 12 13 5 6 7 8 9 10 11
12 13 14 15 16 17 18 10 11 12 13 14 15 16 14 15 16 17 18 19 20 12 13 14 15 16 17 18
19 20 21 22 23 24 25 17 18 19 20 21 22 23 21 22 23 24 25 26 27 19 20 21 22 23 24 25
26 27 28 29 30 24 25 26 27 28 29 30 28 29 30 26 27 28 29 30 31
31

For such a year, the dominical letter is DC, February 29 is on a Sunday, and Friday the 13ths occur on February 13 and August 13. Such years occur 13 times in the 400-year cycle of the Gregorian calendar and once in the 28-year cycle of the Julian calendar.

Occurrences in the Gregorian cycle (mod 400)
4 32 60 88
128 156 184
224 252 280
320 348 376

In the Julian calendar, such years occur when the year reduces to 0 mod 28 (or is divisible by 28).

Starting on Friday[edit source]

Leap year with dominical letter CB
January February March April
Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat
1 2 1 2 3 4 5 6 1 2 3 4 5 1 2
3 4 5 6 7 8 9 7 8 9 10 11 12 13 6 7 8 9 10 11 12 3 4 5 6 7 8 9
10 11 12 13 14 15 16 14 15 16 17 18 19 20 13 14 15 16 17 18 19 10 11 12 13 14 15 16
17 18 19 20 21 22 23 21 22 23 24 25 26 27 20 21 22 23 24 25 26 17 18 19 20 21 22 23
24 25 26 27 28 29 30 28 29 27 28 29 30 31 24 25 26 27 28 29 30
31
May June July August
Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat
1 2 3 4 5 6 7 1 2 3 4 1 2 1 2 3 4 5 6
8 9 10 11 12 13 14 5 6 7 8 9 10 11 3 4 5 6 7 8 9 7 8 9 10 11 12 13
15 16 17 18 19 20 21 12 13 14 15 16 17 18 10 11 12 13 14 15 16 14 15 16 17 18 19 20
22 23 24 25 26 27 28 19 20 21 22 23 24 25 17 18 19 20 21 22 23 21 22 23 24 25 26 27
29 30 31 26 27 28 29 30 24 25 26 27 28 29 30 28 29 30 31
31
September October November December
Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat
1 2 3 1 1 2 3 4 5 1 2 3
4 5 6 7 8 9 10 2 3 4 5 6 7 8 6 7 8 9 10 11 12 4 5 6 7 8 9 10
11 12 13 14 15 16 17 9 10 11 12 13 14 15 13 14 15 16 17 18 19 11 12 13 14 15 16 17
18 19 20 21 22 23 24 16 17 18 19 20 21 22 20 21 22 23 24 25 26 18 19 20 21 22 23 24
25 26 27 28 29 30 23 24 25 26 27 28 29 27 28 29 30 25 26 27 28 29 30 31
30 31

For such a year, the dominical letter is CB, February 29 is on a Monday, and a Friday the 13th occurs on May 13. Such years occur 15 times in the 400-year cycle of the Gregorian calendar and once in the 28-year cycle of the Julian calendar.

Occurrences in the Gregorian cycle (mod 400)
16 44 72
112 140 168 196
208 236 264 292
304 332 360 388

In the Julian calendar, such years occur when the year reduces to 12 mod 28.

Starting on Saturday[edit source]

Leap year with dominical letter BA
January February March April
Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat
1 1 2 3 4 5 1 2 3 4 1
2 3 4 5 6 7 8 6 7 8 9 10 11 12 5 6 7 8 9 10 11 2 3 4 5 6 7 8
9 10 11 12 13 14 15 13 14 15 16 17 18 19 12 13 14 15 16 17 18 9 10 11 12 13 14 15
16 17 18 19 20 21 22 20 21 22 23 24 25 26 19 20 21 22 23 24 25 16 17 18 19 20 21 22
23 24 25 26 27 28 29 27 28 29 26 27 28 29 30 31 23 24 25 26 27 28 29
30 31 30
May June July August
Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat
1 2 3 4 5 6 1 2 3 1 1 2 3 4 5
7 8 9 10 11 12 13 4 5 6 7 8 9 10 2 3 4 5 6 7 8 6 7 8 9 10 11 12
14 15 16 17 18 19 20 11 12 13 14 15 16 17 9 10 11 12 13 14 15 13 14 15 16 17 18 19
21 22 23 24 25 26 27 18 19 20 21 22 23 24 16 17 18 19 20 21 22 20 21 22 23 24 25 26
28 29 30 31 25 26 27 28 29 30 23 24 25 26 27 28 29 27 28 29 30 31
30 31
September October November December
Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat
1 2 1 2 3 4 5 6 7 1 2 3 4 1 2
3 4 5 6 7 8 9 8 9 10 11 12 13 14 5 6 7 8 9 10 11 3 4 5 6 7 8 9
10 11 12 13 14 15 16 15 16 17 18 19 20 21 12 13 14 15 16 17 18 10 11 12 13 14 15 16
17 18 19 20 21 22 23 22 23 24 25 26 27 28 19 20 21 22 23 24 25 17 18 19 20 21 22 23
24 25 26 27 28 29 30 29 30 31 26 27 28 29 30 24 25 26 27 28 29 30
31

For such a year, the dominical letter is BA, February 29 is on a Tuesday, and a Friday the 13th occurs on October 13. Such years occur 13 times in the 400-year cycle of the Gregorian calendar and once in the 28-year cycle of the Julian calendar.

Occurrences in the Gregorian cycle (mod 400)
0 28 56 84
124 152 180
220 248 276
316 344 372

In the Julian calendar, such years occur when the year reduces to 24 mod 28.