Leap years

What is a leap year?

A leap year is a year that does not have 365 days like a normal year, but 366 days. The additional day ("leap day") is the 29th of February. A leap year occurs only every four years (for exceptions see below).

When is the next leap year?

The next leap year is 2020.  2020 Calendar.  The previous leap year was 2016.

Why are there leap years?

A tropical year (also called a solar year) is the time it takes for the earth to circle around the sun. This period is not exactly 365 days long, but 365.2422 days (365 days and a little less than 6 hours). By inserting a leap year, the calendar year is extended at regular intervals and thus synchronized with the tropical year. Without leap years, the calendar year and the seasons would slowly diverge.

Why is the 29th of February used as leap day?

In the Roman calendar, the month Februarius (which gave the name to today's month of February) was originally at 12th, and thus last, position at the end of the year, and was therefore the month to which a leap day was added (see Februarius and Julian Calendar on Wikipedia).

How are leap years calculated?

To align the tropical year of about 365.25 days in length with the 365-day calendar year, an extra day is added every four years. However, since the tropical year is slightly shorter than 365.25 days, a leap year is occasionally omitted. This is the case for years which are smoothly divisible by 100 (e.g., 1900 and 2100). However, there is an exception: years that are smoothly divisible by 400 (eg. 1600, 2000, and 2400) are leap years. Therefore three times in 400 years a leap year is omitted.

As a result of these adjustments, the average calendar year is 365.2425 days, so the deviations add up to just about one day in 3200 years.

On Wikipedia you will find further, very detailed information on the exact length of the tropical year and on the calculation of leap years.

For readers with interest and knowledge of programming here is the calculation of a leap year in pseudocode:

if year modulo* 400 is 0 then is a leap year

else if year modulo 100 is 0 then is not a leap year

else if year modulo 4 is 0 then is a leap year

else is not a leap year

(*modulo: remainder of the division n divided by m, e.g. 2000 modulo 400 = 0)

List of leap years from 1600 to 2400

1600
1604
1608
1612
1616
1620
1624
1628
1632
1636
1640
1644
1648
1652
1656
1660
1664
1668
1672
1676
1680
1684
1688
1692
1696
1700
1704
1708
1712
1716
1720
1724
1728
1732
1736
1740
1744
1748
1752
1756
1760
1764
1768
1772
1776
1780
1784
1788
1792
1796
1800
1804
1808
1812
1816
1820
1824
1828
1832
1836
1840
1844
1848
1852
1856
1860
1864
1868
1872
1876
1880
1884
1888
1892
1896
1900
1904
1908
1912
1916
1920
1924
1928
1932
1936
1940
1944
1948
1952
1956
1960
1964
1968
1972
1976
1980
1984
1988
1992
1996
2000
2004
2008
2012
2016
2020
2024
2028
2032
2036
2040
2044
2048
2052
2056
2060
2064
2068
2072
2076
2080
2084
2088
2092
2096
2100
2104
2108
2112
2116
2120
2124
2128
2132
2136
2140
2144
2148
2152
2156
2160
2164
2168
2172
2176
2180
2184
2188
2192
2196
2200
2204
2208
2212
2216
2220
2224
2228
2232
2236
2240
2244
2248
2252
2256
2260
2264
2268
2272
2276
2280
2284
2288
2292
2296
2300
2304
2308
2312
2316
2320
2324
2328
2332
2336
2340
2344
2348
2352
2356
2360
2364
2368
2372
2376
2380
2384
2388
2392
2396
2400
Explanation:
  • 1700: The years 1700, 1800, 1900, 2100, 2200 and 2300 are not leap years, even though they are divisible
       by 4 without a remainder.
  • 1600: The years 1600, 2000 and 2400 are leap years, even though they are divisible by 100 without a remainder.
  • Annual shift of the summer solstice

    The following graph illustrates the annual shift of the summer solstice between 1750 and 2250 due to the leap year adjustment every four years and the leap year rules for years divisible by 100 and 400 years. The X axis (at the bottom, horizontal) shows the year numbers, the Y axis (left side, vertical) shows the date of the summer solstice in June (20th to 23rd).
    Annual shift of the summer solstice between 1750 and 2250 caused by the leap year adjustment every four years. Graph: Wikimedia creative commons
    Annual shift of the summer solstice between 1750 and 2250 caused by the leap year adjustment every four years. Graph: Wikimedia creative commons

    Additional information

    On Wikipedia you'll find detailed information on leap years, the Gregorian calendar, which is the basis of our current calendar and which sets the rules for leap years as described above, and its predecessor, the Julian Calendar.

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