Day of the Week Calculator

weekday = (whole days since 1 January 1970 + 4) mod 7, where 0 is Sunday

dayNumber

Whole days since 1 January 1970, which was a Thursday — hence the constant 4

dayOfYear

The date's position in its own year, with 1 January as 1

daysLeft

The days left in the year: 365 or 366 minus that position

isoWeek

The week containing the year's first Thursday, numbered 1 to 53

Use the calculator to settle a date, to get the week number a schedule expects, or to see how much of the year is left. The weekday is the easy part; the week number is where tools disagree, because an ISO week belongs to the year containing its Thursday, so 1 January 2021 reports week 53 of 2020. What it cannot do is convert between calendars — every date here is proleptic Gregorian, the calendar historians use for dates before 1582 and the one in which the ten dropped days of October 1582 never happened.

1. 19 September 2026

   1. Whole days since 1 January 1970: 20715. Adding the 4-day offset gives 20719, and 20719 mod 7 = 6 — Sunday is 0, so the date is a Saturday
   2. Day of the year: the eight completed months hold 31 + 28 + 31 + 30 + 31 + 30 + 31 + 31 = 243 days, and 243 + 19 = 262
   3. Days left: 2026 is a common year of 365 days, and 365 − 262 = 103
   4. ISO week: the Monday of that week is 14 September 2026, which falls in the 38th week of the ISO year

   Four answers from one date. The weekday is checkable against any paper calendar; the week number is the one that disagrees between tools, because the week is defined by its Thursday rather than by the day it starts on.

2. 1 January 2021 — a January date in week 53

   1. 1 January 2021 is a Friday, so the week containing it runs from Monday 28 December 2020 to Sunday 3 January 2021
   2. An ISO week belongs to the year containing its Thursday, and that Thursday is 31 December 2020
   3. The week therefore takes the last number of 2020, which is 53 — a date in 2021 reports a week of the previous year
   4. dayOfYear and daysLeft ignore all of this: they are 1 and 364, because they count inside the calendar year

   This is the boundary that earns the week number a place on the page. 2020 has 53 ISO weeks and 2021 has 52, and the first three days of January 2021 belong to the earlier year's count.

3. 29 February 2024 — the leap day

   1. 2024 is divisible by 4 and not by 100, so it is a leap year and February holds 29 days
   2. Day of the year: 31 days of January plus 29 is 60 — in 2023 the date does not exist and 1 March holds position 60 instead
   3. Days left: 366 − 60 = 306
   4. Weekday: 29 February 2024 is a Thursday, and the Monday of its week is 26 February

   The leap day shifts every later position by one, so dayOfYear is the output on this page that cannot be read off a calendar for a non-leap year.

Every date here is proleptic Gregorian: the calendar extended backwards, not the calendar people actually used, so October 1582 shows no gap and the year 1000 is a weekday no chronicle would recognise. The week number is the ISO one, where weeks start on Monday and belong to the year containing their Thursday — the United States convention, which starts weeks on Sunday and keeps week 1 inside January, will differ on a handful of dates each year. Nothing here converts timezones, because a date's weekday does not depend on one.

How do I find the day of the week for a date?

Count whole days from a known reference and take the remainder on division by seven. 1 January 1970 was a Thursday, so a date 20715 days later gives 20715 + 4 = 20719, and 20719 mod 7 = 6, which is a Saturday. Any calendar trick that avoids the arithmetic is really doing the same count.

What is the ISO week number?

It is the numbering in ISO 8601: weeks begin on Monday, and week 1 is the week containing the year's first Thursday. That rule ties every week to exactly one year, which is why a date in early January can belong to week 52 or 53 of the year before it. It is the numbering most of Europe and most scheduling software uses.

Why does a date in January show week 53?

Because the ISO week belongs to the year containing its Thursday, not its Monday. The week of 1 January 2021 ran from Monday 28 December 2020 to Sunday 3 January 2021, and its Thursday fell in 2020, so it took 2020's last number, 53. The other end behaves the same: 31 December 2026 is a Thursday, so it sits in week 53 of 2026.

Does the time of day or my timezone change the answer?

No, a calendar date has a weekday regardless of where it is read, and this tool never converts through a local timezone. The real failure mode is an implementation that builds a date with local-time methods and then reads the day back: it returns the day before for users west of the machine that computed it, and only for them.

What is the day of the year used for?

It is the date's position in its own calendar year, with 1 January as 1 and 31 December as 365 or 366. Ordinal dates are how some industries write deadlines — day 262 of 2026 is 19 September — and the days left is simply the year length minus that position, so the two always add up to the year length.

• UTS #35: Unicode Locale Data Markup Language, Part 4: Dates — Unicode Consortium
• ISO 8601: International Standard Date and Time Notation — Markus Kuhn, University of Cambridge