Enter a date, and the tool calculates its ISO 8601 week number, day of year, and week-year.
Under ISO 8601, weeks start on Monday and week 1 is the week containing the first Thursday of the year (equivalently, the week with January 4th).
If the first days of January fall before that year's first Thursday, they belong to the last week of the previous ISO year — which is why the week-year can differ from the calendar year.
Yes. Years starting on a Thursday, and leap years starting on a Wednesday, have 53 ISO weeks.