ISO week date - Wiki slovník

Current week expressed according to ISO 8601
Date	2024-07-04
Week	2024-W27
Week with weekday	2024-W27-4

The ISO week date system is effectively a leap week calendar system that is part of the ISO 8601 date and time standard issued by the International Organization for Standardization (ISO) since 1988 (last revised in 2019) and, before that, it was defined in ISO (R) 2015 since 1971. It is used (mainly) in government and business for fiscal years, as well as in timekeeping. This was previously known as "Industrial date coding". The system specifies a week year atop the Gregorian calendar by defining a notation for ordinal weeks of the year.

The Gregorian leap cycle, which has 97 leap days spread across 400 years, contains a whole number of weeks (20871). In every cycle there are 71 years with an additional 53rd week (corresponding to the Gregorian years that contain 53 Thursdays). An average year is exactly 52.1775 weeks long; months (1⁄12 year) average at exactly 4.348125 weeks/month.

An ISO week-numbering year (also called ISO year informally) has 52 or 53 full weeks. That is 364 or 371 days instead of the usual 365 or 366 days. These 53 week years occur on all years that have Thursday as the 1st of January and on leap years that start on Wednesday the 1st. The extra week is sometimes referred to as a leap week, although ISO 8601 does not use this term.

Weeks start with Monday and end on Sunday. Each week's year is the Gregorian year in which the Thursday falls. The first week of the year, hence, always contains 4 January. ISO week year numbering therefore usually deviates by 1 from the Gregorian for some days close to 1 January.

Examples of contemporary dates around New Year's Day
English short		ISO
Sat 1 Jan 1977	1977-01-01	1976-W53-6
Sun 2 Jan 1977	1977-01-02	1976-W53-7

Sat 31 Dec 1977	1977-12-31	1977-W52-6
Sun 1 Jan 1978	1978-01-01	1977-W52-7
Mon 2 Jan 1978	1978-01-02	1978-W01-1

Sun 31 Dec 1978	1978-12-31	1978-W52-7
Mon 1 Jan 1979	1979-01-01	1979-W01-1

Sun 30 Dec 1979	1979-12-30	1979-W52-7
Mon 31 Dec 1979	1979-12-31	1980-W01-1
Tue 1 Jan 1980	1980-01-01	1980-W01-2

Sun 28 Dec 1980	1980-12-28	1980-W52-7
Mon 29 Dec 1980	1980-12-29	1981-W01-1
Tue 30 Dec 1980	1980-12-30	1981-W01-2
Wed 31 Dec 1980	1980-12-31	1981-W01-3
Thu 1 Jan 1981	1981-01-01	1981-W01-4

Thu 31 Dec 1981	1981-12-31	1981-W53-4
Fri 1 Jan 1982	1982-01-01	1981-W53-5
Sat 2 Jan 1982	1982-01-02	1981-W53-6
Sun 3 Jan 1982	1982-01-03	1981-W53-7
Notes: Both years 1979 start with the same day. 1980 is a leap year. 1980W is 2 days shorter: 1 day longer at the start, 3 days shorter at the end. 1981W begins three days before the end of 1980. 1981W has 53 weeks and ends three days into 1982.

A precise date is specified by the ISO week-numbering 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, the Gregorian date Thursday, 4 July 2024 corresponds to day number 4 in the week number 27 of 2024, and is written as 2024-W27-4 (in extended form) or 2024W274 (in compact form). The ISO year is slightly offset to the Gregorian year; for example, Monday 30 December 2019 in the Gregorian calendar is the first day of week 1 of 2020 in the ISO calendar, and is written as 2020-W01-1 or 2020W011.

Relation with the Gregorian calendar

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.

First week

The ISO 8601 definition for week 01 is the week with the first Thursday of the Gregorian year (i.e. of January) in it. The following definitions based on properties of this week are mutually equivalent, since the ISO week starts with Monday:

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 W01. If it is on a Friday, it is part of W53 of the previous year. If it is on a Saturday, it is part of the last week of the previous year which is numbered W52 in a common year and W53 in a leap year. If it is on a Sunday, it is part of W52 of the previous year.

