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## Day of the Week For Any Date (Revised)

Published on Tuesday, March 01, 2011 in , , ,

Note: If you're interested in calendar calculations, you also might want to check out my Quick Calendar Month Creation tutorial.

## Re-Introduction

In this feat, someone gives you a date, and you quickly state the day of the week on which it fell. This new approach is updated for the 21st century, and employs new tips and tricks that help make this feat simpler to learn and quicker to perform.

## Approach:

The Day of the Week For Any Date feat combines both memory and mental math. A relatively simple mastery of both, though, will create a response far out of proportion to the required work.

Before I describe the basics of the approach, I'd like to help you get a good idea of your goal, as well as what's possible, by seeing this feat performed by various people in the following videos:
Here's the basic principles, broken down into simple steps:

1) Day and Months Number Conversion: To work out the days of the week mentally, we need to convert them into numbers. We'll also need to convert the months into numbers, to adjust for their effects. These are taught in an easy-to-remember manner.

2) Addition of 3 Numbers: Without using a calculator, can you tell me what 6 + 6 + 31 is? That's about as difficult as the basic formula gets. If you're comfortable doing that, you won't have a problem working through the formula.

3) Subtracting Multiples of 7: Let's say you're asked about the 27th of a month. Regardless of the month or year, we can state with certainty that the 27th of a month will fall on the 6th (since it's 3 weeks, or 21 days, earlier). Since adding 6 is simpler than adding 27, and will give the same result, why not use 6? If you learn to subtract multiples of 7, this makes the arithmetic so easy that you won't have to worry about addition problems any tougher than 6 + 6 + 6!

4) Year Number Conversion: After becoming comfortable with all of the above when given dates in the years 2000 to 2003, you'll learn how to remember and adjust the leap years in the 21st century to key dates. After learning those, you'll learn a simple way to adjust for any year from 2000 to 2099, and even adjust for other centuries!

Running through all these principles, there will be an emphasis on recognizing and taking advantage of patterns. The quicker you can recognize a pattern, the quicker will be your calculation.

We'll start with the codes for the days of the week, since that is our goal. All the formulas and patterns you'll learn later will result in a number from 0 to 6. This number is turned into a weekday as follows:

Day of Week Number Mnemonic
Sunday 0 SUNday=NONEday
Monday 1 MONday=ONEday
Tuesday 2 TWOSday
Wednesday 3 Three fingers look like a W
Thursday 4 FOURSday
Friday 5 FIVEday
Saturday 6 SIXturday

To help get you comfortable with converting numbers into days, take the Weekday Codes quiz here. Once you can get a perfect score in a short time, then continue with this tutorial.

Next, you need to learn the codes for the months. Like the weekdays, they range from 0 to 6:

Month Number Mnemonic
January 6 WINTER has 6 letters
February 2 February is 2nd month
March 2 March 2 the beat.
April 5 APRIL has 5 letters (& FOOLS!)
May 0 MAY-0
June 3 June BUG (BUG has 3 letters)
July 5 FIVERworks
August 1 A-1 Steak Sauce at picnic
September 4 FALL has 4 letters
October 6 SIX or treat!
November 2 2 legs on 2rkey
December 4 LAST (or XMAS) has 4 letters

Take the Month Codes quiz here to help reinforce the mnemonics.

Note: It's important to note that, in leap years, January reduces by one to 5, and February reduces by one to 1. The other years don't change in leap years. Leap years will be discussed in more detail later.

Once you're comfortable with both the month and weekday codes, you're ready to start calculating your first dates. In the next tab, you'll learn how to use these codes to work out dates for the years 2000 to 2003.

## Formula

Ready for the formula? Here it is: Month Code + Date + Year Code = Day of Week Code. It's a lot simpler than many people think, but there are some fine points to learn.

We haven't covered year codes yet, so I'm just going to teach you four simple ones with which to start out:
• 2000 = 0
• 2001 = 1
• 2002 = 2
• 2003 = 3
Those shouldn't be too hard to remember, should they? We'll learn more year codes later in this tutorial, but for now, we'll just focus on these years.

Let's start with a simple example. Let's figure out May 1, 2000. The code for May is what? The mnemonic is MAY-0, so May is a 0. The date itself is the first, so we use 1. The year code for 2000 is 0, so our problem is 0 + 1 + 0 = 1.

Which weekday has a code of 1? ONEday is MONday, so Monday is the day of the week on which May 1, 2000 fell. You can verify that at this site. Congratulations, you've just calculated your first date!

Let's try a date that's a little more challenging. Our next date is October 4, 2000. October is 6 (remember “SIX or treat”?), and 2000 is still 0, so that gives us 6 + 4 + 0 = 10. And the weekday that goes with 10 is...

Wait a minute, the weekday codes only range from 0 to 6! What do we do with a 10, or any result higher than 6 for that matter?

If you look on a calendar, the 10th of any month will always fall on the same day of the week as the 3rd, because the 3rd is 7 days earlier. So, with the result, or any number in the formula, we can subtract 7, or any multiples of 7 to reduce the answer. You may want to refresh yourself on the multiples of 7 with the help of Schoolhouse Rock here.

In our October 4, 2000 example, we got 10 as a result, so we can reduce that by 7. 10 - 7 = 3, so our result boils down to 3. Which day of the week is 3? Since 3 fingers looks like the letter W, that's Wednesday. Once again, you can check that here.

This reduction of the multiples of 7 can make the problem itself easier, as well. Let's try figuring out the day of the week for Halloween 2001, or October 31, 2001. October is 6, and 2001 is a 1, so the problem works out to be 6 + 31 + 1 = 38. The closest multiple of 7 to 38 is 35, so we do 38 - 35 = 3, which gives us another Wednesday.

That approach works, but it could be made simpler. When you hear that the date is the 31st, you can reduce that right away by working out that 31 - 28 (the closest multiple of 7 to 31) = 3, and doing 6 + 3 + 1 = 10. True, you would still need to reduce that 10 to 3 again to get Wednesday, but you'd need to subtract multiples of 7 either way.

Note that, by bringing the dates down by multiples of 7, you're making the problem you have to add much simpler. If 6 + 31 + 1 and 6 + 3 + 1 will both give you the same results, wouldn't you prefer to make it easier on yourself?

The scary technical term for subtracting multiples in this manner is modulo arithmetic, which is explained quite clearly at BetterExplained.com.

Let's try this with Valentine's Day in 2003. We start by making sure of the date, February 14, 2003. February is a 2 (remember the mnemonic?), and 2003 is a 3. The problem then becomes 2 + 14 + 3. However, if you spotted that 14 was already a multiple of 7, you should realize that you can drop it out completely! 14, or any multiple of 7, is the same as 0, so you can ignore them. For February 14, 2003, all you really need to add is 2 + 3 = 5. 5 is a FIVEday, or rather a Friday, so that's our answer!

Let's try one last problem before we go. What about February 2, 2000 (Groundhog Day)? February is 2, and 2000 is 0, so the problem we get is 2 + 2 + 0 = 4. 4 is a Thursday (remember FOURSday?), so February 2, 2000 should be a Thursday. Once again, we verify that information here and...OOPS! That site says February 2, 2000 is a Wednesday! What went wrong?

