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The ISO week date system is a leap week calendar system that is part of the ISO 8601 date and time standard. The system is used (mainly) in government and business for fiscal years, as well as in timekeeping.

The system uses the same cycle of 7 weekdays as the Gregorian calendar. Weeks start with Monday. ISO years have a year numbering which is approximately the same as the Gregorian years, but not exactly (see below). An ISO year has 52 or 53 full weeks (364 or 371 days). The extra week is called a leap week, a year with such a week a leap year.

A date is specified by the ISO year in the format YYYY, a week number in the format ww prefixed by the letter W, and the weekday number, a digit d from 1 through 7, beginning with Monday and ending with Sunday. For example, 2006-W52-7 (or in its most compact form 06W527) is the Sunday of the 52nd week of 2006. In the Gregorian system this day is called December 31, 2006.

The system has a 400-year cycle of 146,097 days (20,871 weeks), with an average year length of exactly 365.2425 days, just like the Gregorian calendar. Since non-leap years have 52 weeks, in every 400 years there are 71 leap years.

Relation with the Gregorian calendarEdit

The ISO year number deviates from the number of the Gregorian year on, if applicable, a Friday, Saturday, and Sunday, or a Saturday and Sunday, or just a Sunday, at the start of the Gregorian year (which are at the end of the previous ISO year) and a Monday, Tuesday and Wednesday, or a Monday and Tuesday, or just a Monday, at the end of the Gregorian year (which are in week 01 of the next ISO year). In the period 4 January–28 December and on all Thursdays the ISO year number is always equal to the Gregorian year number.

Mutually equivalent definitions for week 01 are:

  • the week with the year's first Thursday in it
  • the week with the year's first working day in it (if Saturdays, Sundays, and 1 January are no working days)
  • the week with January 4 in it
  • the first week with the majority (four or more) of its days in the starting year
  • the week starting with the Monday in the period 29 December - 4 January
  • the week with the Thursday in the period 1 - 7 January
  • If 1 January is on a Monday, Tuesday, Wednesday or Thursday, it is in week 01. If 1 January is on a Friday, Saturday or Sunday, it is in week 52 or 53 of the previous year.

Note that while most definitions are symmetric with respect to time reversal, one definition in terms of working days happens to be equivalent.

The last week of the ISO year is the week before week 01; in accordance with the symmetry of the definition, equivalent definitions are:

  • the week with the year's last Thursday in it
  • the week with December 28 in it
  • the last week with the majority (four or more) of its days in the ending year
  • the week starting with the Monday in the period 22 - 28 December
  • the week with the Thursday in the period 25 - 31 December
  • the week ending with the Sunday in the period 28 December - 3 January
  • If 31 December is on a Monday, Tuesday, or Wednesday, it is in week 01, otherwise in week 52 or 53.

The following years have 53 weeks:

  • years starting with Thursday
  • leap years starting with Wednesday

ExamplesEdit

  • 2005-01-01 is 2004-W53-6
  • 2005-01-02 is 2004-W53-7
  • 2005-12-31 is 2005-W52-6
  • 2007-01-01 is 2007-W01-1 (both years 2007 start with the same day)
  • 2007-12-30 is 2007-W52-7
  • 2007-12-31 is 2008-W01-1
  • 2008-01-01 is 2008-W01-2 (Gregorian year 2008 is a leap year, ISO year 2008 is 2 days shorter: 1 day longer at the start, 3 days shorter at the end)
  • 2008-12-29 is 2009-W01-1
  • 2008-12-31 is 2009-W01-3
  • 2009-01-01 is 2009-W01-4
  • 2009-12-31 is 2009-W53-4 (ISO year 2009 is a leap year, extending the Gregorian year 2009, which starts and ends with Thursday, at both ends with three days)
  • 2010-01-03 is 2009-W53-7

Examples where the ISO year is three days into the next gregorian year Edit

  • "{{ISOWEEKDATE|2009|12|31}}" gives "2009-W53-4" [1]
  • "{{ISOWEEKDATE|2010|1|1}}" gives "2009-W53-5" [2]
  • "{{ISOWEEKDATE|2010|1|2}}" gives "2009-W53-6" [3]
  • "{{ISOWEEKDATE|2010|1|3}}" gives "2009-W53-7" [4]
  • "{{ISOWEEKDATE|2010|1|4}}" gives "2010-W01-1" [5]

Examples where the ISO year is three days into the previous gregorian year Edit

  • "{{ISOWEEKDATE|2008|12|28}}" gives "2008-W52-7" [6]
  • "{{ISOWEEKDATE|2008|12|29}}" gives "2009-W01-1" [7]
  • "{{ISOWEEKDATE|2008|12|30}}" gives "2009-W01-2" [8]
  • "{{ISOWEEKDATE|2008|12|31}}" gives "2009-W01-3" [9]
  • "{{ISOWEEKDATE|2009|1|1}}" gives "2009-W01-4" [10]

The system does not need the concept of month and is not well connected with the Gregorian system of months: some months January and December are divided over two ISO years.