Week date peculiarities at the beginning and end of a year
Dominical letter(s)^[a]	Days at the start of January							Effect				Days at the end of December^[a]
Dominical letter(s)^[a]	1 Mo	2 Tu	3 We	4 Th	5 Fr	6 Sa	7 Su	W01-1^[b]	week of 01 Jan	...	week of 31 Dec^[a]	1^[c] Mo	2 Tu	3 We	4 Th	5 Fr	6 Sa	7 Su
G(F)	01	02	03	04	05	06	07	01 Jan	W01	...	W01	31 (30)	(31)
F(E)		01	02	03	04	05	06	31 Dec			W01	30 (29)	31 (30)	(31)
E(D)			01	02	03	04	05	30 Dec			W01 (W53)	29 (28)	30 (29)	31 (30)	(31)
D(C)				01	02	03	04	29 Dec			W53	28 (27)	29 (28)	30 (29)	31 (30)	(31)
C(B)					01	02	03	04 Jan	W53		W52	27 (26)	28 (27)	29 (28)	30 (29)	31 (30)	(31)
B(A)						01	02	03 Jan	W52 (W53)^[d]		W52	26 (25)	27 (26)	28 (27)	29 (28)	30 (29)	31 (30)	(31)
A(G)							01	02 Jan	W52		W52 (W01)	25 (31)	26 (25)	27 (26)	28 (27)	29 (28)	30 (29)	31 (30)

Notes

^ ^a ^b ^c Partial dates in parentheses, ( ), apply to leap years.
^ First date of the first week in the year.
^ First date of the last week in the year.
^ W53 for the week of 1 January in common years starting on Saturday (B) applies only if the previous year was a leap year starting on Thursday (DC).

Last week

The last week of the ISO week-numbering year, i.e. W52 or W53, is the week before W01 of the next year. 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 W01 of the next year. If it is on a Thursday, it is in W53 of the year just ending. If on a Friday it is in W52 of the year just ending in common years and W53 in leap years. If on a Saturday or Sunday, it is in W52 of the year just ending.

Summary of last weeks
01 Jan	W01-1	Common year (365 − 1 or + 6)			Leap year (366 − 2 or + 5)
Mon	01 Jan	G	+0	−1	GF	+0	−2
Tue	31 Dec	F	+1	−2	FE	+1	−3
Wed	30 Dec	E	+2	−3	ED	+2	+3
Thu	29 Dec	D	+3	+3	DC	+3	+2
Fri	04 Jan	C	−3	+2	CB	−3	+1
Sat	03 Jan	B	−2	+1	BA	−2	+0
Sun	02 Jan	A	−1	+0	AG	−1	−1

Weeks per year

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 or 31 December 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 following year.

Using only the ordinal year number y, the number of weeks in that year can be determined from a function, $p(y)$ , that returns the day of the week of 31 December:^[1]

{\begin{aligned}p(y)&=\left(y+\left\lfloor {\frac {y}{4}}\right\rfloor -\left\lfloor {\frac {y}{100}}\right\rfloor +\left\lfloor {\frac {y}{400}}\right\rfloor \right){\bmod {7}}\\{\text{weeks}}(y)&=52+{\begin{cases}1{\text{ (long)}}&{\text{if }}p(y)=4{\text{, i.e. current year ends Thursday}}\\&{\text{or }}p(y-1)=3{\text{, i.e. previous year ends Wednesday}}\\0{\text{ (short)}}&{\text{otherwise}}\end{cases}}\end{aligned}}

Zdroj:https://en.wikipedia.org?pojem=ISO_week_date
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Long years per 400-year leap-cycle, highlighted ones also have 29 Feb in them; adding 2000 gives current year numbers
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

[fnp-1] Partial dates in parentheses, ( ), apply to leap years.

[fn1-2] First date of the first week in the year.

[fn2-3] First date of the last week in the year.

[fns-4] W53 for the week of 1 January in common years starting on Saturday (B) applies only if the previous year was a leap year starting on Thursday (DC).

[a]

[b]

[c]

[d]

[1]