I briefly mentioned this at the end of the previous tab, but it needs to be repeated now. Whenever you're working in January or February dates in a leap year, you need to reduce the month code by 1 to compensate. Effectively the extra day, February 29, hasn't happened yet, so we're subtracting one to adjust for that fact. January becomes 5 (6 - 1) and February becomes 1 (2 - 1).

Since February 2, 2000 is a February date in a leap year, the code for February needs to be 1, not 2. Let's try the equation again, with that in mind. February in a leap year is 1, and 2000 is 0, so the equation is 1 + 2 + 0 = 3, which you should know by now is a Wednesday. As we saw when we originally made the error, Wednesday is indeed the correct day of the week.

Practice the Dates: 2000 to 2003 quiz here, making sure to keep an eye out for January and February dates in 2000, and adjusting your calculations accordingly. Practice these dates until you can calculate them with little trouble, and don't forget to subtract multiples of 7 to make your work easier!

Once you're comfortable with dates from 2000 to 2003, we're going to teach you how to better handle leap years in the next section.

## Year Codes: Why?

You'll note that the year codes for 2000-2003 progressed in a nice, simple, 0-1-2-3 order. This is because a normal year consists of exactly 52 weeks (52 × 7 = 364) plus 1 day, to make 365 days. So, from one 365-day year to the next 365-day year, a given date in a given month will fall one day later.

However, a 366-day leap year means that everything must jump ahead 2 days. This also means that the year codes for leap years will jump ahead 2 instead of 1. You might expect 2004 to be a 4, but because it's a leap year, it jumps ahead to 5.

To get you comfortable with the strange nature of leap years, I'm going to start by teaching you the first 7 leap years.

## First 7 Leap Years

Here are the year codes for the first 7 leap years, along with handy mnemonics by which to remember them:

Leap Year Year Code Mnemonic
2000 0 2000 is mostly 0s
2004 5 Count: 4...5...
2008 3 Right half of 8 looks like 3
2012 1 12 ÷ 12 = 1 (See below)
2016 6 16 ends in 6
2020 4 2 + 0 + 2 + 0 = 4
2024 2 24 ÷ 12 = 2 (See below)

With 2012 and 2024, you'll note that all you have to do is divide their last 2 digits by 12 to get their year code. This pattern keeps working all the way through 2096, which will give you a few extra leap year codes quite easily, assuming you know your 12 multiples:
• 2012 = 1
• 2024 = 2
• 2036 = 3
• 2048 = 4
• 2060 = 5
• 2072 = 6
• 2084 = 7 = 0 (Remember to drop any multiples of 7!)
• 2096 = 8 = 1 (Remember to drop any multiples of 7!)
First, practice just recalling the codes with the Leap Year Codes: 2000 to 2024 quiz here.

Once you're comfortable recalling all the codes, practice working out dates for those years with the Leap Year Dates: 2000 to 2024 quiz here. Don't forget that that the month codes for January and February are both reduced by 1 in leap years!

Once you've practiced those years, you're ready to learn how to handle any leap year in the 21st century!

## All Leap Years

If you're given a leap year that ends in a multiple of 12, you can already handle those through 2096 quite easily, of course. What about the remaining leap years?

If there were no such thing as leap years, the pattern year codes would simply repeat every 7 years. Because of the effect of leap years every 4 years, however, the pattern of year codes usually repeats every 28 years.

I say “usually” because years ending in 00 are an exception. Years ending in 00 are only leap years if they're divisible by 400. So, 1600, 2000, and 2400 are leap years, while 1800, 1900, and 2100 are not.

Thanks to the 00 exception the calendar only repeats EXACTLY every 400 years. However, when you're dealing with a range of years in which EVERY (without exception) 4th year is a leap year, then you can still rely on the 28-year rule.

This means that you can depend on the 28-year rule for every leap year from 2000-2096! I'll break this down in a simpler manner, so you can see how this is useful.

For the leap years 2028 through 2052, all you have to do is subtract 28 years, and you'll get a year with the same year code! 2028 - 28 is 2000, which you already know has a year code of 0, so 2028's year code is 0. 2032 - 28 = 2004, whose year code is 5, and so on.

While doing 2028 - 28 = 2000 in your head is simple enough, some people find that working out problems like 2040 - 28 or 2052 - 28 during a performance to be a little challenging. There's a way to make it simpler.

If you're worried about subtracting 28 from a number, add 2 and then subtract 30 instead. For example, instead of doing 2040 - 28, work out 2040 + 2 - 30 = 2042 - 30 = 2012. 2012 is a 1 year, so 2040 is a 1 year as well! What year has the same year code as 2052? Add 2 and subtract 30, and you'll get your answer in no time.

Similarly, for the years 2056 to 2080, you subtract 56 to get the year code. The mathematical short cut here, if you feel you need it, is to add 4 and then subtract 60. What's the year code for 2064? 2064 + 4 - 60 = 2068 - 60 = 2008 = a year code of 3! How about 2068? You should get a year code of 1, just like 2012.

How about 2072? Did you start by adding 4? Stop! 72 is a multiple of 12, so we just work out that 2072 is 6 from the pattern of 12s above. Don't forget to take advantage of the 12 pattern when you can! You should ask yourself if a year is divisible by 12 first, before subtracting.

Finally, for the years 2084 to 2096, just subtract 84. For 2084 and 2096, of course, just use the 12 pattern we discussed earlier.

If you need a shortcut for 84 for the remaining years, simply subtract 4, then subtract 80. 2092 - 4 - 80 = 2088 - 80 = 2008 = year code of 3! I'm sure you have the idea by now.

You can practice this process with the Leap Year Codes: 2000 to 2096 quiz here. Again, don't forget to take advantage of the 12 pattern when you can.

Also, don't forget to practice actual dates in these leap years with this Leap Year Dates: 2000 to 2096 quiz.

Once you're comfortable working through both of these quizzes, it's time to learn how to determine the code for every year from 2000-2099 in the next section!

## 2000-2099

Are you ready to handle any date from 2000 to 2099? You're probably more ready thank you think!

Once you can handle leap years, the remaining years are simple.

When given a non-leap year, you need 2 pieces of information: The year code for the nearest leap year BEFORE the given year, and how far the given year is from that leap year. When you have these two pieces of information, simply add them together (remembering to drop any multiples of 7, as we've discussed before), and you have the year code.

For example, take 2009. The closest leap year is 2008, which has a year code of 3 (remember?), and 2009 is 1 year later. So, we work out 3 + 1 = 4, so 2009's year code is 4!

How about the year code for 2051? The nearest leap year BEFORE that is 2048, and we can use the 12 rule to determine that the year code is 4. Since 2051 is 3 years later, we do 4 + 3 = 7 = 0 (don't forget to drop out multiples of 7!), so 2051 has a year code of 0.

How about a tricky one like 2094? It's 2 years after 2092, which has a year code of 3 (remember how we know that?), so 2 + 3 = 5, so 2094 has a year code of 5.

Since you can't be more than 3 years after a leap year in any date from 2000-2099, this is a relatively simple adjustment.

