Day of the week calculator what day was it on any date

What day of the week was I born on?

The day of the week you were born on is fixed by your date of birth alone: any date on the Gregorian calendar corresponds to exactly one weekday, and the calculator above returns it instantly for any year from 1583 onward, together with a mental calculation you can follow line by line. Someone born on August 15, 1985 was born on a Thursday, someone born on January 1, 2000 arrived on a Saturday, and the first Moon landing on July 20, 1969 took place on a Sunday.

The reason a calculator is needed at all is that the year does not contain a whole number of weeks. A common year has 365 days, which is 52 weeks and one day, so every date slides forward by one weekday from one year to the next. A leap year has 366 days, 52 weeks and two days, so after a February 29 the slide is two weekdays. Your birthday therefore wanders through the week in a pattern that repeats, but only over decades.

Beyond the birth weekday itself, the tool counts how many times your birthday has fallen on each day of the week and finds the next year in which it lands on your birth weekday again, which for most dates happens within 5, 6 or 11 years.

Why does the same date fall on a different day of the week each year?

The same date falls on a different weekday each year because a year is one or two days longer than a whole number of weeks. Divide 365 by 7 and you get 52 with a remainder of 1, so March 14 on a Tuesday this year will be March 14 on a Wednesday next year, provided no February 29 lies between the two dates. If a leap day does lie between them, the remainder is 2 and the date jumps from Tuesday to Thursday.

Over four consecutive years a date advances by 1, 1, 1 and 2 weekdays, 5 in total, and 5 has no simple relationship to 7. Only after 28 years, when the total shift is 35 days, exactly five weeks, does the calendar come back to where it started.

The century years keep this from being a clean 28-year rhythm forever. The Gregorian rule drops the leap day in years divisible by 100 unless they are also divisible by 400, so 1900 and 2100 are common years while 2000 was a leap year. Whenever one of those skipped leap days falls inside a 28-year span the pattern is broken, and only the full 400-year cycle of 146,097 days brings the calendar back exactly.

How to calculate the day of the week in your head with the doomsday rule

The doomsday rule is a mental method invented by the mathematician John Horton Conway in 1973, and it rests on one observation: in any given year, a handful of easily remembered dates all fall on the same weekday. Conway called that weekday the year's doomsday. Once you know the doomsday for a year, you find the weekday of any date by counting forward or back from the nearest of those anchor dates.

The anchor dates are simple to memorise. In the even months the doomsday falls on the date that matches the month number: April 4, June 6, August 8, October 10 and December 12. For the odd months from May to November there is a mnemonic, working nine to five at the 7-Eleven, which gives May 9, September 5, July 11 and November 7. The last day of February is a doomsday, so February 28 in a common year and February 29 in a leap year, and because the last day of February is also March 0, so to speak, March 7, 14, 21 and 28 are doomsdays too. In January the doomsday is January 3 in a common year and January 4 in a leap year.

Finding the doomsday for a year takes three steps. First, take the century anchor: Friday for the 1800s, Wednesday for the 1900s, Tuesday for the 2000s and Sunday for the 2100s. Second, take the last two digits of the year, divide by 4 and drop the remainder, add that quotient to the two digits, and take the remainder after dividing by 7. Third, count that many days forward from the century anchor. For 2026 the two digits are 26, a quarter of 26 is 6, 26 plus 6 is 32, and 32 leaves a remainder of 4 when divided by 7. Four days after Tuesday is Saturday, so every doomsday in 2026 is a Saturday.

Now any date in 2026 is within reach. To find September 28, 2026, start from September 5, a Saturday, add three weeks to reach September 26, and two more days lands on Monday. For August 15, 1985 the anchor is Wednesday, 85 plus 21 is 106, which leaves a remainder of 1, so doomsday 1985 is a Thursday, and August 15 is a week after August 8, a Thursday as well.

A faster year step, published by Chamberlain Fong and Michael Walters in 2011, is the odd plus 11 method: take the last two digits, add 11 if odd, halve, add 11 again if odd, take the remainder after dividing by 7 and subtract it from 7. For 26 the steps are 26, 13, 24, remainder 3, and 7 minus 3 is 4, the same four days from Tuesday.

What is Zeller's congruence and how does a day of the week formula work?

Zeller's congruence is a formula published by the German mathematician Christian Zeller in 1882 that returns the weekday of any date as a number from 0 to 6. Where the doomsday rule is built for the human memory, Zeller's formula is built for a pen or a processor: one line of arithmetic, no anchor dates to recall.

The trick inside the formula is to treat January and February as the 13th and 14th months of the previous year. That moves the irregular month, February, to the end of the counting year, so the number of days from March 1 to the first of any later month follows a smooth pattern, which the expression 13 times the month plus 1, divided by 5 and rounded down, reproduces exactly.

In its Gregorian form the formula adds the day of the month, that month term, the year within the century, a quarter of that year, a quarter of the century and five times the century, then takes the remainder modulo 7, where 0 stands for Saturday, 1 for Sunday and so on to 6 for Friday. Both methods give the same answer for the same Gregorian date. The calculator uses exact day counting, which is equivalent, and prints the doomsday steps because they are the ones you can reproduce in your head.

When will my birthday fall on the same day of the week as when I was born?

Your birthday returns to the weekday of your birth after 5, 6 or 11 years, and in every case again 28 years after the previous match, as long as no skipped century leap day such as 2100 falls within the span. The interval depends on where the leap years sit relative to your birthday, because each common year moves the date one weekday and each leap year moves it two.

