The
March 2018 Week Mon Tue Wed Thu Fri Sat Sun W09 26 27 28 01 02 03 04 W10 05 06 07 08 09 10 11 W11 12 13 14 15 16 17 18 W12 19 20 21 22 23 24 25 W13 26 27 28 29 30 31 01 Contents 1 Relation with the Gregorian calendar 1.1 First week 1.2 Last week 1.3 Weeks per year 1.4 Weeks per month 1.5 Dates with fixed week number 1.6 Equal weeks 2 Advantages 3 Disadvantages 4 Calculation 4.1 Calculating the week number of a given date 4.2 Calculating a date given the year, week number and weekday 5 Other week numbering systems 6 See also 7 Notes 8 External links Relation with the Gregorian calendar[edit] The ISO week year number deviates from the Gregorian year number in one of three ways. The days differing are a Friday through 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 through 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 to 28 December the ISO week year number is always equal to the Gregorian year number. The same is true for every Thursday. Examples of contemporary dates around New Year’s Day Date Notes Gregorian ISO Sat 1 Jan 2005 2005-01-01 2004-W53-6 Sun 2 Jan 2005 2005-01-02 2004-W53-7 Sat 31 Dec 2005 2005-12-31 2005-W52-6 Sun 1 Jan 2006 2006-01-01 2005-W52-7 Mon 2 Jan 2006 2006-01-02 2006-W01-1 Sun 31 Dec 2006 2006-12-31 2006-W52-7 Mon 1 Jan 2007 2007-01-01 2007-W01-1 Both years 2007 start with the same day. Sun 30 Dec 2007 2007-12-30 2007-W52-7 Mon 31 Dec 2007 2007-12-31 2008-W01-1 Tue 1 Jan 2008 2008-01-01 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. Sun 28 Dec 2008 2008-12-28 2008-W52-7 Mon 29 Dec 2008 2008-12-29 2009-W01-1 ISO year 2009 begins three days before the end of Gregorian 2008. Tue 30 Dec 2008 2008-12-30 2009-W01-2 Wed 31 Dec 2008 2008-12-31 2009-W01-3 Thu 1 Jan 2009 2009-01-01 2009-W01-4 Thu 31 Dec 2009 2009-12-31 2009-W53-4 ISO year 2009 has 53 weeks and ends three days into Gregorian year 2010. Fri 1 Jan 2010 2010-01-01 2009-W53-5 Sat 2 Jan 2010 2010-01-02 2009-W53-6 Sun 3 Jan 2010 2010-01-03 2009-W53-7 First week[edit]
The
It is the first week with a majority (4 or more) of its days in January. Its first day is the Monday nearest to 1 January. It has 4 January in it. Hence the earliest possible first week extends from Monday 29 December (previous Gregorian year) to Sunday 4 January, the latest possible first week extends from Monday 4 January to Sunday 10 January. It has the year's first working day in it, if Saturdays, Sundays and 1 January are not working days. If 1 January is on a Monday, Tuesday, Wednesday or Thursday, it is in week 01. If 1 January is on a Friday, it is part of week 53 of the previous year. If it is on a Saturday, it is part of the last week of the previous year which is numbered 52 in a common year and 53 in a leap year. If it is on a Sunday, it is part of week 52 of the previous year. Last week[edit] The last week of the ISO week-numbering year, i.e. the 52nd or 53rd one, is the week before week 01. This week’s properties are: It has the year's last Thursday in it. It is the last week with a majority (4 or more) of its days in December. Its middle day, Thursday, falls in the ending year. Its last day is the Sunday nearest to 31 December. It has 28 December in it. Hence the earliest possible last week extends from Monday 22 December to Sunday 28 December, the latest possible last week extends from Monday 28 December to Sunday 3 January. If 31 December is on a Monday, Tuesday or Wednesday, it is in week 01 of the next year. If it is on a Thursday, it is in week 53 of the year just ending; if on a Friday it is in week 52 (or 53 if the year just ending is a leap year); if on a Saturday or Sunday, it is in week 52 of the year just ending. Weeks per year[edit] The long years, with 53 weeks in them, can be described by any of the following equivalent definitions: any year starting on Thursday (dominical letter D or DC) and any leap year starting on Wednesday (ED) any year ending on Thursday (D, ED) and any leap year ending on Friday (DC) years in which 1 January and 31 December (in common years) or either (in leap years) are Thursdays All other week-numbering years are short years and have 52 weeks. The number of weeks in a given year is equal to the corresponding week number of 28 December, because it is the only date that is always in the last