To get practiced with this approach for determining year codes for any year, use this Year Codes: 2000 to 2099 quiz.

Once you get comfortable with that quiz, move on to the Dates: 2000 to 2099 quiz here.

Being able to determine the day of the week for any date in the 21st century is an impressive feat on its own. Once you're comfortable with doing that, you can move on learning how to handle dates in other centuries in the next section.

## Other Centuries

Often you'll get asked about dates in the 20th century, especially if you're discussing someone's birthday. How do you handle those?

For dates from 1900 to 1999, simply work out the similar date for the 2000s, and then add 1. That's it!

For example, Let's say someone tells you they were born on January 20, 1985. Start as if you were working out January 20, 2085. 85 is a 1 year and January is a 6, so 1 + 6 = 7 = 0. Reduce 20 to 6 (cast out multiples of 7!) to get 6, and add 1 for the 20th century to get 7, which drops to 0. That 0 is the code for Sunday, and sure enough, January 20, 1985, was a Sunday.

Once you've worked out the day of the week for a given date in the 21st century, there's a simple pattern to alter the day for other centuries:
• 2300 to 2399 = add 1
• 2200 to 2299 = add 3
• 2100 to 2199 = add 5
• 2000 to 2099 = add 0
• 1900 to 1999 = add 1
• 1800 to 1899 = add 3
• 1700 to 1799 = add 5
• 1600 to 1699 = add 0
There is one VERY important note here for January and February dates in the years ending in 00: If a year ends in 00, it's only a leap year if it's divisible by 400. The years 1600, 2000, and 2400, and so on are leap years, while years like 1900, 1800, and 2100 are not. If you're given a January or February date in a year ending in 00, double check whether it's a leap year before you make the leap year adjustment.

Take a few minutes to study these adjustments, and then practice using them in the Dates: 1600 to 2399 quiz here.

Assuming you've put in the practice, you should be ready to give the day of the week for any date. In the next section, I'll provide a few tips and some background that can help improve your performance.

## Calendar Background

The current calendar system we use is known as the Gregorian calendar, since it was introduced by Pope Gregory XIII. It was first put into use in 1582 by the Catholic countries, so the calculations you've learned aren't really effective for dates before 1600.

In addition, many non-Catholic countries didn't adopt the Gregorian calendar until much later. Britain and its colonies didn't adapt the calendar until 1752. The use of the Gregorian calendar as a worldwide standard, however, didn't happen until the 1920s!

## Tips

• I can't emphasize enough the speed advantages of dropping multiples of 7, and becoming comfortable with that process. After you get use to doing this for dates from the 7th to the 31st several times, it almost becomes automatic.

• Carry a perpetual calendar! It's one thing to do this feat and know you're right. When you're doing it for an audience, they'll need some way to verify that you're correct. Originally, this meant carrying around a bulky book of calendars, but many mobile devices today make this much easier.

You'll generally want an app that mainly generates calendars for a wide variety of year, without appointment features, such as QuickCal for the iPhone and iPod Touch. iPad users can use YearViewer, and Android users can use Two Hundred Year Calendar or Day of Week.

• Want to practice on the go? Download these free mp3 files that give a date, then pause, then give the day of the week. The pauses range from 30 seconds down to 3 seconds, so you can challenge yourself as you get better. They're available in both DATE/MONTH/YEAR order (common in the UK, Australia, and Europe) and MONTH/DATE/YEAR (common in the US).

• As you've seen, working out year codes can take longer than just remembering the month, date, and week codes. When performing, the smart thing to do is ask for the year first, work out the year code as needed (including whether a leap adjustment will be needed), and only then ask for the specific date.

That way, not only do you get the year calculation out of the way, but you'll be able to determine the weekday more quickly and it will appear more impressive to your audience.

• When you're comfortable performing the feat this way, but you find you desire to be quicker, there is a more advanced step you can take. You can completely eliminate the calculations of the year code by memorizing the 100 codes needed for the years 2000-2099.

To do this, you'll need to be familiar with the Link System, the Shape Peg System and the Phonetic Peg System (AKA the Major System) (with images for 0 to 99).

Once you've practiced those systems and are comfortable with them, you use the Phonetic Peg System for images to represent the last two digits of the year (0 to 99), and the Shape Peg system for the year code (from 0 to 6). You then use the Link System to mentally link those two images together.

If you decide to go this method, here's a complete chart of the years from 2000 to 2099 with their corresponding year codes. Because the images people use with the above systems are so widely varied, I've avoided suggesting any mnemonics.

Year Year Code
2000 0
2001 1
2002 2
2003 3
2004 5
2005 6
2006 0
2007 1
2008 3
2009 4
2010 5
2011 6
2012 1
2013 2
2014 3
2015 4
2016 6
2017 0
2018 1
2019 2
2020 4
2021 5
2022 6
2023 0
2024 2
2025 3
2026 4
2027 5
2028 0
2029 1
2030 2
2031 3
2032 5
2033 6
2034 0
2035 1
2036 3
2037 4
2038 5
2039 6
2040 1
2041 2
2042 3
2043 4
2044 6
2045 0
2046 1
2047 2
2048 4
2049 5
2050 6
2051 0
2052 2
2053 3
2054 4
2055 5
2056 0
2057 1
2058 2
2059 3
2060 5
2061 6
2062 0
2063 1
2064 3
2065 4
2066 5
2067 6
2068 1
2069 2
2070 3
2071 4
2072 6
2073 0
2074 1
2075 2
2076 4
2077 5
2078 6
2079 0
2080 2
2081 3
2082 4
2083 5
2084 0
2085 1
2086 2
2087 3
2088 5
2089 6
2090 0
2091 1
2092 3
2093 4
2094 5
2095 6
2096 1
2097 2
2098 3
2099 4

### 296 Response to Day of the Week For Any Date (Revised)

June 19, 2011 at 1:47 PM

Hello,

Great explanation (as always). Small typo on the first tab: "The other years don't change in leap years" --> the other months.

Bram

October 11, 2011 at 3:12 PM

Thank you so much! It was so worth it! And couldn't have found a better teacher! XD

October 11, 2011 at 4:34 PM

The difficult part is finding the nearest leap year. Or is it just me that's missing something?

October 11, 2011 at 6:14 PM
This comment has been removed by the author.
October 11, 2011 at 6:19 PM

In Portuguese, the days of the week are ordinal numbers, so it's even easier for me to apply the rules. This is great, thank you!

Anonymous
October 11, 2011 at 9:57 PM

Maybe I'm doing it wrong, but November 18, 1969 doesn't seem to work. 2+4+6+1=13, which makes it a 6, so it should be Saturday? But, instead it is Tuesday?

October 11, 2011 at 11:30 PM
This comment has been removed by the author.
October 11, 2011 at 11:31 PM

November = 2
Day=18
Year=2
1900's= +1

Explanation:

68 is the nearest leap year, minus 56 (68-56=12) since 12 goes to 2012, or the multiple of 12 rule it actually equals 1. Plus the distance from your year of 1969 (1+1) makes the yearcode 2.