Week numberEdit

Anchor dates with a fixed week number in any year other than a leap year starting on Thursday (DC)
W01W02W03W04W05W06W07W08W09W10W11W12W13W14W15W16W17W18W19W20W21W22W23W24W25W26W27W28W29W30W31W32W33W34W35W36W37W38W39W40W41W42W43W44W45W46W47W48W49W50W51W52W53
Jan04Jan11Jan18Jan25 Feb01Feb08Feb15Feb22 Mar01Mar08Mar15Mar22Mar29 Apr05Apr12Apr19Apr26 May03May10May17May24May31 Jun07Jun14Jun21Jun28 Jul05Jul12Jul19Jul26 Aug02Aug09Aug16Aug23Aug30 Sep06Sep13Sep20Sep27 Oct04Oct11Oct18Oct25 Nov01Nov08Nov15Nov22Nov29 Dec06Dec13Dec20Dec27

The day of the week for these days are related to Doomsday because for any year, the Doomsday is the day of the week that the last day of February falls on. These dates are one day after the Doomsdays, except that in January and February of leap years the dates themselves are Doomsdays. In leap years the week number is the rank number of its Doomsday.

All other month dates can fall in one of two weeks, except for 29 December through 2 January which can be in W52, W53 or W01.

Mapping of week dates to month dates in common years
Type Jan01Jan02Jan03Jan04Jan05Jan06Jan07Jan08Jan09Jan10Jan11Jan12Jan13Jan14Jan15Jan16Jan17Jan18Jan19Jan20Jan21Jan22Jan23Jan24Jan25Jan26Jan27Jan28Jan29Jan30Jan31 Feb01Feb02Feb03Feb04Feb05Feb06Feb07Feb08Feb09Feb10Feb11Feb12Feb13Feb14Feb15Feb16Feb17Feb18Feb19Feb20Feb21Feb22Feb23Feb24Feb25Feb26Feb27Feb28 Mar01Mar02Mar03Mar04Mar05Mar06Mar07Mar08Mar09Mar10Mar11Mar12Mar13Mar14Mar15Mar16Mar17Mar18Mar19Mar20Mar21Mar22Mar23Mar24Mar25Mar26Mar27Mar28Mar29Mar30Mar31 Apr01Apr02Apr03Apr04Apr05Apr06Apr07Apr08Apr09Apr10Apr11Apr12Apr13Apr14Apr15Apr16Apr17Apr18Apr19Apr20Apr21Apr22Apr23Apr24Apr25Apr26Apr27Apr28Apr29Apr30 May01May02May03May04May05May06May07May08May09May10May11May12May13May14May15May16May17May18May19May20May21May22May23May24May25May26May27May28May29May30May31 Jun01Jun02Jun03Jun04Jun05Jun06Jun07Jun08Jun09Jun10Jun11Jun12Jun13Jun14Jun15Jun16Jun17Jun18Jun19Jun20Jun21Jun22Jun23Jun24Jun25Jun26Jun27Jun28Jun29Jun30 Jul01Jul02Jul03Jul04Jul05Jul06Jul07Jul08Jul09Jul10Jul11Jul12Jul13Jul14Jul15Jul16Jul17Jul18Jul19Jul20Jul21Jul22Jul23Jul24Jul25Jul26Jul27Jul28Jul29Jul30Jul31 Aug01Aug02Aug03Aug04Aug05Aug06Aug07Aug08Aug09Aug10Aug11Aug12Aug13Aug14Aug15Aug16Aug17Aug18Aug19Aug20Aug21Aug22Aug23Aug24Aug25Aug26Aug27Aug28Aug29Aug30Aug31 Sep01Sep02Sep03Sep04Sep05Sep06Sep07Sep08Sep09Sep10Sep11Sep12Sep13Sep14Sep15Sep16Sep17Sep18Sep19Sep20Sep21Sep22Sep23Sep24Sep25Sep26Sep27Sep28Sep29Sep30 Oct01Oct02Oct03Oct04Oct05Oct06Oct07Oct08Oct09Oct10Oct11Oct12Oct13Oct14Oct15Oct16Oct17Oct18Oct19Oct20Oct21Oct22Oct23Oct24Oct25Oct26Oct27Oct28Oct29Oct30Oct31 Nov01Nov02Nov03Nov04Nov05Nov06Nov07Nov08Nov09Nov10Nov11Nov12Nov13Nov14Nov15Nov16Nov17Nov18Nov19Nov20Nov21Nov22Nov23Nov24Nov25Nov26Nov27Nov28Nov29Nov30 Dec01Dec02Dec03Dec04Dec05Dec06Dec07Dec08Dec09Dec10Dec11Dec12Dec13Dec14Dec15Dec16Dec17Dec18Dec19Dec20Dec21Dec22Dec23Dec24Dec25Dec26Dec27Dec28Dec29Dec30Dec31