Take a birthday on March 14. From 2026 to 2031 the shifts are 1 in 2027, 2 in 2028, 1 in 2029, 1 in 2030 and 1 in 2031, a total of 6, which is not a multiple of 7. Continue to 2032 and the shift is 8, then 2033 gives 9, 2034 gives 10, 2035 gives 11, 2036 gives 13 and 2037 gives 14. So March 14, 2037 lands on the same weekday as March 14, 2026, an 11-year gap. For a birthday placed differently relative to the leap years the first match comes after 5 or 6 years instead.

Across any 28 consecutive years inside one century, a birthday falls on each of the seven weekdays exactly four times, so a person who lives to 84 has had 12 birthdays on each day of the week. The calculator tallies these counts for your actual dates and lists the next years in which your birthday falls on your birth weekday.

People born on February 29 are a special case. Their exact birthday exists only in leap years, so its weekday advances by 5 days every four years and returns to the start after 28 years, when seven such jumps add up to 35 days, five whole weeks.

How often does the calendar repeat with the same days of the week?

A full-year calendar repeats when the year starts on the same weekday and has the same length, which for a common year happens 6, 11 or 28 years later and for a leap year happens 28 years later. That is why an old wall calendar from 1998 could be reused in 2009, 2015 and 2026, all common years beginning on a Thursday, and why the calendar for the leap year 2024 will next be valid in 2052.

The rhythm is not perfectly regular because of the century rule. In the Gregorian calendar the years 1700, 1800, 1900 and 2100 are common years, so the 28-year cycle breaks across those boundaries. Only the complete 400-year cycle repeats without exception, since 400 years contain 97 leap days and 146,097 days in total, and 146,097 is exactly 7 times 20,871.

One consequence of the 400-year cycle is that the days of the week are not spread perfectly evenly across dates. The count of times each weekday falls on a given date over 400 years is fixed, and it is not the same for all seven days. The best known example, worked out by B. H. Brown in the American Mathematical Monthly in 1933, is that the 13th of a month falls on a Friday 688 times per cycle, more than on any other weekday. The cycle also means a date in 2426 has the same weekday as the same date in 2026.

Which calendar does the day of the week calculator use for old dates?

The calculator uses the Gregorian calendar for every date, including dates before the calendar existed, which is called the proleptic Gregorian calendar. For any date from October 15, 1582 onward in a country that had already adopted the reform, the result is the weekday people actually lived through. For earlier dates, or for later dates in countries that were still using the Julian calendar, the day label on the historical record and the label in the calculator can differ.

The reform itself was decreed by Pope Gregory XIII in 1582, and in the countries that applied it first, October 4, 1582 was followed directly by October 15, 1582, dropping ten days to bring the calendar back in line with the seasons. The Polish-Lithuanian Commonwealth adopted the new calendar between 1582 and 1586. Great Britain and its colonies, including the future United States, switched in September 1752, when September 2 was followed by September 14. Russia moved to the Gregorian calendar in February 1918, by which time the gap had grown to 13 days.

The weekday itself was never interrupted by any of these changes. The seven-day cycle ran on without a break and only the date labels jumped. So the weekday written beside a Julian date in an old document is correct, but entering the same numbers into a Gregorian calculator will usually give a different weekday, because the Gregorian calendar assigns those numbers to a different physical day. George Washington's birth is the classic example: recorded as February 11, 1731 under the Julian calendar then used in the colonies, it is February 22, 1732 in the Gregorian calendar used today.

For family history, convert a Julian date to its Gregorian equivalent first, then enter that date. The difference is 10 days from 1582 to February 1700, 11 days from March 1700 to February 1800, 12 days from March 1800 to February 1900 and 13 days from March 1900 to February 2100.

Where does the seven-day week come from?

The seven-day week comes from the ancient Near East, where both Mesopotamian tradition and the Jewish Sabbath cycle counted days in sevens, and it spread through the Roman world alongside a separate seven-day cycle named after the planets. The Romans assigned each day to one of the seven classical wandering bodies in the order Sun, Moon, Mars, Mercury, Jupiter, Venus and Saturn, and that planetary week survives in the names still used across much of Europe.

The week became a matter of law when the emperor Constantine decreed in the year 321 that Sunday was to be a day of rest for courts and city workers. From that point the seven-day week ran continuously through the Roman, medieval and modern calendars without a single interruption, which is the reason the weekday of any past date can be reconstructed at all: the cycle never reset.

Unlike the year and the month, the week has no astronomical basis. It tracks neither the Moon nor the Sun, and that independence is what makes weekday arithmetic clean: days can be counted in groups of seven from any known anchor, forward or back, without reference to the sky.

What do the names of the days of the week mean in English?

The English day names are a blend of the Roman planetary week and the gods of the Germanic peoples who settled Britain. Sunday and Monday are the days of the Sun and the Moon, translated directly from the Latin. Saturday keeps the Roman god Saturn. The four days in between swapped the Roman deities for Germanic ones that were felt to match: Tuesday for Tiw, a god of war standing in for Mars; Wednesday for Woden, standing in for Mercury; Thursday for Thor, the thunder god standing in for Jupiter; and Friday for Frigg, standing in for Venus.

Other languages numbered the days instead. Lithuanian counts them from the first day, pirmadienis, to the sixth, šeštadienis, and Portuguese runs from segunda-feira for Monday to sexta-feira for Friday. Conventions also differ on where the week begins: the international standard ISO 8601 numbers Monday as day 1 and Sunday as day 7, while calendars in the United States, Canada and much of the English-speaking world print Sunday in the first column.

In English folklore the weekday of birth has a rhyme of its own. The verse beginning Monday's child is fair of face, Tuesday's child is full of grace was first written down in 1838 in A. E. Bray's Traditions of Devonshire and gives each of the seven days a line. It is a nursery rhyme and a piece of tradition, not a claim that the day has any bearing on character.