So November + 18 + 1969= X
Or 2 + 18 + 2 = 22
22/7(Remember to remove the 7 multiples) = 21 remainder ONE.
Now, because it is in the 1900's we add 1 to the day code giving us TWO for TWOsday.
So, November 18th, 1969 is a Tuesday.

I choose not to worry about the 7 multiples in the daycode. It makes no difference if you do it with the day code, or add them all together and then do the multiple of 7, so I do multiples last and just add everything straight up. It makes easier memorization of all the number jumbo in my head.

Hope that helped you, it took me a few tries to learn this. Please let know if it helped and if not ill try to re-explain!

Best of Luck,
CaptainNegatory

Anonymous
October 12, 2011 at 12:11 AM

My question is what's the method behind the month code? Rather than memorize them (and forget), I'd prefer to be able to figure it out (and forget the method ;).

After looking at the first 7 leap-year codes, I found it easier to divide the year by 4, then multiply that number by 5 to get the year code. For example, 2068 is a leap year. 68/4 = 17, 17 * 5 = 85. If you remove the multiples of 7 you get 1, which is the year code. Or you could just add the 85 in and do the multiples at the end.

Anonymous
October 12, 2011 at 1:11 AM

Also, the '00 leap-year exception doesn't seem to apply when finding year codes. For instance, to find the code for 1703, you would use the code for 1700 (0) and add 3, even though 1700 isn't divisible by 400 and thus isn't actually a leap year.

October 12, 2011 at 2:55 AM

Amazing stuff..thanks for the explanation

October 12, 2011 at 8:42 AM

For the 1969 example I get that 68 is the nearest leap year, but where does the -56 come from?

October 12, 2011 at 11:47 AM
This comment has been removed by the author.
October 12, 2011 at 11:49 AM

@Calicocal

Regardless of what century you are in, when you do a year that is 56-80 (or something close, he says the exact part under leap year tab) You subtract 56, for 84-99 you subtract 84 and for 28-52 you subtract 28. Does that make sense?

@schmozerbeast
I'm not the author of this post, but I'm not sure what you're saying. 1700 is a leap year.

Anonymous
October 12, 2011 at 3:03 PM

October 12, 2011 at 11:15 PM

TRY THIS;

EG DATE: 16/5/2020

Add the Mod7 of the years past 2000
[20]mod7 = 6

to the rounding down of years past 2000 / 4
20/4 = 5

to value of the corresponding month value from the following table;
Jan = 1 | Feb = 4 | Mar = 4
Apr = 7 | May = 2 | Jun = 5
Jul = 7 | Aug = 3 | Sep = 6
Oct = 1 | Nov = 4 | Dec = 6

therefore May = 2

and

6 + 5 + 2 = 13

Now, add that to the day minus 1
13 + 16 - 1 = 28

[28]mod7 = 0

0 = Sat
1 = Sun
2 = Mon
3 = Tue
4 = Wed
5 = Thu
6 = Fri

The only time this doesn't work is between Jan 1st to Feb 29th of any leap year... These days are simply the day before what is calculated, EG/ Saturday will become Friday.

Try is out, and let me know if you can break it.

Dan

October 15, 2011 at 11:50 PM

Forget memorizing the whole damn century! the pattern makes it easy to calculate.

Simply divide the year by 4 and add that (without the remainder) to the year, then subtract the nearest multiple of 7 and you have the year code for the '00's.

For example 2025:
25/4 = 6; 6+25=31; 31-28=3
3 is the date code for 2025

October 16, 2011 at 12:16 AM

@schmmozer

with regard to the month codes, I am like you I want to know how to derive it rather than memorize it - I don't know why it starts with 6 but the pattern is simple and rather than memorize all 12, I have simply memorized january and july and calculate from there.

the differences between the month codes are simply the number of days between that month and the previous minus the nearest mult of 7. February is simply 6 (january) plus the number of days in January minus 28.
6 + 31 - 28 = 9 - 7 = 2

I find it easy to simply add the number of days over 28 in each of the months to the 6 for january or 5 for july to get the month code. for example november:
5 (july) + 3 (july has 31 days) + 3 (august) + 2 (sept) + 3 (oct) = 16 (-14) = 2 the month code for nov

March 17, 2012 at 11:24 PM

Great article
Two tips. I find the month code easier to remember as pattern if you start with spring month March. Then it's 250 351 462 462

How to figure first day of month
date of first day of the month is the month code plus year code plus 1 (minus 1 for January and February in leap years only).
Example March 2012
Year code 1 + Month code 2 + 1 = 4, day code of first day in March, Thursday
April 2012
1 + 5 + 1 = 7/0, day code of first day in April, Sunday.
May 2012
1+0+1 = 2 first day in May, Tuesday
But Jan 2012
1+6 = 7/0 first day in January, Sunday

Try it. It works for 2013. Etc.

July 25, 2012 at 10:28 AM

hey, i seem to be stumped by this one:
On which day of the week is January 14, 1900?
Sunday
Saturday

January = 6
Day = 0
Year = 0
1900s = 1
and 1900 is not a leap year.

these sites back me up: http://www.dayoftheweek.org/?m=January&d=14&y=1900&go=Go
http://en.wikipedia.org/wiki/January_1900

error in the quiz? or help me see what i'm doing wrong.

thanks!

August 2, 2012 at 4:20 AM

Hi My name is kanthesh
I am helping my son to tell a day
but according to formula
month code + date + yearcode = week code
october 7th of 1974 is comming wrong
monthcode is 6.
date is 7
year code is 1
6 + 7 + 1 = 0
0 is Sunday actually correct answer is Monday

August 2, 2012 at 9:30 AM

Kanthesha,

October = 6
Day = 7
Year = 1
1900s = 1

You forgot to add 1 to account for it being in the 1900s versus the 2000s.

(http://gmmentalgym.blogspot.com/2011/03/day-of-week-for-any-date-revised.html?showComment=1343237285090#ndate1900s)

hope that helps!

August 2, 2012 at 9:44 PM

Oho! So nice of you Kristi,

I am very thankful to you.

thank you very much.

October 17, 2012 at 2:10 PM

This is incredible! You're wonderful! So much fun, thank you!

December 9, 2012 at 1:11 PM

Can someone tell me how they arrived at 2091 being year code 1 using their way to compute year codes (this is in the quiz, Dates:2000 to 2099)? I thought it would have been 0.

December 17, 2012 at 1:13 PM

@study29

How would it end up being 0?

2088-84= 2004 (year code 5)

2091-2088 = 3

5 + 3 = 8

8 - 7 = 1

March 10, 2013 at 6:25 PM

How might one calculate days of the week prior to 1600 and after 2399?

March 10, 2013 at 8:28 PM

After 2399 the pattern of century codes should just repeat. As mentioned here, prior to 1600 the Gregorian calendar was not really in use, so this trick doesn't work for there.

April 10, 2013 at 6:43 PM
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April 11, 2013 at 5:51 PM
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May 13, 2013 at 12:16 PM

excellent stuff,,,, gud explanation,,, keep it up!!

