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Contents
How often is 53 weeks in a year?
Thus, a company operating under this reporting convention has a 53-week fiscal year every five to six years. The following is a deeper look at the 52/53-week reporting convention. First, there is a discussion of the benefits, disadvantages, and best practices involved in choosing a 52/53-week fiscal year.
What do you call a year with 53 weeks?
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.
Can there be 53 weeks in a year?
Most years have 52 weeks, but if the year starts on a Thursday or is a leap year that starts on a Wednesday, that particular year will have 53 numbered weeks. These week numbers are commonly used in some European and Asian countries; but not so much in the United States.
How many is 52weeks?
One year has approximately 52 weeks.
Are there 53 weeks in 2021?
There are 52 weeks in 2021.
Why does 2021 have 53 weeks?
What is a 53-week year? Due to the layout of the 4-5-4 Calendar (52 weeks x 7 days = 364 days), which results in one remaining day each year, and the occurrence of Leap Year, it is sometimes necessary to add a 53rd week to the end of the calendar for sales reporting purposes only.
How many weeks are in a full year?
52 weeks. That’s the average number of weeks in a normal year. While 52 full weeks is a nice rounded number (not as nice as 50, though), the hard facts actually give us another more precise number. The true number of weeks in a year, to the exact decimal point, is 52.143 weeks.
Who invented the 7 day week?
For centuries the Romans used a period of eight days in civil practice, but in 321 CE Emperor Constantine established the seven-day week in the Roman calendar and designated Sunday as the first day of the week.
What is today full date?
Today’s date in India right now is Thursday, July 21, 2022, 4:13:42 AM IST (GMT +05:30 Hours).
Is there a week 53 in 2020 payroll?
– It is not possible to make a week 53 appear in Payroll Manager unless it actually exists – e.g. in 2020-21 there are 53 Mondays (the first being 6th April 2020 and the 53rd being 5th April 2021) – so if the weekly pay date is a Monday employees will receive 53 payments in the tax year.
What was the 13 month called?
Undecimber or Undecember is a name for a thirteenth month in a calendar that normally has twelve months. Duodecimber or Duodecember is similarly a fourteenth month.
Why is 2020 not a leap year?
Leap years are always multiples of four — 2016, 2020, 2024 — but a year that is a multiple of four is not always a leap year. There are exceptions, such as 1900 and 2100, both multiples of four, yet neither a leap year. A year ending with 00 is obviously a multiple of four, but is usually not a leap year.
Can there be 54 weeks in a year?
The 54-Week Calendar contains exactly 54 weeks per year. Some weeks are shortened to 6 days, though. In a leap year with 366 days, all adjacent months contain exactly 9 weeks (or 61 days) together and every month has one week with only 6 days in it.
How many weeks are in a mouth?
The days are grouped together as 7-day weeks, so, one year has 52 weeks + 1 day.
How many weeks are in a fortnight year?
There are approximately 26 fortnights in a year. The word ‘fortnight’ refers to a duration of 14 nights, or approximately 2 weeks.
Are there 52 weeks in every year?
A year has 52 weeks plus 1 day. One calendar year has 365 days, which are divided into 7-day weeks. To know how many weeks there are in a year, you just divide the number of days there are in a year (365) by how many days there are in a week (7).
Is there a week 53 in 2022 payroll?
If you pay your employees weekly, two weekly or four weekly on Monday 4 April 2022, you’ll have an extra pay run at the end of the 2021-22 tax year. If you pay your employees monthly, you won’t have a week 53.
How many weeks are there in a year 2021?
A calendar year consists of 52 weeks, 365 days in total. 2021 marks the beginning of a new decade. 2021 began on Friday, January 1 and will end on Friday, December 31, 2021. Usually, a year consists of 12 months and 52 weeks.
What years have 53 Fridays?
2021 has 53 Fridays which means that, for many employers, 2021 will be a Pay Period Leap Year (if you didn’t already celebrate one in 2020).
How Long is a Year? – The CPA Journal
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- Most searched keywords: Whether you are looking for How Long is a Year? – The CPA Journal Updating In Brief Although many businesses operate on a fiscal year distinct from the calendar year, some use a distinctive 52/53-week fiscal year. This reporting
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ISO week date – Wikipedia
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Contents
Relation with the Gregorian calendar[edit]
Advantages[edit]
Differences to other calendars[edit]
Algorithms[edit]
Other week numbering systems[edit]
References[edit]
External links[edit]
Navigation menu
How Do Week Numbers Work?
