Shortest Day of The Year

December 21st, 2016 - Winter Solstice
Place mouse cursor over the image to see latitude and length of daytime in any location of the World during winter solstice - December 21, 2016
 
Figure 1 (left) - Shadowed World map in Mercator projection. The darker the area the shorter the day. Figure 2 (right) - latitude vs. length of daytime relation plot.
Sources: Mercator map - wikipedia, author: Strebe; shadow overlay, latitude-daytime script and figure 2 - time.unitarium.com
Equinox
March
Solstice
June
Equinox
September
Solstice
December
YearDayTimeDayTimeDayTimeDayTime
20132011:022105:042220:442117:11
20142016:572110:512302:292123:03
20152022:452116:382308:202204:48
20162004:302022:342214:212110:44
20172010:282104:242220:022116:28
20182016:152110:072301:542122:23
20192021:582115:542307:502204:19
20202003:502021:442213:312110:02
Table 1 Exact dates and times (UTC) of equinoxes and solstices.

Circle of Latitude Latitude Daytime
Arctic Night > 67° 25' N (67.417°) 00:00
Arctic Circle 66° 33′ 44″ N (66.5622°) 02:12
Tropic of Cancer 23° 26′ 16″ N (23.437778°) 10:42
Equator 12:07
Tropic of Capricorn 23° 26′ 16″ S (-23.437778°) 13:35
Antarctic Day >65° 42′ 30″ S (-65.708305°) 24:00
Antarctic Circle 66° 33′ 44″ S (-66.5622°) 24:00
Table 2 - Length of daytime on the Circles of Latitude, Arctic Night and Antarctic Day circles

When is the shortest day of the year?

The shortest day and the longest night of the year in the Northern Hemisphere occur during winter solstice which is usually observed on december 21st or sometimes on december 22nd UTC (see table 1). In 2016 winter solstice is observed on december 21, exactly at 10:44 UTC. This is also the day of the longest day and the shortest night in the Southern Hemisphere. The opposite case takes place during june solstice - the longest day and the shortest night occur in the Northern Hemisphere and the shortest day and the longest night are observed in the Southern Hemisphere.

How long is the shortest day of the year?

As you can see on Figure 1,2 and Table 2,3, the length of the day depends on the latitude of the place on the Earth - the higher the latitude, the shorter the day but the dependency is nonlinear (see Figure 2). Table 3 shows some cities located on different latitudes around the World sorted by latitude in descending order, as you can see, the day is shorter, for example, in New York City, NY (latitude: 40° 45' 10'' N) then in Los Angeles, CA (latitude: 34° 03' 10'' N). Extreme situation takes place far on the North (and South) where the sunrise and the sunset do not occur - there is no daytime in the first case (north) and no night in the second (south). So, answering the question 'how long is the shortest day in the year', the shortest day on the Earth lasts 0 hours, but more accurately, you could say - 'it depends on latitude'.

Exact day length, sunrise and sunset time for any day of the year for over 200.000 places can be found here: Sunrise & sunset database

Some interesting facts (e.g. Why the day on the Equator is longer than 12 hours?)

As shown in table 2 the daylight duration on the Equator is not exactly 12 hours and the polar circles (Arctic and Antarctic) are not the borders where 24-hour night or 24-hour day begins. Arctic Night (24-hour night) starts on winter solstice circa 51 arcminutes (latitude) above Arctic Circle, Antarctic Day (24-hour daylight) starts 51 arcminutes (latitude) above Antarctic Circle. That's because of atmospheric refraction (deviation of light from a straight line) and the size of the Sun. Sunrise occurs when the Sun's upper limb, rather than its center, appears to cross the horizon. Similarly, the sunset occurs when upper limb of the Sun hides over the horizon. These phenomena give us a little longer daytime (7 minutes) on the Equator, smaller Arctic Night Circle and bigger Antarctic Daylight Circle.

See also: Longest Day of the Year, Earth Illumination Now

Table 3 - Cities around the World, sunrise and sunset times, day length, times of civil, nautical, astronomical twilight during Winter Solstice, December 21, 2016 . Sorted by latitude. All times are local.
Location Day Civil Twilight Nautical Twilight Astronomical Twilight
City Country Latitude Longitude Sunrise Sunset Day Length Begin End Length Begin End Length Begin End Length
ThuleGreenland77° 29' 21''-69° 19' 55''NoneNone00:00NoneNone00:0011:5515:1403:1909:0918:0108:52
TromsoNorway69° 40' 00''18° 58' 00''NoneNone00:0009:3113:5204:2107:4715:3707:5106:2816:5610:27
FairbanksUS, AK64° 54' 02''-148° 09' 39''11:0014:4003:4009:3516:0606:3108:2217:1808:5607:2118:2010:60
AnchorageUS, AK61° 09' 49''-149° 59' 31''10:1315:4205:2909:1116:4407:3208:1217:4409:3207:1818:3711:19
St.PetersburgRussia59° 53' 39''30° 15' 51''10:5916:5405:5510:0217:5107:4909:0518:4809:4208:1419:3911:25
MoscowRussia55° 45' 07''37° 36' 56''09:5716:5707:0109:1017:4408:3408:2118:3310:1207:3619:1811:42
LondonUK51° 30' 00''0° 07' 34''08:0315:5307:5007:2316:3309:1006:4017:1710:3705:5917:5711:58
New York CityUS, NY40° 45' 10''-73° 58' 21''07:1616:3109:1506:4517:0210:1706:1017:3611:2605:3718:1012:33
BeijingChina39° 55' 44''116° 23' 16''07:3216:5209:2007:0117:2210:2106:2717:5611:2905:5418:2912:35
TokyoJapan35° 41' 06''139° 45' 03''06:4616:3109:4506:1816:5910:4105:4617:3111:4505:1518:0212:47
Los AngelesUS, CA34° 03' 10''-118° 15' 50''06:5416:4709:5306:2617:1510:4805:5517:4611:5105:2518:1712:52
MiamiUS, FL25° 48' 44''-80° 14' 24''07:0317:3410:3206:3817:5911:2206:0918:2812:1905:4118:5613:16
HonoluluUS, HI21° 19' 15''-157° 50' 20''07:0417:5410:5006:4018:1811:3806:1218:4612:3405:4519:1313:29
MumbaiIndia18° 58' 30''72° 49' 32''07:0718:0610:5906:4318:3011:4706:1518:5712:4205:4819:2413:36
SingaporeSingapore1° 17' 35''103° 51' 21''07:0119:0412:0306:3819:2612:4806:1219:5213:4005:4620:1814:33
La ConcordiaEcuador0° 00' 00''-79° 22' 59''06:1118:1912:0705:4918:4112:5205:2319:0713:4504:5619:3414:37
Rio de JaneiroBrazil-22° 54' 00''-43° 13' 59''06:0419:3713:3305:3920:0214:2305:0920:3215:2304:3721:0316:26
Cape TownSouth Africa-33° 55' 00''18° 25' 00''05:3219:5714:2505:0320:2615:2304:2721:0216:3503:4721:4117:54
MelbourneAustralia-37° 49' 00''144° 58' 01''05:5420:4114:4705:2321:1215:5004:4321:5217:0803:5922:3618:38
Puerto WilliamsChile-54° 55' 59''-67° 37' 00''04:4722:0917:2203:4923:0719:17NoneNone24:00NoneNone24:00