May 25, 2013 at 11:18 PM

help! July 23 1991

so in 1991:
for 91 the code is 5
for 1900-1999 the code is 1
so 1991 = 6

for July code is 5

23 is 23

5 + 6 + 23 = 34 ---> reduce to 6 making it saturday, but the quiz here says its tuesday ..

June 27, 2013 at 7:04 AM

Hi Kenn,

July 23 1991
5 + 2(23-21) + 1 + 1 (1900 - 1999 => 1)
5+2+1+1 = 9 - 7 = 2
2 is Tuesday > you can see in this page only on top.

July 2, 2013 at 12:26 PM

Dear kanthesta,
Why 1 is added twice when we know for 1900 to 1999 its to b added only once

July 2, 2013 at 12:28 PM

Solve for 01 march 2011

September 23, 2013 at 9:52 AM

NIce Job Pi !
You can see my efforts on: calendar-in-mind.blogspot.com

January 7, 2014 at 5:48 PM
This comment has been removed by the author.
January 7, 2014 at 5:58 PM

I tried this with my birthday: June 2, 1978 which came out to 4 = Thursday, but when I checked it online, my birthday fell on a Friday. Am I doing the math wrong??

June = 3
the 2nd of the month = 2
1978 = 2072 + 6 +1 = 6 + 6 + 1 = 13

Therefore, June 2, 1978 = 3 + 2 +13 = 18

and 18 mod 7 = 4 = Thursday!

January 10, 2014 at 12:02 PM

Hi Doug, I think the problem with the way you solved it is that there is a leap year in between 2072 and 2078 which would increase it by 1.

I did this
2078 - 56 = 2022. I know from the chart that 2020 = 4. So 4+2 = 6. Add the 1 for it being in the 1900s. 6+1=7 for our year code.

3 for January, 2 for the date. 3+2+7=12. 12 - 7 = 5.
5 is Friday.
__________________

I was taking the quiz and there is a date that I cannot solve.
January 24, 2068.
The quiz and other places online tell me it's Tuesday, but I keep coming up with Wednesday.
January = 6
24 can be factored to = 3
2068 - 56 = 2012. Chart tells me that is = 1

6+3+1=10. 10-7 = 3. Wednesday...
Is there something I'm overlooking?

January 10, 2014 at 11:34 PM

Doug 78 = 76 not 72

January 13, 2014 at 4:55 PM

Nevermind, I found my mistake. This paragraph must have gone straight through my brain...
"Note: It's important to note that, in leap years, January reduces by one to 5, and February reduces by one to 1. The other years don't change in leap years. Leap years will be discussed in more detail later."

January 14, 2014 at 10:34 PM

I like the idea of a quiz on each phase of the calculation, but the First Sunday Doomsday Algorithm is simpler and easier to remember. http://firstsundaydoomsday.blogspot.com
The months codes are especially easy there, because of the mnemonic "I work 9-5 at the 7-11" (So the month code for September is 5 and the month code for November is 7), and that every even month is its own month code. For instance the month code of October is 10, or April is 4. These two rules combined cover every month except Jan and Feb, which also have relatively simple rules.

February 17, 2014 at 2:29 PM

CaptainNegatory commented that finding the nearest leap year was causing trouble. I've found reducing the year by 28,56 or 84 first simplifies this.

For example to get the year code for 2091 I'd think of it as 'What do I need to add to 84 to get to 91" then I simply use 2007 as my year which is 2004 (5) + 3 = 8 = 1.

This way I can get the year code in a couple of seconds.

Hope this helps someone!

June 21, 2014 at 6:03 PM

What's winter got to do with January? Oh right, some of you don't know the southern hemisphere exists.

August 13, 2014 at 11:58 PM

Can anybody please tell me how to calculate January and February in leap year between 2000-2099. Example :- 7 February 2016

August 19, 2014 at 2:17 AM

Hi Aki,

You may try this!

Eg: 7-Feb-2016

for the year 2016, the code is 6

for the month Feb, the code is 1. Since it is a leap year, you need to subtract 1 from the month code and this applies for Jan month as well for leap year calculation.

For the 7th day, it is 7-7 = 0

Now, Day code + Month code + Year code

0 + 1 + 6 = 7 which is 0 (7 - 7 = 0)

0 stands for week day code "SUNDAY"

Hope it has helped you!

KUMAR

October 5, 2014 at 6:39 AM

Hola. Me gustaria saber cuÃ¡les son los cÃ³digos del dÃ­a-mes y aÃ±o. Gracias.

October 24, 2014 at 8:34 AM

what's the year code of 2015? and why?

October 25, 2014 at 11:01 AM

The mnemonics for the month numbers make no sense to people outside the United States.

November 3, 2014 at 6:54 AM
This comment has been removed by the author.
November 10, 2014 at 10:07 AM

january 1, 2020
6+1+4=11
11/7= 1 and 4/7
4= thursday, why is it wednesday in calendar?
did i compute something wrong?

November 12, 2014 at 12:48 PM

@reginald skibba
2020 is a leap year. So month code for January will be Winter (6) minus 1 ie 5.

November 12, 2014 at 12:51 PM

Excellent tutorial! I won't find those "genius's" on discovery much fascinating anymore ;)
The mnemonics have simply stuck in my head. Wonderful teaching methodology.
Going to practice this as often.
Thanks a ton! Cheers! :)

November 22, 2014 at 6:39 AM

my birthday is December 24 1991. based on the formula the result is 1- monday. but its Tuesday n the calendar​

November 23, 2014 at 10:56 PM

@eusy paul

I believe instead of year code 1, you are using year code 0.

91-84=07
closest to 07 is 04 which is year code 5
5+3=8 (since 7 is 3 away from 4)
8=1
Day=24-21=3
Month=4
4+3+1=8+1(because of the date being in the 1900's)=9
9-7=2 which is Tuesday.

What I find myself doing often is when the year is below 10 for some reason, I skip a step. Instead of doing 2004= year code 5 and then adding 3 for 2007, ill just take 2007 and use year code 7 instead to get 0 because it ends in 7, which is what I think you did. I'm not sure why my brain does that, but it occasionally chooses to skip that step. probably what you are doing. hope that helped.

November 27, 2014 at 11:31 PM

i computed 10-16-1981 my answer is 4 i checked it the right answer is 5. ived already add 1 for years 1900.. pls help thanks

December 2, 2014 at 4:35 AM

I do 17th of January 1936 over an over again and I always find Saturday but it's a Friday... Here's how i do it :
1936 is a 3 year : 36/12=3
January is 6, and finally 17 is... well 17!
Therefore : 3+6+17=26 With +1 for the 19's hundreds it's 6 --> Saturday!!!
So why, why is it a Friday then?? Thanks.

December 2, 2014 at 4:50 AM

Christopher :
1981 is 3 : 81=12x6+9 and 6+9=15 --> 15-14=1 and finally you have to add 2 leap years.
Then October is 6. Now we add everything up : 3+6+16=25 ; 25-21=4
And the +1 for the 19's hundreds, it's : 5!!!
Hope it helped.