week of the year since it is a week before 4 January which is always in the first week of the year. Using only the ordinal year number, the number of weeks in that year can be determined:[1] weeks ( year ) = 52 + 1 (long) if p ( year ) = 4 or p ( year − 1 ) = 3 0 (short) otherwise p ( year ) = ( year + ⌊ year 4 ⌋ − ⌊ year 100 ⌋ + ⌊ year 400 ⌋ ) mod 7 displaystyle begin aligned text weeks ( text year )&=52+ begin cases 1 text (long) & text if p( text year )=4\& text or p( text year -1)=3\0 text (short) & text otherwise end cases \p( text year )&=left( text year +leftlfloor frac text year 4 rightrfloor -leftlfloor frac text year 100 rightrfloor +leftlfloor frac text year 400 rightrfloor right) bmod 7 end aligned The following 71 years in a 400-year cycle have 53 weeks (371 days); years not listed have 52 weeks (364 days); add 2000 for current years: 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. On average, a year has 53 weeks every 400⁄71 = 5.6338… years, and these long ISO years are 43 times 6 years apart, 27 times 5 years apart, and once 7 years apart (between years 296 and 303). The Gregorian years corresponding to these 71 long years can be subdivided as follows: 27 Gregorian leap years, emphasized in the list above: 14 starting on Thursday, hence ending on Friday, and 13 starting on Wednesday, hence ending on Thursday; 44 Gregorian common years starting, hence also ending on Thursday. The Gregorian years corresponding to the other 329 short ISO years (neither starting nor ending with Thursday) can also be subdivided as follows: 70 are Gregorian leap years. 259 are Gregorian common years. Thus, within a 400-year cycle: 27 week years are 5 days longer than the month years (371 − 366). 44 week years are 6 days longer than the month years (371 − 365). 70 week years are 2 days shorter than the month years (364 − 366). 259 week years are 1 day shorter than the month years (364 − 365). Weeks per month[edit]
The ISO standard does not define any association of weeks to months. A
date is either expressed with a month and day-of-the-month, or with a
week and day-of-the-week, never a mix.
Weeks are a prominent entity in accounting where annual statistics
benefit from regularity throughout the years. Therefore, in practice
usually a fixed length of 13 weeks per quarter is chosen which is then
subdivided into 5 + 4 + 4 weeks, 4 + 5 + 4 weeks or 4 + 4 + 5 weeks.
The final quarter has 14 weeks in it when there are 53 weeks in the
year.
When it is necessary to allocate a week to a single month, the rule
for first week of the year might be applied, although
Overview of dates with a fixed week number in any year other than a leap year starting on Thursday Month
Dates
January 04 11 18 25 01–04 February 01 08 15 22 05–08 March 01 08 15 22 29 09–13 April 05 12 19 26 14–17 May 03 10 17 24 31 18–22 June 07 14 21 28 23–26 July 05 12 19 26 27–30 August 02 09 16 23 30 31–35 September 06 13 20 27 36–39 October 04 11 18 25 40–43 November 01 08 15 22 29 44–48 December 06 13 20 27 49–52 During leap years starting on Thursday (i.e. the 13 years numbered 004, 032, 060, 088, 128, 156, 184, 224, 252, 280, 320, 348, 376 in a 400-year cycle), the ISO week numbers are incremented by 1 from March to the rest of the year. This last occurred in 1976 and 2004 and will not occur again before 2032. These exceptions are happening between years that are most often 28 years apart, or 40 years apart for 3 pairs of successive years: from year 088 to 128, from year 184 to 224, and from year 280 to 320. 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. Equal weeks[edit]
W06 05 06 07 08 09 10 11 W10 05 06 07 08 09 10 11 W45 05 06 07 08 09 10 11 W07 12 13 14 15 16 17 18 W11 12 13 14 15 16 17 18 W46 12 13 14 15 16 17 18 W08 19 20 21 22 23 24 25 W12 19 20 21 22 23 24 25 W47 19 20 21 22 23 24 25 The pairs 02/41, 03/42, 04/43, 05/44, 15/28, 16/29, 37/50, 38/51 and triplets 06/10/45, 07/11/46, 08/12/47 have the same days of the month in common years. Of these, the pairs 10/45, 11/46, 12/47, 15/28, 16/29, 37/50 and 38/51 share their days also in leap years. Leap years also have triplets 03/15/28, 04/16/29 and pairs 06/32, 07/33, 08/34. The weeks 09, 19–26, 31 and 35 never share their days of the month with any other week of the same year. Advantages[edit] All weeks have exactly 7 days, i.e. there are no fractional weeks. Every week belongs to a single year, i.e. there are no ambiguous or double-assigned weeks. The date directly tells the weekday. All week-numbering years start with a Monday and end with a Sunday. When used by itself without using the concept of month, all week-numbering years are the same except that some years have a week 53 at the end. The weeks are the same as used with the Gregorian calendar. Disadvantages[edit]