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52 Weeks Plus 1 Day
Monday or Sunday First
Not ISO 8601 in US & Canada
Which Years Have 53 Weeks
When Is the Weekend
Babylonian Origins
Elsewhere on timeanddatecom
53 weeks is how many months?
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Error 403 (Forbidden)
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53 weeks in months | How long is 53 weeks?
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How to transform weeks into months
Weeks to months conversion chart near 53 weeks
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How Long is a Year?
In Brief
Although many businesses operate on a fiscal year distinct from the calendar year, some use a distinctive 52/53-week fiscal year. This reporting convention can enhance the comparability of periods and the convenience of reporting timeframes, but it also comes with disadvantages and may not be fully understood by market participants. This article reviews the use of the 52/53-week convention of the past several decades and notes that although its use may be declining overall, it remains popular in certain industries. *** Accounting professionals are well aware that companies have choices about how to define a fiscal year. After all, many businesses operate on a fiscal year that does not coincide with the calendar year. In some industries, a variation of the fiscal year concept known as the 52/53-week fiscal year is also common. In fact, the National Retail Federation encourages the use of a 52/53-week fiscal year, also known as the 4-5-4 calendar (https://bit.ly/3GqbUfx). The basic idea of this calendar is to think in terms of 52 weeks rather than 12 months. This approach results in a fiscal year with 364 days (52 weeks × 7 days), which means there is one remaining day each year (or two days in a leap year). Those extra days accumulate such that approximately every five to six years, an extra week must be added to the fiscal year. Thus, a company operating under this reporting convention has a 53-week fiscal year every five to six years. The following is a deeper look at the 52/53-week reporting convention. First, there is a discussion of the benefits, disadvantages, and best practices involved in choosing a 52/53-week fiscal year. This is followed by a review of some of the unintended capital market consequences associated with this reporting convention. The article concludes with data on the popularity of this reporting structure over time and across industries.
Benefits of a 52/53-Week Reporting Convention The primary reason to choose a 52/53-week fiscal year is comparability. In many industries (e.g., retail, apparel, restaurants, hotels) sales can fluctuate dramatically between week-days and weekends. In addition, the number of weekends in a calendar month varies from one year to the next. The solution is to create a fiscal year in which the same number of weekends appears in comparable months, and in which holiday periods are lined up. For example, Bloomin’ Brands noted that the primary reason the company switched to a 52/53-week fiscal year in 2014 was to improve comparability between periods because of these aforementioned reasons (https://bit.ly/3nmUHw2). The 52/53-week fiscal year improves comparability between periods by dividing the year into four quarters that each have three months based on a 4 weeks/5 weeks/4 weeks format (totaling 13 weeks per quarter). This format also has the benefit of lining up internal accounting procedures with external financial reporting, as many managers choose to look at comparable monthly periods from an internal perspective regardless of the external reporting framework. As explained by Mark Bauman (“The Effect of the 53-Week Year on Annual Growth Rates,” The CPA Journal, April 2013, pp. 65–67), another benefit of choosing a 52/53-week fiscal year is that the end of every period always occurs on the same day of the week, and companies can choose whichever day best suits their needs. Such a schedule can be helpful for planning manufacturing schedules and various end-of-period accounting activities. For example, Kopin Corporation in 2004 stated that changing to a 52/53-week year end “was made to better match our production and shipping cycle, which is organized on a weekly basis” (https://bit.ly/3rhmLSQ). In addition, some manufacturers that use the 52/53-week fiscal year choose Friday to be the last day of their reporting period, because that always gives them the weekend to count inventory without causing a disruption to production (Rick Johnston, Andrew J. Leone, Sundaresh Ramnath, and Ya-wen Yang, “14-Week Quarters,” Journal of Accounting and Economics, 2012, vol. 53, pp. 271–289).