Anonymous
December 6, 2014 at 8:36 AM

1st August 1997

2097 nearest leap year is 2096 which has year code of 8-7 = 1
so 2097 year code is 2

1+6+2 = 9

for 1900's we need to add 1 so net result is 9+1=10
10-7 = 3 which is Wednesday

But the actual result should be Friday

December 10, 2014 at 7:05 PM

@sasank samudrala
You are correct the tens year code is 2 and the century year code is 1 for a year code of 3.

The month code for August is 1, this is where I think you made your mistake.

And the first is a 1.

1, Aug, 1998
1+1+3=5 which is Friday

December 16, 2014 at 1:21 PM

thanq so much for posting such a useful post like this :)

January 14, 2015 at 1:04 PM

2038, January, 5th
5 + 6 + 5 = 16
16 - 7 = 9
9 = ???

January 18, 2015 at 7:48 AM

I have a lot easier method of remembering the Year Codes. That is to make a periodic table of Year codes. there is only one rule for all the year codes. I had developed this 35 years ago. Anyone interested should send a request on anandnb124@yahoo.com. It is all free.

January 18, 2015 at 7:54 AM

Sample of the table. for complete explanation please write to me on the above email address.

Yr.Cod5 3 1 6 4 2 0

L/Years Table (codes for Years 1,2&3 are 1,2&3 respectively)
4 8 12 16 20 24 28
32 36 40 44 48 52 56
60 64 68 72 76 80 84
88 92 96 00

January 31, 2015 at 12:55 AM

How to calculate the year code... explain clearly...plzzzz

Anonymous
March 26, 2015 at 4:48 AM

Hi, I'd like to ask you if I can translate your post into Czech and post it on my blog with a link on this site. Thank you for answer.

April 11, 2015 at 12:17 PM

i am unable to figure out the logic for this question what was the day of the week on 17 august 1983 ?

May 7, 2015 at 9:09 AM

@rohit pushkar

Closest Leap Year to 1983 is 1980. 80-56 = 24. 2024 = 12/2 = 2 + 3 (1983-1980). So the year code is 5
+1 for 1900s
+3 (17-14)
+1 (August)
--------------------
10-7 = 3 Which is Wednesday

May 25, 2015 at 4:38 PM

Count me among those who find the recommended procedure for developing the year number to be too fussy, with too many steps/shortcuts/mnemonics to juggle. I've reduced it to a simpler process for my own use:

For the years of the current century, simply take the last two digits of the year, add the number of 4's you have accumulated on the way to that number, and then do your modulo 7.
Example: for 2050, take 50, add 12 (because there are 12 fours in 50), and you have 62. Divide out the 7's, and you are left with 6. Neat!

As always, you can mod your 7's at any stage; so 50+12=62 will give you the same year-number result as 1 (50 mod 7) + 5 (12 mod 7).

May 29, 2015 at 8:30 AM

Tell me about the processof calculating year codes..plz

July 9, 2015 at 4:48 AM

What is the year code for 2006? And how do you figure it out

July 20, 2015 at 9:44 AM

2006 code = 0(century) + 1 (6 div 4) + 6 (6 mod 7) = 7 = 0

July 22, 2015 at 9:00 AM

i tried march 23,2018
march=2
23rd=3*7=21. 23-21=2
2018=3
2+2+3=7.7-7=0(sunday) why is it diff in the calendar? did i do something wrong?

July 25, 2015 at 7:58 PM

March = 2.
23-21=2.
2018 goes to 2016 =6 +2 =8 =1
2+2+1 =5 = Friday.

July 28, 2015 at 10:57 AM

For feb that has 29 days , the method doesn't work .
Eg. 14 feb 2248
Month = 2
Year 4+3
9-7=2
But it falls on Monday instead

July 30, 2015 at 6:12 PM

Your mistake is that in leap years february goes down by 1 to 1 so your result is only 8.

July 30, 2015 at 6:20 PM

The only thing I can't figure out is for the 00's, this is a leap year so we can use the same code as 2000 adding the code for the centuries, but these are the only leap years when you don't go down jan and feb by 1 is that it?

August 3, 2015 at 10:42 AM

20/10/2056 ?
having prblm in the year calculation ...

September 2, 2015 at 6:20 PM

Jan 31 1722 and Jan 31 2139 share the same equation.

Jan(6) + 31 + 17(5)22(6) =48 = Saturday
Jan(6) + 31 + 21(5)39(6) =48 = Wednesday

both are suupose to be saturdays. Please assist.

October 11, 2015 at 10:12 AM

We can stop the formulas use. I have prepared a calendar book. Used only 10 pages ( 5 sheets) of papper for one centuary. In this book there are four consecutive centuary calendar. (18th,19th,20th and 21st centuary) From this book we can find any day of any date since the Gregorian calendar was instituted.(1582 Oct 15th) Need not to do any calculation. Just follow the direction for use diagram.Within seconds you can find out particular day.
Just see the One year calander
2015 Feb Jun Sep Apr Jan May Aug
Mar Dec Jul Oct
Nov - - - - - -
1 8 15 22 29 Mon Tue Wed Thu Fri sat Sun
2 9 16 23 30 Tue Wed Thu Fri Sat Sun Mon
3 10 17 24 31 Wed Thu Fri Sat Sun Mon Tue
4 11 18 25 * Thu Fri Sat Sun Mon Tue Wed
5 12 19 26 * Fri Sat Sun Mon Tue Wed Thu
6 13 20 27 * Sat Sun Mon Tue Wed Thu Fri
7 14 21 28 * Sun Mon Tue Wed Thu Fri Sat

October 30, 2015 at 10:55 PM

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November 22, 2015 at 10:41 PM

december-1-2015 can anyone solve me for this?

November 27, 2015 at 1:02 PM

November 27, 2015 at 1:03 PM

http://sonyalpha.org/

December 30, 2015 at 1:18 PM

I realised why this formula does not work before 1752.
The reason is because the gregorian calendor wasn't implemented until 1752. So it is pretty useful after September 1752 only. So if someone someone tests your knowledge of correct weekday before 1752, you will be 100% wrong. So make sure to inform the people who you're doing the trick for. :)

January 7, 2016 at 9:15 AM

Dec 1 2015
Year 2012=1 + 3 =4
Month 4
Day 1
= 4+4+1 = 9 = 2
=tuesday.

This whole thing is simple enough, even with adding-
2300-1
2200-3
2100-5
2000-0
1900-1
1800-3
1700-5

And even with -1 for Jan & Feb on a leap year.

BUT
When it says 1900 and 2100 are NOT leap years...
How possibly does anyone come to this conclusion?
2000 leap year
2004, 2008, 2012, 2016...every 4 years.
2020 leap year
2040, 2060, 2080...every 20 years is a leap year...

Meaning, 2100 is also a leap year.

16 Jan 2100=
Day = 2
Month = 6
YEAR= 6
= 6+6+2 = 14 (-1 for Jan leap year)
= 13 minus the 7...
= 6 = Saturday. Because it's a leap year...

Sooo, is it meant to just refer to the 00 year always being WORTH 0 for year score, every 400 years..?
And regardless of its division by 400, it is still and always will be a leap year, if it is divisible by 4...