A W52 W01 W02 W03 W04 W05 W06 W07 W08 W09 W10 W11 W12 W13 W14 W15 W16 W17 W18 W19 W20 W21 W22 W23 W24 W25 W26 W27 W28 W29 W30 W31 W32 W33 W34 W35 W36 W37 W38 W39 W40 W41 W42 W43 W44 W45 W46 W47 W48 W49 W50 W51 W52
B W52 W01 W02 W03 W04 W05 W06 W07 W08 W09 W10 W11 W12 W13 W14 W15 W16 W17 W18 W19 W20 W21 W22 W23 W24 W25 W26 W27 W28 W29 W30 W31 W32 W33 W34 W35 W36 W37 W38 W39 W40 W41 W42 W43 W44 W45 W46 W47 W48 W49 W50 W51 W52
B* W53
C W53 W01 W02 W03 W04 W05 W06 W07 W08 W09 W10 W11 W12 W13 W14 W15 W16 W17 W18 W19 W20 W21 W22 W23 W24 W25 W26 W27 W28 W29 W30 W31 W32 W33 W34 W35 W36 W37 W38 W39 W40 W41 W42 W43 W44 W45 W46 W47 W48 W49 W50 W51 W52
D W01 W02 W03 W04 W05 W06 W07 W08 W09 W10 W11 W12 W13 W14 W15 W16 W17 W18 W19 W20 W21 W22 W23 W24 W25 W26 W27 W28 W29 W30 W31 W32 W33 W34 W35 W36 W37 W38 W39 W40 W41 W42 W43 W44 W45 W46 W47 W48 W49 W50 W51 W52 W53
E W01 W02 W03 W04 W05 W06 W07 W08 W09 W10 W11 W12 W13 W14 W15 W16 W17 W18 W19 W20 W21 W22 W23 W24 W25 W26 W27 W28 W29 W30 W31 W32 W33 W34 W35 W36 W37 W38 W39 W40 W41 W42 W43 W44 W45 W46 W47 W48 W49 W50 W51 W52 W01
F W01 W02 W03 W04 W05 W06 W07 W08 W09 W10 W11 W12 W13 W14 W15 W16 W17 W18 W19 W20 W21 W22 W23 W24 W25 W26 W27 W28 W29 W30 W31 W32 W33 W34 W35 W36 W37 W38 W39 W40 W41 W42 W43 W44 W45 W46 W47 W48 W49 W50 W51 W52 W01
G W01W02W03W04W05W06W07W08W09W10W11W12W13W14W15W16W17W18W19W20W21W22W23W24W25W26W27W28W29W30W31W32W33W34W35W36W37W38W39W40W41W42W43W44W45W46W47W48W49W50W51W52W01
Mapping of week dates to month dates in leap years
Type Jan01Jan02Jan03Jan04Jan05Jan06Jan07Jan08Jan09Jan10Jan11Jan12Jan13Jan14Jan15Jan16Jan17Jan18Jan19Jan20Jan21Jan22Jan23Jan24Jan25Jan26Jan27Jan28Jan29Jan30Jan31 Feb01Feb02Feb03Feb04Feb05Feb06Feb07Feb08Feb09Feb10Feb11Feb12Feb13Feb14Feb15Feb16Feb17Feb18Feb19Feb20Feb21Feb22Feb23Feb24Feb25Feb26Feb27Feb28Feb29 Mar01Mar02Mar03Mar04Mar05Mar06Mar07Mar08Mar09Mar10Mar11Mar12Mar13Mar14Mar15Mar16Mar17Mar18Mar19Mar20Mar21Mar22Mar23Mar24Mar25Mar26Mar27Mar28Mar29Mar30Mar31 Apr01Apr02Apr03Apr04Apr05Apr06Apr07Apr08Apr09Apr10Apr11Apr12Apr13Apr14Apr15Apr16Apr17Apr18Apr19Apr20Apr21Apr22Apr23Apr24Apr25Apr26Apr27Apr28Apr29Apr30 May01May02May03May04May05May06May07May08May09May10May11May12May13May14May15May16May17May18May19May20May21May22May23May24May25May26May27May28May29May30May31 