week number

There are multiple systems for numbering weeks. The basic method is that week 1 is the week that has January 1st. This is regardless of whether or not January 1st is on the first day of the week, the middle of the week, or the last day of the week. This method is used by Apple, Microsoft (confirmed in Outlook), and even sites like www.calendar-365.com and apps like Calendars 5.

The method that you are referring to considers week 1 to be the week containing January 4th or the first Tuesday of the month. Unfortunately there isn't a way to change which method you use in iOS. You can submit feedback to http://www.apple.com/feedback/ but they would need to have a lot of people request it and then wait for Apple to actually implement it in a future release. From what I understand this only happens about once every 11 years so Apple putting too much into making a change that would be implemented in 2016 probably isn't very high.

Edit: I was wrong on the every 11 years. Looks like it is every 5 to 6 years. The next years that will have 53 weeks based on the ISO week date standard are 2020, 2026, and 2032.

Although there might be several ways to determine week numbers, the by far most widely used is the one specified by ISO 8601 (International Organization for Standardization). It defines week 01 as follows:

The ISO 8601 definition for week 01 is the week with the year's first Thursday 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 dates are 29 December through 4 January, the latest 4 through 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 on a Saturday, it is part of week 52 (or 53 if the previous year was a leap year); if on a Sunday, it is part of week 52 of the previous year.

Further more, if you search Google for "week number", at least the top 5 results follows the above ISO standard.

Following this ISO standard, week 01 of 2016 starts on Monday, January 4 2016. In iOS however, week 01 starts on Monday, December 28 2015 (provided that you have set Monday as the first day of a week in your settings).