Anonymous
January 12, 2016 at 4:42 AM

I've been using this method now for a few years, much to the annoyance of my family (well nobody likes a smart alec), but is there a similar method for the Julian Calendar? This method works very nicely on British dates down to Thursday, 14 Sept 1752 (or, I imagine, many European countries from 1582 - see https://en.wikipedia.org/wiki/Gregorian_calendar#Adoption ) which was the day the Gregorian Calendar came into use there (preceded by Wednesday, 2 September, by the way), but dates such as 22 August 1485 (A Monday and the day Richard III of England came second in the 'Who's King From Tomorrow?' competition held at Bosworth Field) are more difficult. One solution is to add the conversion factor, D = INT(Y/100)-INT(Y/400)-2,* cited in the same article (https://en.wikipedia.org/wiki/Gregorian_calendar#Difference_between_Gregorian_and_Julian_calendar_dates) works, but the resulting mental effort causes facial contortion.
Any ideas?

*That is, century number minus the integer value of [the year divided by four hundred] minus two.

For example, 1485 gives D = 14 - INT(1485/400) - 2
or D = 14 - 3 - 2 = 9 (which can be reduced to 2, as we "cast out multiples of seven")

22 August 1485
century 3
year 1
month 1
day 1
------
6 - a Saturday using the above, Gregorian Calendar, method.
------

Adding D, calculated as 2 above, gives Monday - verified at
http://www.timeanddate.com/calendar/custom.html?year=1485&country=23&display=0&df=1

January 12, 2016 at 5:40 AM

D = INT(Y/100)-INT(Y/400)- 2

Could be slightly more easily executed, mentally, as
D = CC - INT(CC/4) - 2
Where CC is the century portion of the year.
Hence, for the 1485 example above,
D = 14 - INT(14/4) - 2
or 14 - 3 - 2 = 9

the INT(CC/4) calculation can be done easily as we do not need to bother with anything other than whole numbers - the nearest lower multiple of four is twelve: three times four.

what I'd propose is:
Century minus two (to get it out of the way) minus the nearest lower multiple of four.

D = 14 - 2 - 3

Unless it's easier to sort out the multiples of four first and start with 3+2, then subtracting the resulting 5 from 14 - or adding 14 to -5, of course.

January 12, 2016 at 6:06 AM

SO. Herewith conversion factors down to the first century AD. No, I don't have any truck with CE - Ano Domini or Christian Era, it's still AD to me.

0 -2
100 -1
200 0
300 1
400 1
500 2
600 3
700 4
800 4
900 5
1000 6
1100 0
1200 0
1300 1
1400 2
1500 3
1600 3
1700 4

To answer Seth C's post of December 30, 2015 at 1:18 PM, Seth, you won't be 100% wrong for dates 200-299 or 1100-1299 - Although you will have possible problems with the fact that the year was held to begin in March - as we all will. I haven't managed to figure whether that's a problem yet or not.

January 12, 2016 at 6:39 AM

PS!
Combining the year correction values from the above calculation and the Gregorian figures seems to provide accurate values down to 1100
thereafter, things are one out.
These year values to use for Julian dates seem to be valid (although I have no idea if the start of year in March will be a problem. Empirical data anybody?)
1100 1
1200 0
1300 6
1400 5
1500 4
1600 3
1700 2

Anonymous
January 13, 2016 at 2:48 AM

As I understand it, in England, New Year was counted as being March 25th from 1155 until 1752; this, in the Christian calendar, is the Feast Of The Annunciation, which commemorates the visit of the angel Gabriel to the Virgin Mary and is (or, now that it has fallen from common use) known as 'Lady Day' - a contraction of 'Lady's Day' and, possibly, 'Our Lady's Day' as The Virgin Mary is also known as 'Our Lady'. It is the first of the four traditional English quarter days and falls almost at the Vernal (also known as the March or Spring) Equinox in the northern hemisphere, much as Christmas Day is very close to the Winter solstice. The quarters are, or were:
Midsummer Day (24 June)
Michaelmas (29 September)
Christmas (25 December)

HOWEVER.
"The date at which the year commenced varied at different periods and in different countries. When Julius Caesar reformed the calendar (45 B.C.) he fixed 1 January as New Year's Day, a character which it seems never quite to have lost, even among those who for civil and legal purposes chose another starting point. The most common of such starting points were 25 March ... and 25 December...

In England before the Norman Conquest (1066) the year began either on 25 March or 25 December;

from 1087 to 1155 on 1 January;

and from 1155 till the reform of the calendar in 1752 on 25 March, so that 24 March was the last day of one year, and 25 March the first day of the next. But though the legal year was thus reckoned,
it is clear that 1 January was commonly spoken of as New Year's Day." - http://www.newadvent.org/cathen/03738a.htm#beginning

This has lead to some head-scratching moments for historians for the first three months of the English year.
For example, Samuel Pepys' Diary for 12 Jan 1663 (http://www.pepysdiary.com/diary/1663/01/12/) is entitled Monday 12 January 1662/63 - this means, I believe, legally it is still 1662 but it is after new year so it is 1663.
Now. Using our formula, we can calculate 12 Jan 1662 Julian
(using the amalgamated century figures from above, that is
1100 1
1200 0
1300 6
1400 5
1500 4
1600 3
1700 2)

century 3
year 7 ---> 0
Jan (non leap year) 6
day 12 ---> 5
total 21 - A Sunday

and 12 Jan 1663 Julian
century 3
year 8 ---> 1
Jan (non leap year) 6
day 12 ---> 5
total 15 - A Monday

Our formula will calculate the 'from January' year, rather than the legal year.

In conclusion, we must take care with reported dates when Lady Day, 25 March, is used as a new year, but realise that our formula will give us the day-to-day year (if you'll pardon the pun) not the LEGAL year at that time.

January 13, 2016 at 6:48 AM
This comment has been removed by the author.
January 14, 2016 at 8:09 AM

@Craig Mason, January 7, 2016 at 9:15 AM
16 Jan 2100
century = 5
year = 0
month = 6
day = 16 ---> 2

total 13, minus 7 = 6 - a Saturday and not a leap year.

http://www.timeanddate.com/calendar/custom.html?year=2100&country=9&display=0&df=1

Century years 1800, 1900, 2000, 2100 etc, are only leap years if wholly divisible by 400. That's the rule put into the whole Gregorian date system to help keep it accurate - remember the Julian system which preceded it had slipped eleven days by 1752 and the Earth does not oblige us by taking an exact number of days to travel round the sun, so adjustments have to be made.

pseudocode from wikipedia:

if (year is not exactly divisible by 4) then

(it is a common year)

else if (year is not exactly divisible by 100) then

(it is a leap year)

else if (year is not exactly divisible by 400) then

(it is a common year)

else

(it is a leap year)

endif

I wouldn't write code with so many negatives in, myself, because I like my work to readable, quickly understandable and easy to maintain, but it gets the point across - I'm not going to fix it just because it's ugly.

So.
To answer your question "Sooo, is it meant to just refer to the 00 year always being WORTH 0 for year score, every 400 years..?"
00 is always worth zero, but you must use the correct century modifier - that's 5, not 6, for 2100. (Possibly where the misunderstanding has crept in).

