Day of the Week Calculator

Seven day cycles, no exceptions

The weekday of a date is a remainder problem. Count the days from a known date, divide by seven, and the remainder tells you how far the weekday has moved. The USNO notes that weeks have formed an uninterrupted sequence for the whole span of recorded calendar history, which is why this count works backwards as well as forwards.

Two facts make the count practical. A normal year is 365 days, which is 52 weeks and one day, so the same date lands one weekday later next year. A leap year is 366 days, which leaves a remainder of two, so dates after February jump two weekdays instead of one.

The USNO Julian date converter uses the same idea in its purest form: a Julian day number counts days continuously from a fixed epoch, and the remainder mod 7 of that number is the weekday, because the seven day week never skips.

That is the whole mechanism. There is no lookup table of years, no formula that needs the month name spelled out, and no exception for leap days beyond the shift of two described above.

Worked example: 20 October 2026

1 January 2026 is a Thursday. The gap to 20 October 2026 is 292 days, which is 41 whole weeks plus 5 days. Five places after Thursday is Tuesday, so 20 October 2026 is a Tuesday.

The same answer arrives from the other direction. 20 October is day 293 of 365, so there are 72 days left in the year, and counting back from 31 December, a Thursday, gives the same weekday.

Two checks cost nothing and catch most arithmetic slips. First, the count of days between the two dates has to include the leap day if February 29 falls between them, which for 2026 it does not. Second, the weekday must advance by the remainder, not by the quotient: 41 weeks cancel out entirely, and only the leftover 5 matters.

A third check works on a year scale. 2027 starts one weekday later than 2026 because 2026 is a normal year, so 1 January 2027 is a Friday. 2028 starts one further along, then jumps two for 2029 because 2028 is a leap year, landing on a Monday.

Which dates in a month fall on a given weekday

The reverse question is the one people ask at a calendar: which Fridays are free, when is the third Tuesday, what date is the first Monday. The count follows from the length of the month and the weekday of its first day.

A 31 day month covers four full weeks plus three extra days, so the weekday of the 1st, the 2nd and the 3rd each occur five times. A 30 day month has two extra days, so only the first two weekdays occur five times. February in a normal year is exactly four weeks, so every weekday occurs four times; in a leap year one weekday occurs five times.

Where each month of 2027 begins, which is the number needed for the whole year at once:

Five Fridays in a month is not rare, it happens in any 31 day month that starts on a Wednesday, Thursday or Friday, and in any 30 day month that starts on a Thursday or Friday. Once every few years a month has five Fridays, five Saturdays and five Sundays, which takes a 31 day month starting on a Friday.

Counting weekdays in a year

A normal year is 52 weeks and one day, so one weekday appears 53 times and the rest appear 52 times. The weekday that gets the extra day is the one the year starts on. A leap year has two extra days, so the weekday of January 1 and the one after it both appear 53 times.

This is why a payroll calendar, a rent schedule or a gym schedule built on a fixed weekday drifts against a calendar built on a fixed date. A year with 53 Mondays pays out 53 weekly installments instead of 52, and a monthly budget that assumes 52 weeks is short by one week in those years.

The day counter gives the raw number of days between two dates, which is the input this page uses, and the days between dates calculator covers the same span with weekdays excluded.

Doomsday anchors that fit in your head

The doomsday method gives every year a single anchor weekday, and a short list of memorable dates that fall on it. Once the anchor is known, any other date in that year is a few days of counting away.

The anchor dates inside a year are 4/4, 6/6, 8/8, 10/10 and 12/12, plus 5/9 and 9/5, 7/11 and 11/7, and 3/14. January and February depend on the leap year: 1/3 and 2/28 in a normal year, 1/4 and 2/29 in a leap year.

For 2026 the anchor is Saturday, because 3 January 2026 is a Saturday. October 10 is therefore a Saturday, and 20 October is ten days later, which is three days past a week, so Tuesday. The same rule gives 4 July 2026 as a Saturday, since 4/4 is the anchor and July's doomsday is 7/11.

The method is a shortcut for the remainder arithmetic, not a different calendar. If a date lands on the wrong weekday by the doomsday method, the anchor is wrong, and the century table below is the place to look.

Century anchors and the 400 year cycle

Each century has its own anchor weekday, and the sequence repeats every four centuries. For the years 1800 to 1899 the anchor is Friday, for 1900 to 1999 it is Wednesday, for 2000 to 2099 it is Tuesday, and for 2100 to 2199 it is Sunday.

The repetition is exact. The Gregorian calendar has 97 leap years and 303 normal years in 400 years, which comes to 146,097 days, and 146,097 divided by 7 is 20,871 with nothing left over. So 20 October 2026 and 20 October 2426 fall on the same weekday, and any calendar can be reused 400 years later.

Century years are where the cycle is decided. The USNO leap year rule makes 2000 a leap year, but 1700, 1800, 1900 and 2100 are not, because a century year has to divide by 400. Skipping that rule puts every date after February 2100 one weekday off.

Within a century the pattern is easier: dates repeat after 28 years while no century year intervenes, because 28 years contain exactly 7 leap days and 28 x 365 + 7 = 10,227 days, which divides by 7. 2026 and 2054 therefore share a calendar.

Recurring dates that have to move off a weekend

Rent, invoices, settlement dates and delivery windows often carry a rule like the first business day of the month. That rule needs two calendar facts: the weekday of the target date, and the next or previous weekday when the target lands on a weekend.

November 2026 is the clean example. The 1st is a Sunday, so a due date of the 1st falls on a weekend and moves either back to Friday 30 October or forward to Monday 2 November. Which direction applies is a contract term, not a calendar fact, and the two choices can move a payment by three days.

The same question appears in payroll, where a Friday payday in a year with 53 Fridays means one extra pay period, and in school calendars, where a term that starts on the first Monday can begin as late as 7 January.

If a schedule repeats on a fixed weekday rather than a fixed date, count the occurrences rather than assuming four or five. The month length table earlier in this page gives the count directly, and the weekday calculator covers the related question of ISO week numbers for the same date.

Leap days, time zones and the edges of the method

29 February is the one date that moves predictably but rarely. In 2028 the leap day is a Tuesday, and because the leap day sits inside the year, every date after it shifts by two weekdays relative to the year before rather than one. A person born on 29 February sees a weekday birthday once every 28 years in most centuries.

Time zones are the other edge. A calendar date is a civil convention, so the weekday belongs to the local date, not to the instant. A meeting at 23:30 on a Monday in Tokyo is still Monday locally while it is already Monday afternoon in London and Monday morning in New York, but a deadline at 00:30 Tuesday in Tokyo is Monday evening in New York, and the two sides will disagree about which weekday the deadline sits on unless the time zone is written down.

ISO 8601 numbers the weekdays Monday 1 through Sunday 7 and starts weeks on Monday, which is why a date can be in the last week of the previous ISO year in late December. The official US time service publishes the current date and time for the US time zones when a live reference is needed.

The calculator avoids the time zone problem by treating the date as a plain calendar date with no clock attached, which is the right model for a birthday, a due date or a holiday.