List of Years Calendar Calculator: Find Any Date

This calculator works out the day of the week for any date in the Gregorian calendar, and also tells you the day number of the year, whether it’s a leap year, and how many days are left in the year. You enter a date (or just a year) and get back the weekday, the ordinal day, and more. It’s built for students, planners, historians, and anyone who needs quick date facts without opening a full calendar app.

Formula

The day of the week uses Zeller’s congruence, adapted for the Gregorian calendar. For a date with month m, day d, and year y, we first adjust the month and year so that March is month 1: let a = floor((14 – m) / 12), then y’ = y – a, and m’ = m + 12*a – 2. The weekday number is then computed as:

h = (d + floor((31 * m’) / 12) + y’ + floor(y’/4) – floor(y’/100) + floor(y’/400)) mod 7

Here, h = 0 means Saturday, 1 = Sunday, 2 = Monday, …, 6 = Friday. The day of the year is found using the standard cumulative month offsets (for non-leap years: Jan 31, Feb 59, Mar 90, etc.), with a +1 adjustment for leap years after February. The leap year rule is: a year is a leap year if it is divisible by 4 but not by 100, unless it is also divisible by 400.

Worked Example

Using the default date: June 15, 2024.

Step 1: Adjust month and year: a = floor((14 – 6)/12) = 0, so y’ = 2024, m’ = 6 + 0 – 2 = 4.

Step 2: Compute h = (15 + floor((31*4)/12) + 2024 + floor(2024/4) – floor(2024/100) + floor(2024/400)) mod 7 = (15 + 10 + 2024 + 506 – 20 + 5) mod 7 = 2540 mod 7 = 6 (since 2540 = 7*362 + 6). h=6 corresponds to Saturday.

Step 3: Day of year: For June 15 in a leap year, the day number is 31+29+31+30+31+15 = 167.

Step 4: Leap year? 2024 % 4 = 0, 2024 % 100 != 0, so yes, it’s a leap year.

Step 5: Days left in year: 366 – 167 = 199.

So the calculator returns: Saturday, day 167, leap year, 199 days left.

How to Choose

When picking a calendar calculator, consider the range of dates it supports. Some only work within the Gregorian calendar (from 1582 onward), while others also handle the Julian calendar for older dates. Check if it gives the day of the week, the day number, and leap year status—many online tools only give the weekday. Also, look at whether it accounts for the proleptic Gregorian calendar (extending the Gregorian rules before 1582) if you work with historical dates. The best tool is one that matches your needs: for everyday use, a simple weekday calculator is enough; for genealogy or astronomy, you might need a full Julian/Gregorian converter.

Frequently Asked Questions

Q: What is the difference between the Julian and Gregorian calendars?
A: The Julian calendar, introduced by Julius Caesar in 45 BC, has a leap year every 4 years without exception. The Gregorian calendar, introduced in 1582, skips leap years on century years not divisible by 400, making it more accurate. The two calendars differ by 10 days in 1582, and the gap grows by 3 days every 400 years.

Q: Why does the day of the week formula use March as the first month?
A: Zeller’s congruence shifts the start of the year to March to handle the leap day at the end of February. This simplifies the formula because the leap day becomes the last day of the year, avoiding special cases in the calculation.

Q: Can this calculator work for dates before 1582?
A: Yes, it uses the proleptic Gregorian calendar, which extends the Gregorian rules backward. This is common for astronomical calculations, but historical dates before 1582 are often recorded in the Julian calendar. The calculator doesn’t convert between the two; it only gives the Gregorian weekday.

Q: How do I find the day of the week for my birthday?
A: Simply enter your birth year, month, and day. The calculator will show the weekday. For example, if you were born on July 4, 1990, it returns Wednesday.

Q: What is the day of the year for December 31?
A: In a non-leap year, December 31 is day 365; in a leap year, it’s day 366. The calculator automatically adjusts for leap years.

Q: Why does the calculator show a different day number than some other tools?
A: Some tools count January 1 as day 0, while others count it as day 1. This calculator uses the convention that January 1 is day 1, which is the most common in calendars and date math.

Final Thoughts

This calculator gives you the essential facts about any date in the Gregorian calendar: the weekday, the day number, leap year status, and days remaining. It’s a handy tool for planning, historical research, or just satisfying curiosity. The formula is transparent, so you can verify the results by hand if you like. Whether you’re checking a date for a project or just want to know what day of the week your next birthday falls on, this calculator has you covered.

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in y | Year | - | 2024 | 1
in m | Month | - | 6 | 1
in d | Day | - | 15 | 1
out dow | Day of week | - | (floor((14 - m) / 12) + y - floor((14 - m) / 12) + floor((y - floor((14 - m) / 12)) / 4) - floor((y - floor((14 - m) / 12)) / 100) + floor((y - floor((14 - m) / 12)) / 400) + floor((31 * (m + 12 * floor((14 - m) / 12) - 2)) / 12) + d - 1) % 7 | 0
out daynum | Day of year | - | d + floor((153 * (m + 12 * floor((14 - m) / 12) - 3) + 2) / 5) + 365 * (y - floor((14 - m) / 12)) + floor((y - floor((14 - m) / 12)) / 4) - floor((y - floor((14 - m) / 12)) / 100) + floor((y - floor((14 - m) / 12)) / 400) - (y - floor((14 - m) / 12)) * 365 - floor((y - floor((14 - m) / 12) - 1) / 4) + floor((y - floor((14 - m) / 12) - 1) / 100) - floor((y - floor((14 - m) / 12) - 1) / 400) - 1 | 0
out leap | Leap year | - | (y % 4 == 0 && y % 100 != 0) || y % 400 == 0 ? 1 : 0 | 0
out daysleft | Days left in year | - | 365 + ((y % 4 == 0 && y % 100 != 0) || y % 400 == 0 ? 1 : 0) - (d + floor((153 * (m + 12 * floor((14 - m) / 12) - 3) + 2) / 5) + 365 * (y - floor((14 - m) / 12)) + floor((y - floor((14 - m) / 12)) / 4) - floor((y - floor((14 - m) / 12)) / 100) + floor((y - floor((14 - m) / 12)) / 400) - (y - floor((14 - m) / 12)) * 365 - floor((y - floor((14 - m) / 12) - 1) / 4) + floor((y - floor((14 - m) / 12) - 1) / 100) - floor((y - floor((14 - m) / 12) - 1) / 400) - 1) | 0