Week years

Introducing week-years

Most of the time, dates are represented as a year, month and day in a particular calendar system - occasionally with an era as well. An alternative approach is to represent a date as a year, week, and day-of-week.

For example, using the ISO-8601 rule, the year/month/day combination "2016, February, 4" is equivalently year 2016, week 5, Thursday. All of this is performed relative to a specific calendar system.

However, under the same rule the year/month/day combination "2014, December, 29th" is equivalently year 2015, week 1, Monday: the "year" part of a year/month/day representation isn't always the same as the year part of the year/week/day-of-week representation for the same date. To avoid ambiguity, I refer to the year part of a year/week/day-of-week representation as a week-year.

The two representations are exactly equivalent: every day can be represented in either form. Week-years are more widely used in some countries than in others, typically in business or educational settings.

There are different ways of mapping between year/month/day and week-year/week/day-of-week representations, which we refer to as week-year rules.

Noda Time features for week-years

As of Noda Time 2.0, week-year rules are entirely separate from calendar systems. A rule is represented by the IWeekYearRule interface, and built-in implementations are obtained via factory members in the WeekYearRules static class.

Although the GetWeeksInWeekYear and GetLocalDate methods require a CalendarSystem, we also provide extension methods in WeekYearRuleExtensions that default to the ISO calendar system, delegating to the existing IWeekYearRule methods. This reduces the burden of implementing IWeekYearRule, but allows callers who are only using the ISO calendar system to omit it.

There are two methods to convert from year-month-day representation to week-based representation: GetWeekYear and GetWeekOfWeekYear, both accepting a LocalDate. There is no equivalent to obtain the day of week, as that does not change based on the rule or even on the calendar system.

Noda Time 2.0 comes with two kinds of rule: ISO-like rules, and BCL rules.

ISO-like rules

Let's start with the most common rule: WeekYearRules.Iso, which implements the rule specified in ISO-8601. Under this rule:

  • All weeks are Monday-to-Sunday
  • If the week that contains the first day of the year has four days or more in that year, then the whole of that week is in week 1 of that year; otherwise, the whole of that week is in the final week of the previous year.

To put the "four days or more" rule in a different way: if the first day of the calendar year is Monday, Tuesday, Wednesday or Thursday, then the week containing that day is week 1 of the same year; if the calendar year starts on a Friday, Saturday or Sunday, then that week is in the previous week-year.


  • January 1st 2013 is a Tuesday, so 2013 week 1 runs from 2012-12-31 to 2013-01-06 inclusive
  • January 1st 2014 is a Wednesday, so 2014 week 1 runs from 2013-12-30 to 2013-01-05 inclusive
  • January 1st 2015 is a Thursday, so 2015 week 1 runs from 2014-12-29 to 2015-01-04 inclusive
  • January 1st 2016 is a Friday, so 2015 week 53 runs from 2015-12-28 to 2016-01-03 inclusive, and 2016 week 1 runs from 2016-01-04 to 2016-01-10 inclusive.
  • January 1st 2017 is a Sunday, so 2016 week 52 runs from 2016-12-26 to 2017-01-01 inclusive, and 2017 week 1 runs from 2017-01-02 to 2017-01-08 inclusive.

Although this is the canonical ISO-8601 rule, we can construct rules which behave similarly, which I call "ISO-like" rules. These provide two other axes of flexibility:

  • First day of week. For example, if you want Sunday-to-Saturday weeks, but still "four days or more" then the first day of the calendar year is in week 1 if it's a Sunday, Monday, Tuesday or Wednesday.
  • The required number of days in the week containing the first day of the calendar year to make that day part of week 1. For example, with a Monday-to-Sunday week, and a "minimum days in first week" value of 7, the first day of the calendar year will only be in week 1 if it's a Monday. At the other extreme, a "minimum days in first week" value of 1 means the first day of the calendar year is always in week 1.

Use the WeekYearRules.ForMinDaysInFirstWeek(int) and WeekYearRules.ForMinDaysInFirstWeek(int, IsoDayOfWeek) methods to construct ISO-like rules. The first overload defaults to using Monday as the first day of the week.

The rule returned by WeekYearRules.Iso property is equivalent to the rule returned by WeekYearRules.ForMinDaysInFirstWeek(4, IsoDayOfWeek.Monday).

BCL rules

BCL rules are obtained via WeekYearRules.FromBclRule, which accepts two parameters:

These mirror the second and third parameters to the Calendar.GetWeekOfYear method in the BCL.

It's easiest to think of the BCL rules as being equivalent to the ISO-like rules in most respects, with a mapping from CalendarWeekRule to "minimum number of days in first week" of:

  • FirstDay: 1
  • FirstFourDayWeek: 4
  • FirstFullWeek: 7

There's then one subtle difference between ISO-like rules and BCL-like rules:

In an ISO-like rule, every week has exactly seven days. In a BCL-like rule, if the start of the first week of a week-year is in the previous calendar year, that week is split into two, so that the week-year of a date is never more than the calendar year of the same date.

It's easiest to see this in action with a couple of examples. The BCL rule using CalendarWeekRule.FirstFourDayWeek and Monday as a first day of the week is equivalent to WeekYearRules.Iso. Let's see what happens around the turn of the year for two years. First 2014/2015:

Date Day of week ISO week BCL week
2014-12-28 Sunday 2014 week 52 2014 week 52
2014-12-29 Monday 2015 week 1 2014 week 53
2014-12-30 Tuesday 2015 week 1 2014 week 53
2014-12-31 Wednesday 2015 week 1 2014 week 53
2015-01-01 Thursday 2015 week 1 2015 week 1
2015-01-02 Friday 2015 week 1 2015 week 1
2015-01-03 Saturday 2015 week 1 2015 week 1
2015-01-04 Sunday 2015 week 1 2015 week 1
2015-01-05 Monday 2015 week 2 2015 week 2

As you can see, 2015 started on a Thursday. In the ISO rule, that means that the whole Monday-to-Sunday week is 2015 week 1. In the BCL rule, Monday to Wednesday are in 2014 week 53, and Thursday to Sunday are in 2015 week 1. For the BCL rule, 2014 week 53 and 2015 week 1 are "short" weeks.

Compare that with the 2015/2016 boundary:

Date Day of week ISO week BCL week
2015-12-27 Sunday 2015 week 52 2015 week 52
2015-12-28 Monday 2015 week 53 2015 week 53
2015-12-29 Tuesday 2015 week 53 2015 week 53
2015-12-30 Wednesday 2015 week 53 2015 week 53
2015-12-31 Thursday 2015 week 53 2015 week 53
2016-01-01 Friday 2015 week 53 2015 week 53
2016-01-02 Saturday 2015 week 53 2015 week 53
2016-01-03 Sunday 2015 week 53 2015 week 53
2016-01-04 Monday 2016 week 1 2016 week 1

2016 starts on a Friday, which means there are only three days of that Monday-to-Sunday week in 2016... which means that in both the BCL and ISO rules, those days are in the final week of 2015. The first week of 2016 starts on Monday January 4th, and the BCL and ISO rules behave identically, with all weeks being a regular seven days.