Disadvantages of a 52/53-Week Reporting Convention One disadvantage of the 52/53-week reporting convention is that equal quarter length, and year-over-year comparable monthly periods come at the cost of traditional month-to-month comparisons because some fiscal months have four weeks and some have five weeks. A similar problem exists when comparing traditional months (i.e., not all months have the same number of days), but the differences are usually only one day (and no more than three days). Several firms have adopted a system that overcomes this problem by creating 13 four-week periods (https://cnb.cx/3tjE746). In that system, however, one quarter has an extra four-week period (month), meaning one quarter is much longer than all the rest. Another disadvantage of using a less common reporting structure is that reporting periods may not align with customer and vendor reporting periods. For example, Excel Switching Corporation stated that the company would move away from a 52/53-week year in 1998 “to better synchronize the Registrant’s fiscal periods with the majority of its customers and suppliers” (https://bit.ly/33wTVp4).
Best Practices of a 52/53-Week Reporting Convention There are a few best practices that managers should consider when contemplating a 52/53-week reporting convention. First, reporting periods should end on a day that makes sense for the company (for inventory counts, production schedules, timekeeping schedules, etc.). For example, Learning Tree International, Inc. chooses to end its reporting periods on Fridays because its courses run based on calendar weeks; this allows for efficiencies with recognition of revenue and direct costs related to courses (https://bit.ly/3qoQH07). Second, because the fiscal year always ends on the same day of the week in a specific calendar month, managers can choose to define the year end as either the last date on which that day of the week occurs in the specific month, or on whatever date that day of the week falls on that is closest to the end of the specific month. For example, Apple Inc.’s fiscal year is defined as ending on the last Saturday of September, so its fiscal year always ends on one of the last seven dates in September (i.e., September 24–30). On the other hand, The Home Depot, Inc.’s fiscal year is defined as ending on the Sunday nearest to January 31, so its fiscal year always ends on one of seven dates from January 28 through February 3. Third, as with any fiscal year selection process, year (and quarter) ends should be at convenient times of the year; many entities choose a slower time of the year. For example, it is rare to see a retail business with a December 31 year end. Finally, keeping all subsidiaries on the same reporting structure eases the consolidation process. In fact, issues related to consolidation (e.g., from merger and acquisition activity) are commonly cited as reasons why a company switches either to or away from a 52/53-week fiscal year. For example, Clark Holdings Inc. switched to a 52/53-week fiscal year due to the acquisition of a company in 2008 (https://bit.ly/3qnN0HS), and Monterey Gourmet Foods switched from a 52/53-week fiscal year in 2005 “to accommodate the consolidation process of newly acquired subsidiaries” (https://bit.ly/3zVlUuU).
Do Capital Markets Understand the 52/53-Week Year End? Interestingly, there is evidence to suggest that capital market participants overlook non-standard reporting periods. For example, Johnston, Leone, Ramnath, and Yang (“14-Week quarters,” Journal of Accounting and Economics, 2012) found that for entities using 52/53-week financial reporting conventions, financial analysts do not incorporate the sales and earnings effects of the extra week in 14-week fiscal quarters into their forecasts of firm performance. Thus, on average, they underestimate both revenues and earnings in such quarters. Forecast estimation errors recur, albeit in the opposite direction, four fiscal quarters later in a year following a 14-week quarter. In a similar vein, investors do not appear to incorporate the impact of the additional week in 14-week quarters, and their surprise at the “unexpected” increase in revenues and earnings results in stock price adjustments that lead to abnormal stock returns. These results would not be expected in a fully efficient market. In addition to analysts and investors overlooking a 53rd week when it arises, other researchers have studied opportunistic behavior, such as whether these longer periods give rise to executive pay increases. Jorgensen, Rock, and Simpson [“What a Difference a Day Makes (In Executive Compensation),” working paper, 2016] found that companies which use a 52/53-week fiscal year increase CEO pay in 53-week years, but do not appear to adjust CEO compensation back down in subsequent 52-week years. Differences in corporate governance characteristics among companies (e.g., the relative independence of the board of directors) do not mitigate this phenomenon, notwithstanding the Dodd-Frank Act’s requirement that shareholder “say-onpay” votes must occur at least once every three years. Following the theme of opportunistic behavior, there is also anecdotal evidence that managers use the 52/53-week reporting convention to their advantage in other ways. In 2018, New Brunswick (NB) Liquor Corporation added a 53rd week to the provincially owned corporation’s fiscal year, but management did not raise corporate profit targets to reflect the extra week of sales. This resulted in inflated corporate bonuses and enabled management to avoid reporting an earnings decline that would otherwise have occurred. Not only did NB Liquor’s management fail to disclose the change in its fiscal year reporting convention—it actually ascribed an “unusually” large C$9 million increase in sales to good management (https://bit.ly/3nnXgOG).