The year number of the ISO week very often differs from the Gregorian
year number for dates close to 1 January. For example, 29 December
2014 is ISO 2015-W01-1, i.e., it is in year 2015 instead of 2014. A
programming bug confusing these two year numbers is probably the cause
of some Android users of
To the day of: Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Add: 0 31 59 90 120 151 181 212 243 273 304 334 For leap years: 0 31 60 91 121 152 182 213 244 274 305 335 Method: Using ISO weekday numbers (running from 1 for Monday to 7 for Sunday), subtract the weekday from the ordinal date, then add 10. Divide the result by 7. Ignore the remainder; the quotient equals the week number. If the week number thus obtained equals 0, it means that the given date belongs to the preceding (week-based) year. If a week number of 53 is obtained, one must check that the date is not actually in week 1 of the following year. week ( date ) = ⌊ ordinal ( date ) − weekday ( date ) + 10 7 ⌋ week = lastWeek ( year − 1 ) , week < 1 1 , week > lastWeek ( year ) displaystyle begin aligned text week ( text date
)&=leftlfloor frac text ordinal ( text date )- text weekday
( text date )+10 7 rightrfloor \ text week &= begin cases
text last
Friday 26 September 2008 Ordinal day: 244 + 26 = 270
Weekday: Friday = 5
270 − 5 + 10 = 275
275 ÷ 7 = 39.28…
Result:
Calculating a date given the year, week number and weekday[edit] This method requires that one know the weekday of 4 January of the year in question.[3] Add 3 to the number of this weekday, giving a correction to be used for dates within this year. Method: Multiply the week number by 7, then add the weekday. From this sum subtract the correction for the year. The result is the ordinal date, which can be converted into a calendar date using the table in the preceding section. If the ordinal date thus obtained is zero or negative, the date belongs to the previous calendar year; if greater than the number of days in the year, to the following year. ordinal ( date ) = week ( date ) × 7 + weekday ( date ) − ( weekday ( year ( date ) , 1 , 4 ) + 3 ) if ordinal < 1 then ordinal = ordinal + daysInYear ( year − 1 ) if ordinal > daysInYear ( year ) then ordinal = ordinal − daysInYear ( year ) displaystyle begin aligned text ordinal ( text date )= &
text week ( text date )times 7+ text weekday ( text date )\&
-( text weekday ( text year ( text date ),1,4)+3)\[4pt] text if
ordinal < & text 1 then ordinal = text ordinal + text
daysIn
Example: year 2008, week 39, Saturday (day 6) Correction for 2008: 5 + 3 = 8 (39 × 7) + 6 = 279 279 − 8 = 271 Ordinal day 271 of a leap year is day 271 − 244 = 27 September Result: 27 September 2008 Other week numbering systems[edit] 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, i.e. 53 or 54 weeks. An advantage is that no separate year numbering like the ISO year is needed. Correspondence of lexicographical order and chronological order is preserved (just like with the ISO year-week-weekday numbering), but partial weeks make some computations of weekly statistics or payments inaccurate at end of December or beginning of January. A variant of this US scheme groups the possible 1 to 6 days of December remaining in the last week of the Gregorian year within week 1 in January of the next Gregorian year, to make it a full week, bringing a system with accounting years having also 52 or 53 weeks and only the last 6 days of December may be counted as part of another year than the Gregorian year. The US broadcast calendar counts the week containing 1 January as the first of the year, but otherwise works like ISO week numbering without partial weeks. See also[edit] Week 4–4–5 calendar Notes[edit] ^ Gent, Robert H. "The Mathematics of the
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