What Day Was I Born?

A date already fixes the weekday

Every date on the Gregorian calendar has one weekday, and it never changes. July 4, 1990 was a Wednesday and it will be a Wednesday in every calendar that prints it. That is because the calendar is a fixed cycle of 7-day weeks running through a pattern of 365-day and 366-day years, so the weekday is a property of the date rather than something anyone has to remember.

What the calculator does is walk that cycle. It counts the days from a known anchor, folds in the leap years, and takes the remainder after dividing by 7. The remainder points at a weekday. No lookup table of every date is needed, and the same arithmetic works for a date in 1650 or 2400.

The one wrinkle is which calendar you mean. The United States and most of the world use the Gregorian calendar, introduced in 1582 and adopted by Britain and its colonies in 1752. Before that switch, English records used the Julian calendar, which had drifted 11 days out of step. A birth date from a colonial church register can therefore land on a different weekday than the same numbers would today.

Leap years: four, one hundred, four hundred

The Gregorian leap rule has three tests, and a year has to pass the right combination of them. The rule exists because a solar year is 365.2422 days, not 365, and the calendar has to absorb that leftover fraction without drifting into summer.

• Divisible by 4: a leap year, with 366 days and a February 29.
• Divisible by 100: not a leap year, even though it passes the first test.
• Divisible by 400: a leap year again, overriding the century rule.

So 1996, 2000 and 2024 are leap years, while 1900 and 2100 are not. The 100 rule exists because four years of 365.25 days overshoots by about 3 days every 400 years. The 400 rule puts most of that back: 97 leap days per 400 years instead of 100, which leaves an error of about one day in 3,000 years.

The US Naval Observatory explanation of leap years works through the same arithmetic from the astronomical side, including why the rule is a compromise rather than an exact fit.

How the weekday calculation works

The method below is the one built into the calculator, and it can be done on paper. It uses a month code, a year term, and the day of the month.

1. Take the year, and if the month is January or February, subtract 1 from the year and treat the month as 13 or 14.
2. Compute the year term: year + floor(year ÷ 4) - floor(year ÷ 100) + floor(year ÷ 400).
3. Add the month code from the table below.
4. Add the day of the month.
5. Divide by 7 and keep the remainder. 0 is Sunday, 1 is Monday, and so on to 6 for Saturday.

The year term is where the leap rule enters. Floor division by 4 counts the leap years, division by 100 removes the century years, and division by 400 adds back the century leap years. Those three terms together are the number of leap days since year 1.

Zeller's congruence is the better known version of the same idea, and it produces the same answer with a different set of constants. Both rely on the calendar being periodic, which is why a single 400-year cycle can be memorized and reused.

Worked example: July 4, 1990

Run the five steps on July 4, 1990. July is past February, so the year stays 1990 and the month stays 7.

• Year term: 1990 + 497 - 19 + 4 = 2,472. The 497 is the leap year count, 19 is the century correction, and 4 is the 400-year correction.
• Month code for July: 5.
• Day of the month: 4.
• Total: 2,472 + 5 + 4 = 2,481.
• 2,481 divided by 7 is 354 with a remainder of 3, which is Wednesday.

Check it against a second method. January 1, 1990 was a Monday. The 184 days from January 1 to July 4 leave a remainder of 2 when divided by 7, and Monday plus 2 days is Wednesday. Both routes agree, which is the useful part: the arithmetic can be checked without a calendar.

The same date in 1990 was day 185 of the year, because January through June add up to 181 days and July 4 is four days past that. Because 1990 is not a leap year, the year has 365 days and the day number is 185 out of 365.

Day of the year and week numbers

Two other numbers fall out of a date and are worth knowing. The day of the year runs from 1 on January 1 to 365 or 366 on December 31, and it is the sum of the month lengths before your month plus the day. The week number is messier, because there are two competing systems.

The ISO standard, used in most of the world and in business software, starts week 1 on the Monday of the week that contains January 4. A year has 52 or 53 ISO weeks, and the first days of January can belong to week 52 or 53 of the year before. December 31, 1985 fell in week 1 of 1986 for exactly that reason.

The US convention is different: weeks start on Sunday, and week 1 begins on January 1 whatever weekday that is, which produces a short first week. A date in early January can therefore be week 1 in the US system and week 53 in the ISO system. The calculator reports the ISO number and the ISO year, because that is the version that survives a spreadsheet import.

The last column is the one people come for. It is a plain subtraction of two dates, and the calculator does it in whole days, ignoring the time of day.

Days old and weeks old

Days old is the cleanest measure of age, because it has no months of varying length in it. Subtract the birth date from today and count the days. Someone born July 4, 1990 was 13,254 days old on October 17, 2026.

Weeks old is that number divided by 7, with the remainder kept. 13,254 divided by 7 is 1,893 with 3 left over, so the answer is 1,893 weeks and 3 days. Months and years are less exact, because a month is 28 to 31 days and a year is 365 or 366, which is why two people born a day apart can disagree about their age in months.

For a newborn the count is more useful than it sounds. Pediatric visits are scheduled in weeks and months from birth, and a parent counting 45 days to the next checkup is doing the same arithmetic the office does. The same subtraction gives the day of the week for a future date, which is how you find out whether a birthday lands on a weekend.

The Gregorian cycle closes neatly here. Four hundred years hold 146,097 days, which is exactly 20,871 weeks, so the calendar repeats every 400 years down to the weekday. That also means each of the seven weekdays appears 20,871 times in the cycle, a balance the older Julian calendar never managed.

Leap day birthdays

About 1 in 1,461 people is born on February 29. The date exists only in leap years, so the practical question is what to do with the other three years.

Most families mark February 28 or March 1, and most legal systems accept either for age-based rules. A driver's license or a passport will usually print February 29 and treat the person as a year older on March 1 in non-leap years. For a birthday party, the choice is entirely social.

The weekday pattern is the interesting part. A February 29 birthday returns on the same weekday every 28 years in most of the 20th and 21st centuries, because 28 years hold 7 leap days and 28 × 365 is a multiple of 7. Century years break the pattern: 2100 is not a leap year, so anyone born on February 29, 2096 waits eight years for the next one.

Midnight, time zones and the birth certificate

The weekday belongs to the date on the birth certificate, not to the moment of birth in some other time zone. A baby born at 11:58 pm on a Tuesday is a Tuesday baby, and a baby born six minutes later is a Wednesday baby. The hospital records local time, and that is the date every later document will use.

Time zones only matter when a birth is recorded in one place and celebrated in another. A birth at 1:00 am in New York on July 4 is still July 4 in New York, even though it is July 3 in Los Angeles. Converting the timestamp would change the date and the weekday, and it would be wrong, because the certificate is a local record.

Calendar systems matter in the same way. A date from a country that used the Julian calendar in 1700 will not match a Gregorian calculation, and the gap was 10 or 11 days depending on the year. The US Naval Observatory calendar pages document the switch, and the NIST time and frequency division covers how official time is kept today.

This is a calendar calculation, not a legal or genealogical record. For a birth certificate, an immigration form or a historical claim, use the date on the official document.