Are Companies Choosing the 52/53-Week Reporting Convention More or Less Often? Identifying companies that report on a 52/53-week convention is a nontrivial task. To begin, the authors used the Python programming language to extract fiscal year–end dates from 10-K filings for all filings available on the SEC’s Edgar system during 1996–2017. These dates were then compared with reporting dates in the Compustat database, because the Compustat database standardizes dates to the closest month-end. Thus, date differences between these two sources serve as an initial identifier of years where the company is operating on a 52/53-week reporting convention. This condition, however, is not a perfect identification tool, because companies that use the 52/53-week reporting convention will occasionally have fiscal years that fall on the end of the month, just by nature of the calendar. Therefore, the authors manually checked the coding for all companies that had at least one year that was initially identified as a year where the company employed the 52/53-week reporting convention (thanks to Michelle Wilson for assistance). Exhibit 1 presents the breakdown of companies operating on a 52/53-week year-end convention over time. For the 1996–2017 period, 11.9% of all fiscal years were reported under the 52/53-week convention, which suggests that this is not an insignificant phenomenon. The raw number of entities using this reporting convention has decreased over time, but so has the total number of entities. On a relative basis, Exhibit 1 shows that the percentage of companies using this reporting convention in a given year is also decreasing over time. In 1996, 15.1% of companies used a 52/53-week reporting convention; in 2017, only 8.5% used that approach. Although it appears there is a decline in the popularity of this reporting convention over time, this data does not provide insights as to why this occurred. Exhibit 1 Use of 52/53-Week Fiscal Year Over Time One potential reason for a decline in the popularity of the 52/53-week reporting convention could be that existing companies are switching away from its use. To examine this possibility, Exhibit 2 presents the number of companies that switched to or from a 52/53-week year end across the sample period. Interestingly, there does not appear to be a dramatic difference between companies switching to or from this reporting convention. In fact, over the sample period there are more companies switching to a 52/53-week reporting convention (181) than switching away from this convention (139). Overall, this does not appear to be the cause of the decline. Exhibit 2 Companies Changing Reporting Convention, By Year Another potential reason for the decline in popularity could be due to a shift away from this convention in certain industries, or to a trend whereby the industries in which this convention is popular are declining (or consolidating) such that the relative size of those industries is decreasing. Exhibit 3 presents the industry breakdown of companies using the Fama-French 30 industry classification system derived from Standard Industrial Classification (SIC) codes. From Exhibit 1, the total number of publicly traded companies covered by the Compustat database has decreased from 6,015 in 1996 to 4,733 in 2017; those two years are represented in Exhibit 3. As expected, Exhibit 3 also shows that the 52/53-week reporting convention is most common in certain industries. In 2017, the following industries all have greater than 50% of companies operating on a 52/53-week reporting convention: apparel; textiles; retail; and restaurants, hotels, motels. Given that the National Retail Federation encourages the use of the 52/53-week fiscal year, it is somewhat surprising that only 58% of firms in the retail industry in 2017 follow that recommendation. Exhibit 3 Industry Breakdown of Companies, 1996 vs. 2017 The final column of Exhibit 3 presents the difference between the percentage of companies in an industry that used a 52/53-week reporting convention in 1996 versus 2017. The data shows that, although some industries have increased usage of the 52/53-week reporting convention between 1996 and 2017, many industries have decreased usage. It appears that the overall decline in usage over time shown in Exhibit 1 is due, at least in part, to a general decline in usage across many, but not all, industries. Although this may at first seem inconsistent with Exhibit 2 (showing more firms switching to a 52/53-week reporting convention during the sample period), Exhibit 2 does not account for new companies entering and others exiting the sample period. Table 3 also presents evidence that is consistent with a relative decline in the importance of certain industries that also happen to have high concentrations of firms reporting under the 52/53-week convention. For example, in 1996 the retail industry made up 5.8% of all publicly traded companies. In 2017, however, the industry made up only 3.3% of all publicly traded companies. In fact, all industries that had at least 10% of entities reporting under the 52/53-week convention saw declines in the industry’s relative size between 1996 and 2017. On the other hand, the two industries with the largest increases in relative size (banking, insurance, real estate, trading and healthcare, medical equipment, pharmaceutical products) had only 0.4% and 2.2% of entities reporting under the 52/53-week convention, respectively. Thus, the most salient explanation for the decline of businesses using the 52/53-week reporting convention appears to be that the relative size of the industries where that convention is most common has decreased.