Jun01Jun02Jun03Jun04Jun05Jun06Jun07Jun08Jun09Jun10Jun11Jun12Jun13Jun14Jun15Jun16Jun17Jun18Jun19Jun20Jun21Jun22Jun23Jun24Jun25Jun26Jun27Jun28Jun29Jun30 Jul01Jul02Jul03Jul04Jul05Jul06Jul07Jul08Jul09Jul10Jul11Jul12Jul13Jul14Jul15Jul16Jul17Jul18Jul19Jul20Jul21Jul22Jul23Jul24Jul25Jul26Jul27Jul28Jul29Jul30Jul31 Aug01Aug02Aug03Aug04Aug05Aug06Aug07Aug08Aug09Aug10Aug11Aug12Aug13Aug14Aug15Aug16Aug17Aug18Aug19Aug20Aug21Aug22Aug23Aug24Aug25Aug26Aug27Aug28Aug29Aug30Aug31 Sep01Sep02Sep03Sep04Sep05Sep06Sep07Sep08Sep09Sep10Sep11Sep12Sep13Sep14Sep15Sep16Sep17Sep18Sep19Sep20Sep21Sep22Sep23Sep24Sep25Sep26Sep27Sep28Sep29Sep30 Oct01Oct02Oct03Oct04Oct05Oct06Oct07Oct08Oct09Oct10Oct11Oct12Oct13Oct14Oct15Oct16Oct17Oct18Oct19Oct20Oct21Oct22Oct23Oct24Oct25Oct26Oct27Oct28Oct29Oct30Oct31 Nov01Nov02Nov03Nov04Nov05Nov06Nov07Nov08Nov09Nov10Nov11Nov12Nov13Nov14Nov15Nov16Nov17Nov18Nov19Nov20Nov21Nov22Nov23Nov24Nov25Nov26Nov27Nov28Nov29Nov30 Dec01Dec02Dec03Dec04Dec05Dec06Dec07Dec08Dec09Dec10Dec11Dec12Dec13Dec14Dec15Dec16Dec17Dec18Dec19Dec20Dec21Dec22Dec23Dec24Dec25Dec26Dec27Dec28Dec29Dec30Dec31
AG W52W01W02W03W04W05W06W07W08W09W10W11W12W13W14W15W16W17W18W19W20W21W22W23W24W25W26W27W28W29W30W31W32W33W34W35W36W37W38W39W40W41W42W43W44W45W46W47W48W49W50W51W52W01
BA W52 W01 W02 W03 W04 W05 W06 W07 W08 W09 W10 W11 W12 W13 W14 W15 W16 W17 W18 W19 W20 W21 W22 W23 W24 W25 W26 W27 W28 W29 W30 W31 W32 W33 W34 W35 W36 W37 W38 W39 W40 W41 W42 W43 W44 W45 W46 W47 W48 W49 W50 W51 W52
CB W53 W01 W02 W03 W04 W05 W06 W07 W08 W09 W10 W11 W12 W13 W14 W15 W16 W17 W18 W19 W20 W21 W22 W23 W24 W25 W26 W27 W28 W29 W30 W31 W32 W33 W34 W35 W36 W37 W38 W39 W40 W41 W42 W43 W44 W45 W46 W47 W48 W49 W50 W51 W52
DC W01 W02 W03 W04 W05 W06 W07 W08 W09 W10 W11 W12 W13 W14 W15 W16 W17 W18 W19 W20 W21 W22 W23 W24 W25 W26 W27 W28 W29 W30 W31 W32 W33 W34 W35 W36 W37 W38 W39 W40 W41 W42 W43 W44 W45 W46 W47 W48 W49 W50 W51 W52 W53
ED W01 W02 W03 W04 W05 W06 W07 W08 W09 W10 W11 W12 W13 W14 W15 W16 W17 W18 W19 W20 W21 W22 W23 W24 W25 W26 W27 W28 W29 W30 W31 W32 W33 W34 W35 W36 W37 W38 W39 W40 W41 W42 W43 W44 W45 W46 W47 W48 W49 W50 W51 W52 W53
FE W01 W02 W03 W04 W05 W06 W07 W08 W09 W10 W11 W12 W13 W14 W15 W16 W17 W18 W19 W20 W21 W22 W23 W24 W25 W26 W27 W28 W29 W30 W31 W32 W33 W34 W35 W36 W37 W38 W39 W40 W41 W42 W43 W44 W45 W46 W47 W48 W49 W50 W51 W52 W01
GF W01 W02 W03 W04 W05 W06 W07 W08 W09 W10 W11 W12 W13 W14 W15 W16 W17 W18 W19 W20 W21 W22 W23 W24 W25 W26 W27 W28 W29 W30 W31 W32 W33 W34 W35 W36 W37 W38 W39 W40 W41 W42 W43 W44 W45 W46 W47 W48 W49 W50 W51 W52 W01

