Day of the Week Calculator
Find the day of the week for any date, plus week number and day of year.
What Is the Day of the Week Calculator?
Which day of the week a date falls on looks like trivia until you need it for a deadline, a delivery, a court hearing, a payslip or a shift pattern. The calculation is a pure algorithm with no lookup table and no guessing, which is why calendars can be projected hundreds of years in either direction with perfect accuracy. This calculator returns the weekday in full, the ISO week number, the day of the year, how many days remain in the year, and whether it is a leap year, and it will also shift any date forwards or backwards by a given number of days so you can answer what today plus forty five days is. Leap years and month lengths are the two places most hand calculations go wrong, so both are handled explicitly and an impossible date such as the 29th of a non leap February is explained rather than silently adjusted.
Key Statistics
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4, 100, 400
The three leap year rules condensed into three numbers. A year is a leap year if it divides by 4, unless it divides by 100, in which case it must divide by 400 to qualify. The century rule exists because a year is about 365.2422 days, so leap years are added roughly every four years to correct the drift, with the 100 and 400 exceptions keeping that correction on track over long periods.
Source: Leap year, Wikipedia
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Monday to Sunday
The ISO 8601 definition of a week, which is why the week number here follows ISO rather than the American convention of Sunday to Saturday. Under ISO rules week 1 is the week containing the first Thursday of the year, which is why 1 January 2021 correctly falls in week 53 of 2020 rather than week 1 of 2021.
Source: ISO 8601 week date, Wikipedia
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1752
The year Great Britain lost eleven days by skipping from 2 September to 14 September overnight, because the British calendar had drifted a day from the solar year and Julian reckoning had fallen behind the actual equinoxes. Day of the week calculations that span this date must account for the discontinuity, which is why most systems use the proleptic Gregorian calendar throughout.
Source: Calendar Act of 1752, Wikipedia
The Formula
The weekday is found with Sakamoto's algorithm, which is pure arithmetic with no lookup table. Reduce the year by one if the month is January or February, then take the sum of the year plus a quarter of the year plus a day offset table entry for the month plus the day, and reduce modulo 7. Leap years follow the rule that a year is a leap year if it divides by 4 unless it divides by 100, in which case it must also divide by 400.
Worked Examples
For 10 October 2026 the month is October so the year stays 2026. The offsets give 2026 plus 506 minus 20 plus 5 plus 6 plus 10, which is 2,533. Dividing by 7 leaves a remainder of 6, counting from Sunday, so the sixth day is Saturday.
Finding the weekday for a known date
- Take 1 January 2000, a date many people remember as a Saturday.
- January means the year reduces to 1999 for the calculation.
- Add 1999 plus 499 minus 19 plus 4, plus the month offset of zero, plus the day of 1.
- That is 2,484, and reducing modulo 7 leaves a remainder of 6.
- Counting from Sunday, remainder 6 is Saturday.
1 January 2000 was a Saturday
Confirming a leap year
- Check whether 2024 divides by 4. It does, so it is a candidate.
- Check whether it also divides by 100. It does, so the simple rule would exclude it.
- Apply the final rule: 2024 divides by 400. It does, so 2024 is a leap year.
- February 2024 therefore has 29 days, and 29 February 2024 was a Thursday.
2024 is a leap year with 366 days
Shifting a date forward
- Take 10 October 2026, which is a Saturday.
- Add 45 days to it.
- October has 31 days, so 21 days take you to 31 October.
- The remaining 24 days take you into November, landing on 24 November.
- Because 45 divided by 7 leaves 3, the weekday advances by 3, so Saturday becomes Tuesday.
10 October 2026 plus 45 days is Tuesday 24 November 2026
An impossible date
- Enter 29 February 2023.
- Check the leap year rule: 2023 does not divide by 4.
- February 2023 therefore has only 28 days.
- There is no 29 February 2023, so the calculator explains the problem rather than rolling the date into March.
29 February 2023 does not exist
Real World Use Cases
Business and legal deadlines
Knowing which weekday a filing deadline, court date or contract expiry falls on determines whether you have a working day to act on it. A deadline landing on a weekend usually moves to the next working day, and you cannot tell without knowing the weekday.