ISO week date
Leap week calendar system
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.
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 Tuesday, 12 July 2022 corresponds to day number 2 in the week number 28 of 2022, and is written as 2022-W28-2 (in extended form) or 2022W282 (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 [ 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.
First week [ edit ]
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.
Dominical letter(s) plus weekdays, dates and week numbers at the beginning and end of a year Dominical
letter(s)[a] Days at the start of January Effect[a][b] Days at the end of December[a] 1
Mon 2
Tue 3
Wed 4
Thu 5
Fri 6
Sat 7
Sun [c] W01-1 01 Jan
week no. … 31 Dec
week no. 1
Mon[d] 2
Tue 3
Wed 4
Thu 5
Fri 6
Sat 7
Sun 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 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 ) 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 Numbers and letters in parentheses, ( ), apply to March − December in leap years. ^ Underlined numbers and letters belong to previous year or next year. ^ First date of the first week in the year. ^ First date of the last week in the year.
Last week [ edit ]
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 [ 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)
on Thursday (dominical letter D or DC) and any leap year on Wednesday (ED) any year ending on Thursday (D, ED) and any leap year ending on Friday (DC)
on Thursday (D, ED) and any leap year 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 ) {\displaystyle p(y)} , that returns the day of the week of 31 December:[1]
p ( y ) = ( y + ⌊ y 4 ⌋ − ⌊ y 100 ⌋ + ⌊ y 400 ⌋ ) mod 7 weeks ( y ) = 52 + { 1 (long) if p ( y ) = 4 , i.e. current year ends Thursday or p ( y − 1 ) = 3 , i.e. previous year ends Wednesday 0 (short) otherwise {\displaystyle {\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}}}
Long years per 400-year leap-cycle, highlighted ones also have 29 Feb in them; adding 2000 gives current year numbers 004 009 015 020 026 032 037 043 048 054 060 065 071 076 082 088 093 099 105 111 116 122 128 133 139 144 150 156 161 167 172 178 184 189 195 201 207 212 218 224 229 235 240 246 252 257 263 268 274 280 285 291 296 303 308 314 320 325 331 336 342 348 353 359 364 370 376 381 387 392 398
On average, a year has 53 weeks every 400⁄71 = 5.6338… years; there are 43 times when these long years are 6 years apart, 27 times when they are 5 years apart, and once they are 7 years apart (between years 296 and 303). The Gregorian years corresponding to these 71 long years can be subdivided as follows:
The Gregorian years corresponding to the other 329 short 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).
than the month years (371 − 366). 44 week years are 6 days longer than the month years (371 − 365).
than the month years (371 − 365). 70 week years are 2 days shorter than the month years (364 − 366).
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, a fixed length of 13 weeks per quarter is usually chosen in practice. These quarters may then be 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 ISO 8601-1 does not consider this case explicitly. The resulting pattern would be irregular. There would be 4 months of 5 weeks per normal, 52-week year, or 5 such months in a long, 53-week year. They meet one of the following three criteria:
The first day of the month is a … Thursday and the month has 29 through 31 days. Wednesday and the month has 30 or 31 days. Tuesday and the month has 31 days, ending on a Thursday.
Equivalently, the last day of the month is a … Thursday and it is not the 28th. Friday and it is not in February. Saturday and it is the 31st.
For all years, 8 days have a fixed ISO week number (between W01 and W08) in January and February. With the exception of leap years starting on Thursday, dates with fixed week numbers occur in all months of the year (for 1 day of each ISO week W01 to W52).