AdvantagesEdit

  • The date directly tells the weekday.
  • All years start with a Monday and end with a Sunday.
  • When used by itself without using the concept of month, all years are the same except that leap years have a leap week at the end.
  • The weeks are the same as in the Gregorian calendar.

DisadvantagesEdit

Each equinox and solstice varies over a range of at least seven days. This is because each equinox and solstice may occur any day of the week and hence on at least seven different ISO week dates. For example, there are summer solstices on 2004-W12-7 and 2010-W11-7.

It cannot replace the Gregorian calendar, because it relies on it to define the new year day (Week 1 Day 1).

Leap year cycleEdit

The three types of week leap year are D, DC, and ED.

Dominical letters and Doomsdays
DL Doomsday 1 January
A or BA Tuesday Sunday
B or CB Monday Saturday
C or DC Sunday Friday
D or ED Saturday Thursday
E or FE Friday Wednesday
F or GF Thursday Tuesday
G or AG Wednesday Monday
400-year cycle of years by dominical letter
Centuries 1600 1700 1800 1900
2000 2100 2200 2300
Years
00 BA C E G
85572901 G B D F
86583002 F A C E
87593103 E G B D
88603204DC FE AG CB
89613305 B D F A
90623406 A C E G
91633507 G B D F
92643608 FE AG CB ED
93653709D F A C
94663810 C E G B
95673911 B D F A
96684012 AG CB ED GF
97694113 F A C E
98704214 E G B D
99714315D F A C
 724416 CB ED GF BA
 734517 A C E G
 744618 G B D F
 754719 F A C E
 764820ED GF BA DC
 774921 C E G B
 785022 B D F A
 795123 A C E G
 805224 GF BA DC FE
 815325 E G B D
 825426D F A C
 835527 C E G B
 845628 BA DC FE AG
Years
Centuries 1600 1700 1800 1900
2000 2100 2200 2300
ISO leap years in one 400-year cycle (28-year subcycles arranged horizontally)
DC D D ED D
+004 +009 +015 +020 +026
+032 +037 +043 +048 +054
+060 +065 +071 +076 +082
+088 +093 +099
+105 +111 +116 +122
+128 +133 +139 +144 +150
+156 +161 +167 +172 +178
+184 +189 +195
+201 +207 +212 +218
+224 +229 +235 +240 +246
+252 +257 +263 +268 +274
+280 +285 +291 +296
+303 +308 +314
+320 +325 +331 +336 +342
+348 +353 +359 +364 +370
+376 +381 +387 +392 +398

There are 13 28-year subcycles with 5 leap years each, and 6 remaining leap years in the remaining 36 years (the absence of leap days in the Gregorian calendar in 2100, 2200, and 2300 interrupts the subcycles). The leap years are 27 times 5 years apart, 43 times 6 years, and once 7 years. (A slightly more even distribution would be possible: 26 times 5 years apart, and 45 times 6 years.)

The Gregorian years corresponding to the 71 ISO leap years can be subdivided as follows:

Thus 27 ISO years are 5 days longer than the corresponding Gregorian year, and 44 are 6 days longer. Of the other 329 Gregorian years (neither starting nor ending with Thursday), 70 are Gregorian leap years, and 259 are non-leap years, so 70 ISO years are 2 days shorter, and 259 are 1 day shorter.

Alternative leap year rules Edit

KARL PALMENEdit

The best leap week calendars to convert to Gregorian would be those based on the ISO week or a similar week numbering scheme. I thought of another that interlocks with 28-year cycle that such calendars have, which is interrupted by a dropped leap day.