Shift rotas and rostering
Repeating a shift pattern weekly requires the weekday to be exactly seven days apart each time. Confirming the weekday of the start date catches rota errors before they are published to staff.
Retrospective dating
Identifying the weekday of a historical or personal date, such as a birth, a wedding or an entry in a diary, is often recorded but rarely verified. Knowing the weekday lets you cross check against other records.
Project planning and sprint counting
ISO week numbers give a stable way to refer to weeks across teams and tools, which is why project tracking and reporting use them rather than informal week counting that drifts over a year.
Expert Tips
- ✓ Always check the leap year rule as a whole rather than stopping at divides by 4, since the century exceptions are exactly where people get caught.
- ✓ Prefer ISO week numbers when sharing references across systems, since American and ISO week conventions differ by a day or more at year boundaries.
- ✓ Do not assume a date near a year boundary belongs to the year it is named after. 1 January often falls in the last ISO week of the previous year.
- ✓ When calculating by hand, always reduce the year for January and February, since the algorithm treats those months as belonging to the previous year. Forgetting this is the single most common error.
- ✓ Validate any surprising result by checking it against a known reference such as 1 January 2000, which was a Saturday, before trusting it.
Frequently Asked Questions
How do I find the day of the week for a date? ▼
Use a date algorithm such as Sakamoto's, which is pure arithmetic. For 10 October 2026 the calculation gives 2,533, and reducing that modulo 7 leaves 6, counting from Sunday, which is Saturday. This calculator does exactly that and needs no lookup table.
What is the leap year rule? ▼
A year is a leap year if it divides by 4, unless it also divides by 100, in which case it must divide by 400 as well to qualify. So 2024 is a leap year, 1900 is not, and 2000 is.
How many days are in a leap year? ▼
366, against 365 in a common year. The extra day is 29 February, which exists only in a leap year. 2024 is a leap year, so it has 366 days.
What is an ISO week number? ▼
The ISO 8601 week number, where weeks run Monday to Sunday and week 1 is the week containing the first Thursday of the year. Under this rule 1 January 2021 belongs to week 53 of 2020 rather than week 1 of 2021.
Why is 1 January sometimes in week 53? ▼
Because the ISO week that contains 1 January can begin in the previous December. A year has 53 ISO weeks when it begins on a Thursday, or on a Wednesday in a leap year. 2021 is one of those cases, which is why 1 January 2021 is week 53 of 2020.
Can you check a date that has not happened yet? ▼
Yes. The calculation is entirely arithmetic with no dependency on what has actually occurred, so any valid Gregorian date from year 1 to 9,999 can be resolved. The Gregorian calendar is a projection, but it is a consistent one and is used for all future dates.
What happens if I enter 29 February in a non leap year? ▼
The calculator explains that the date does not exist rather than silently rolling it into the following month. This is deliberate, because a silent rollover would give you a confident answer to the wrong question.
How do I work out what today plus 45 days is? ▼
Enter today's date and set the shift field to 45. The result shows the target date and its weekday. Useful for notice periods, which are nearly always stated in days rather than weeks and are easy to miscount.
Does this use the Gregorian calendar throughout? ▼
Yes. The proleptic Gregorian calendar is applied to every input, including dates before its 1752 adoption in Britain. This is the standard in computing because it gives one continuous rule with no discontinuity to handle.
How accurate is a hand calculated weekday? ▼
It is exact if the leap year rule and the January and February year reduction are both applied correctly. Both are the only places errors occur, and both are handled here so you can cross check rather than trust a single line of mental arithmetic.
Common Mistakes to Avoid
- ⚠ Assuming every year divisible by 4 is a leap year, missing that 1900 and 2100 are not while 2000 is.
- ⚠ Assuming 29 February exists in any year ending in a multiple of 4, when it needs the full 4, 100 and 400 rule.
- ⚠ Using an American week convention and getting a different week number from a European colleague for the same date.
- ⚠ Confusing day of the year with day of the month, which differ by a whole month once you pass February.
- ⚠ Failing to reduce the year for January and February in a hand calculation, which shifts the answer by one day.
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