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 next occur in 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 the “Doomsday” algorithm, which calculates the weekday that the last day of February falls on. The dates listed in the table are all one day after the Doomsday, 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 ]
Some pairs and triplets of ISO weeks have the same days of the month:
W02 and W41 in common years
W03 with W42 in common years and with W15 and W28 in leap years
W04 and W43 in common years and with W16 and W29 in leap years
W05 and W44 in common years
W06 with W10 and W45 in common years and with W32 in leap years
W07 with W11 and W46 in common years and with W33 in leap years
W08 with W12 and W47 in common years and with W34 in leap years
W10 and W45
W11 and W46
W12 and W47
W15 and W28
W16 and W29
W37 and W50
W38 and W51
Some other weeks, i.e. W09, W19 through W26, W31 and W35 never share their days of the month ordinals 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.
Differences to other calendars [ edit ]
Solar astronomic phenomena, such as equinoxes and solstices, vary in the Gregorian calendar over a range spanning three days, over the course of each 400-year cycle, while the ISO Week Date calendar has a range spanning 9 days. For example, there are March equinoxes on 1920-W12-6 and 2077-W11-5 in UT.
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 1986 is ISO 1987-W01-1, i.e., it is in year 1987 instead of 1986. A programming bug confusing these two year numbers is probably the cause of some Android users of Twitter being unable to log in around midnight of 29 December 2014 UTC.[2]
The ISO week calendar relies on the Gregorian calendar, which it augments, to define the new year day (Monday of week 01). As a result, extra weeks are spread across the 400-year cycle in a complex, seemingly random pattern. (However, a relatively simple algorithm to determine whether a year has 53 weeks from its ordinal number alone is shown under “Weeks per year” above.) Most calendar reform proposals using leap week designs strive to simplify and harmonize this pattern, some by choosing a different leap cycle (e.g. 293 years).
Not all parts of the world consider the week to begin with Monday. For example, in some Muslim countries, the normal work week begins on Saturday, while in Israel it begins on Sunday. In much of the Americas, although the work week is usually defined to start on Monday, the calendar week is often considered to start on Sunday.
Algorithms [ edit ]
The week number (WW or woy for week of year) of any date can be calculated, given its ordinal date (i.e. day of the year, doy or DDD, 1–365 or 366) and its day of the week (D or dow, 1–7). When using serial numbers for dates (e.g. in spreadsheets), doy is the serial number for a date minus the serial number for 31st December of the previous year, or alterantively minus the serial number for 1st January the same year plus one.
Algorithm
Subtract the weekday number from the ordinal day of the year. Add 10. Divide by 7, discard the remainder. 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.
Formula y = year ( d a t e ) w = ⌊ 10 + doy ( d a t e ) − dow ( d a t e ) 7 ⌋ woy ( d a t e ) = { weeks ( y − 1 ) , if w < 1 1 , if w > weeks ( y ) w , otherwise. woy ( d a t e ) ∈ [ 1 , 53 ] doy ( d a t e ) ∈ [ 1 , 366 ] dow ( d a t e ) ∈ [ 1 , 7 ] weeks ( y e a r ) ∈ [ 52 , 53 ] {\displaystyle {\begin{aligned}y&={\text{year}}\,(date)\\w&=\left\lfloor {\frac {10+{\text{doy}}(date)-{\text{dow}}(date)}{7}}\right\rfloor \\{\text{woy}}(date)&={\begin{cases}{\text{weeks}}(y-1),&{\text{if }}w<1\\1,&{\text{if }}w>{\text{weeks}}(y)\\w,&{\text{otherwise.}}\end{cases}}\\{\text{woy}}(date)&\in [1,53]\\{\text{doy}}(date)&\in [1,366]\\{\text{dow}}(date)&\in [1,7]\\{\text{weeks}}(year)&\in [52,53]\\\end{aligned}}}
Calculating the week number from a month and day of the month [ edit ]
If the ordinal date is not known, it can be computed from the month (MM or moy) and day of the month (DD or dom) by any of several methods; e.g. using a table such as the following.
Offset for the day of the month to get ordinal day of the year Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Add Common year 0 31 59 90 120 151 181 212 243 273 304 334 dom Leap year 60 91 121 152 182 213 244 274 305 335
Example Find the week number of Saturday 5th November 2016 (leap year): Find the ordinal day number first:
moy = 11 dom = 5 leap = 1 add = 305, from table lookup doy = 305 + 5 = 310.
Alternatively, use spreadsheet serial day numbers instead:
off = 42369, i.e. 31st December 2015 day = 42679 doy = 42679 − 42369 = 310.