002 008 014 020 026
030 036 042 048 054
058 064 070 076 082
086 092 098 104 110 116 122
126 132 138 144 150
154 160 166 172 178
182 188 194 200 206 212 218
222 228 234 240 246
250 256 262 268 274
278 284 290 296 302 308 314
318 324 330 336 342
346 352 358 364 370
374 380 386 392 398

In each row, the leap years are six years apart and first of each row is four years after the last of the previous row. Each row covers 28 years unless it contains a dropped Gregorian leap day, in which case it covers 40 years. The rows are synchronised to the 28-year cycles that occur in any week-number calendar like ISO week date. In particular, the 2nd year of each row is in the Gregorian calendar a leap year starting on Tuesday. A simpler leap week rule would have rows alternating between 28 and 34, but this would be harder to convert to/from the Gregorian calendar.


The following variation matches all even-numbered years with 53 ISO weeks. Red years are one year later than ISO and the blue years are a year early. Gregorian leap years are shown in bold.

014 020 026 032 038
042 048 054 060 066
070 076 082 088 094 100 106
110 116 122 128 134
138 144 150 156 162
166 172 178 184 190
194 200 206 212 218 224 230
234 240 246 252 258
262 268 274 280 286
290 296 302 308 314 320 326
330 336 342 348 354
358 364 370 376 382
386 392 398 004 010

list of ISO 53-week years

As with my original proposal every row has years six years apart. The first year of each row is four years after the previous. Each row has five, unless it spans a dropped leap year, then it has seven. Unlike my original proposal, it is not symmetrical.

To get a leap week rule where every leap week occurs in a Gregorian leap year and furthermore every Gregorian leap year that also has 53 ISO weeks is included amongst them. Take the previously mentioned proposal make the leap weeks in the first and third columns occur two years later, the leap week in the 5th and 7th column occur two years earlier. Then move 100 to 96 and 200 to 204.

016 020 --- 028 032 036 ---
044 048 --- 056 060 064 ---
072 076 --- 084 088 092 096 <<< 104 ---
112 116 --- 124 128 132 ---
138 144 --- 152 156 160 ---
166 172 --- 180 184 188 ---
196 >>> 204 208 212 216 --- 224 228 ---
236 240 --- 248 252 256 ---
264 268 --- 276 280 284 ---
292 296 --- 304 308 312 --- 320 324 ---
332 336 --- 344 348 352 ---
360 364 --- 372 376 380 ---
388 392 --- 000 004 008 ---

The Gregorian leap years with 53 ISO weeks remain in bold. Other changes can be made to the years not shown in bold. For example, the 4th row could be changed to

108 --- 116 120 --- 128 132 ---

CHRISTOPH PÄPEREdit

  • Every year that has a leap week, also has a leap day. 
  • Leap years are divisible by four.

There are 26 leap days per cycle in years without a 53rd week.

​distribution as evenly as possible under these constraintsEdit

round down:

000  004  008   –   016  020   –  
028  032  036   –   044  048   –  
056  060  064   +   072  076   –  
084  088  092   –   100  104   –  
112  116  120   –   128  132   –  
140  144   –   152  156  160   –  
168  172   –   180  184  188   –  
196  200   +   208  212  216   –  
224  228   –   236  240  244   –  
252  256   –   264  268   –   276
280  284   –   292  296   –   304 
308  312   –   320  324   +   332 
336  340   –   348  352   –   360 
364  368   –   376  380   –   388 
392   –

round up:

000   –   008  012   –   020  024  
 –   032  036  040   –   048  052  
 –   060  064  068   +   076  080 
 –   088  092  096   –   104  108 
 –   116  120  124   –   132  136 
 –   144  148   –   156  160  164 
 –   172  176   –   184  188  192 
 +   200  204   –   212  216  220 
 –   228  232   –   240  244  248 
 –   256  260   –   268  272   – 
280  284  288   –   296  300   – 
308  312  316   –   324  328   +  
336  340  344   –   352  356   –  
364  368  372   –   380  384   –  
392  396

The former matches 27, the latter just 20 of the 71 long years according to ISO 8601.

One would now need to select three of the empty places, which do not contain a “leap+leap year”, to remain empty for leap-day years, e.g. – as marked above with plus signs –

068, 204, 328
072, 196, 332

Other week numbering systemsEdit

For an overview of week numbering systems see week number. The US system has weeks from Sunday through Saturday, and partial weeks at the beginning and the end of the year. An advantage is that no separate year numbering like the ISO year is needed, while correspondence of lexicographical order and chronological order is preserved.

External linksEdit

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