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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 Wednesday, 12 February 2025 corresponds to day number 3 in the week number 07 ...
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A calendar date is a reference to a particular day, represented within a calendar system, enabling a specific day to be unambiguously identified. Simple math can be performed between dates; commonly, the number of days between two dates may be calculated, e.g., "25 February 2025" is ten days after "15 February 2025".
Similarly, the last ISO week of a year may have up to three days that are actually in the Gregorian calendar year that is starting; if three, they are Friday, Saturday, and Sunday. The Thursday of each ISO week is always in the Gregorian calendar year denoted by the ISO week-numbering year. Examples: Monday 29 December 2008 is written "2009-W01-1"
The algorithm is rather simple: It uses the Gregorian calendar to get the number of days elapsed since the begin of the Christian Era (0001-01-01) and converts this number in a rounding manner to the number of elapsed weeks ('ew') for the begin of the year in the ISO week calendar. Then it adds the number of elapsed weeks in the year and uses ...
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The day of the week can be easily calculated given a date's Julian day number (JD, i.e. the integer value at noon UT): Adding one to the remainder after dividing the Julian day number by seven (JD modulo 7 + 1) yields that date's ISO 8601 day of the week. For example, the Julian day number of 10 February 2025 is 2460717.