Finally, find the week number:
dow = 6, i.e. Saturday woy = (10 + 310 − 6) div 7 woy = (320 − 6) div 7 woy = 314 div 7 = 44.
Algorithm
Multiply the week number by 7. Then add the weekday number. From this sum subtract the correction for the year: Get the weekday of 4 January.
Add 3. The result is the ordinal date, which can be converted into a calendar date. If the ordinal date thus obtained is zero or negative, the date belongs to the previous calendar year;
if it is greater than the number of days in the year, it belongs to the following year.
Formula y = year ( d a t e ) d = woy ( d a t e ) × 7 + dow ( d a t e ) − ( dow ( y , 1 , 4 ) + 3 ) doy ( d a t e ) = { d + days ( y − 1 ) , if d < 1 d − days ( y ) , if d > days ( y ) d , otherwise. days ( y e a r ) ∈ [ 365 , 366 ] {\displaystyle {\begin{aligned}y&={\text{year}}(date)\\d&={\text{woy}}(date)\times 7+{\text{dow}}(date)-({\text{dow}}(y,1,4)+3)\\{\text{doy}}(date)&={\begin{cases}d+{\text{days}}(y-1),&{\text{if }}d<1\\d-{\text{days}}(y),&{\text{if }}d>{\text{days}}(y)\\d,&{\text{otherwise.}}\end{cases}}\\{\text{days}}(year)&\in [365,366]\\\end{aligned}}}
Other week numbering systems [ edit ]
The US system has weeks from Sunday through Saturday, and partial weeks at the beginning and the end of the year, i.e. 52 full and 1 partial week of 1 or 2 days if the year starts on Sunday or ends on Saturday, 52 full and 2 single-day weeks if a leap year starts on Saturday and ends on Sunday, otherwise 51 full and 2 partial 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 the end of December or the beginning of January or both.
The US broadcast calendar designates the week containing 1 January (and starting Monday) as the first of the year, but otherwise works like ISO week numbering without partial weeks. Up to six days of the previous December may be part of the first week of the year.
A mix of those, wherein weeks start Sunday and “containing 1 January” defines the first week, is used in US accounting, resulting in a system with years having also 52 or 53 weeks.
How Do Week Numbers Work?
Most of us have learned that a year has 52 weeks. So why do some calendars have a week numbered 53?
Weeks numbering varies in different countries. ©timeanddate.com
52 Weeks Plus 1 Day
The reason is that a common year in our Gregorian calendar consists of 52 weeks plus 1 day, while a leap year has 52 weeks plus 2 days.
How Long Is a Tropical Year?
However, countries vary on exactly how they present and number the weeks in their calendars.
Week Number Calculator
Monday or Sunday First?
There are at least six different week numbering systems currently in use around the world.
The most common is the International Standard ISO 8601, where Monday is the first day of the week followed by Tuesday, Wednesday, Thursday, Friday, Saturday, and with Sunday as the seventh and final day. Using ISO 8601 can help diminish uncertainty and confusion when communicating internationally.
Not ISO 8601 in US & Canada
However, not every country follows this standard. Several countries, including the United States, Canada, Australia, and New Zealand, put Sunday at the start of the week on their calendars.
Which Years Have 53 Weeks?
The weeks of the year in a Gregorian calendar are numbered from week 1 to week 52 or 53, depending on several varying factors. Most years have 52 weeks, but if the year starts on a Thursday or is a leap year that starts on a Wednesday, that particular year will have 53 numbered weeks. These week numbers are commonly used in some European and Asian countries; but not so much in the United States.
Weekday Calculator
When Is the Weekend?
As the first day of the week varies in different cultures, so does the weekend. The Christian part of the world marks Sunday as their day of rest and worship, while Muslims refer to Friday as their day of rest and prayer. The Jewish calendar counts Saturday as the Sabbath—the day of rest and worship.
Some countries use a separate color for the weekends and reserve the black or gray for the weekdays.
Babylonian Origins
There are many different opinions as to how the seven-day week originated, but the most common explanation is that it seems to have originated when Babylonian astrologers assigned planet gods to the days of the week around 700 BCE. The Romans later replaced these names with their own planet gods, and Germanic and Norse people later did the same with some of their gods.
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