Begging your pardon, but I'm not wholly sure if this is a question or a statement: "And regardless of its division by 400, it is still and always will be a leap year, if it is divisible by 4..." but, if the year is a century and divisible exactly by 400 (which also means it's divisible by 4, by the way), it's a leap year, otherwise it... isn't.

Let me know if that helps.
QB

January 16, 2016 at 2:45 AM

02-02.2016
2+2+6 = 10-7 = 3 = Wednesday

But 02-02-16 is a Tuesday. Somebody plz explain

Anonymous
January 16, 2016 at 5:31 AM

@Sag January 16, 2016 at 2:45 AM

2016 is a leap year, so February counts as 1, not 2 (just as January counts as 5, not 6).

2+1+6 = 9, 9-7 = 2 = Tuesday.

KCA

January 16, 2016 at 6:08 AM

oh yes Thx @ KCA, so for all leap years Jan n Feb will be 5 & 1

Anonymous
January 16, 2016 at 6:26 AM

@Sag
That's the long and short of it - just remember that, for century years (1800,1900,2000, etc), only those which divide wholly by 400 are leap years - 1600, 2000, 2400, and so on.

Also keep an eye out for past dates which are under the old, Julian, Calendar, rather than the currently used Gregorian Calendar. (Anything prior to Thu 14 September 1752 in Britain, but down to 1582 in various parts of Europe and as late as 1923 for Turkey). There's a recent discussion on the comments about coping with Julian dates, which, by 1752, were 11 days out of sync with our 'modern' calendar.

Good luck
KCA

January 19, 2016 at 1:25 AM

Here's a table from Wikipedia
https://en.wikipedia.org/wiki/Conversion_between_Julian_and_Gregorian_calendars
I can't post it tidily because helpful HTML isn't allowed on the page.

"This table is taken from the book by the Nautical almanac offices of the United Kingdom and United States (1961, p. 417) [Nautical almanac offices of the United Kingdom and United States. (1961). Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac (pp. 410–18 ). London: H. M. Stationery Office.]"

'Year 'Julian date 'Gregorian date 'Difference
'−500 'March 5 'February 28 '
'−500 'March 6 'March 1 '−5
'−300 'March 3 'February 27 '−5
'−300 'March 4 'February 28 '
'−300 'March 5 'March 1 '−4
'−200 'March 2 'February 27 '−4
'−200 'March 3 'February 28 '
'−200 'March 4 'March 1 '−3
'−100 'March 1 'February 27 '−3
'−100 'March 2 'February 28 '
'−100 'March 3 'March 1 '−2
'100 'February 29 'February 27 '−2
'100 'March 1 'February 28 '
'100 'March 2 'March 1 '−1
'200 'February 28 'February 27 '−1
'200 'February 29 'February 28 '
'200 'March 1 'March 1 '0
'300 'February 28 'February 28 '0
'300 'February 29 'March 1 '
'300 'March 1 'March 2 '1
'Year 'Julian date 'Gregorian date 'Difference
'500 'February 28 'March 1 '1
'500 'February 29 'March 2 '
'500 'March 1 'March 3 '2
'600 'February 28 'March 2 '2
'600 'February 29 'March 3 '
'600 'March 1 'March 4 '3
'700 'February 28 'March 3 '3
'700 'February 29 'March 4 '
'700 'March 1 'March 5 '4
'900 'February 28 'March 4 '4
'900 'February 29 'March 5 '
'900 'March 1 'March 6 '5
'Year 'Julian date 'Gregorian date 'Difference
'1000 'February 28 'March 5 '5
'1000 'February 29 'March 6 '
'1000 'March 1 'March 7 '6
'1100 'February 28 'March 6 '6
'1100 'February 29 'March 7 '
'1100 'March 1 'March 8 '7
'1300 'February 28 'March 7 '7
'1300 'February 29 'March 8 '
'1300 'March 1 'March 9 '8
'1400 'February 28 'March 8 '8
'1400 'February 29 'March 9 '
'1400 'March 1 'March 10 '9
'1500 'February 28 'March 9 '9
'1500 'February 29 'March 10 '
'1500 'March 1 'March 11 '10
'Year 'Julian date 'Gregorian date 'Difference
'1582 'October 4 'October 14 '10
'1582 'October 5 'October 15 '10
'1582 'October 6 'October 16 '10
'1700 'February 18 'February 28 '10
'1700 'February 19 'March 1 '11
'1700 'February 28 'March 10 '11
'1700 'February 29 'March 11 '11
'1700 'March 1 'March 12 '11
'1800 'February 17 'February 28 '11
'1800 'February 18 'March 1 '12
'1800 'February 28 'March 11 '12
'1800 'February 29 'March 12 '12
'1800 'March 1 'March 13 '12
'1900 'February 16 'February 28 '12
'1900 'February 17 'March 1 '13
'1900 'February 28 'March 12 '13
'1900 'February 29 'March 13 '13
'1900 'March 1 'March 14 '13
'2100 'February 15 'February 28 '13
'2100 'February 16 'March 1 '14
'2100 'February 28 'March 13 '14
'2100 'February 29 'March 14 '14

January 19, 2016 at 1:25 AM

It shows that the conversion formula D = INT(Y/100)-INT(Y/400)- 2 only works as suggested down to ...1100 AD. Then it's values slip out by a value of one - looks like we're on the right track.

"Using the tables
Dates near leap days that are observed in the Julian calendar but not in the Gregorian are listed in the table. Dates near the adoption date in some countries are also listed. For dates not listed, see below.

The usual rules of algebraic addition and subtraction apply; adding a negative number is the same as subtracting the absolute value, and subtracting a negative number is the same as adding the absolute value.

If conversion takes you past a February 29 that exists only in the Julian calendar, then February 29 is counted in the difference. Years affected are those which divide by 100 without remainder but do not divide by 400 without remainder (e.g., 1900 and 2100 but not 2000).

No guidance is provided about conversion of dates before March 5, -500, or after February 29, 2100 (both being Julian dates).

For unlisted dates, find the date in the table closest to, but earlier than, the date to be converted. Be sure to use the correct column. If converting from Julian to Gregorian, add the number from the "Difference" column. If converting from Gregorian to Julian, subtract."

January 27, 2016 at 12:12 AM
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March 11, 2016 at 11:07 AM

Hey, I prepared such a book from which anybody can find out any day of any date since the Gregorian Calendar was instituted. I used only five sheets of paper for one century Calendar. This book is containing 4 consecutive Centuries Calendar. Each century Calendar repeating after 4 centuries. So, we can use this book to find out any day of any date without doing any calculation,for ever. So I Given the title of this book "CALENDAR FOR EVER". There are so many calculations beyond this book. But, those who are using this book they need not to do any calculation. Everything explained in the pre-face of the BOOK. I need the help of publishers and marketing agencies all over the world. So far nobody has prepared such a book still now.

March 11, 2016 at 11:07 AM

Hey, I prepared such a book from which anybody can find out any day of any date since the Gregorian Calendar was instituted. I used only five sheets of paper for one century Calendar. This book is containing 4 consecutive Centuries Calendar. Each century Calendar repeating after 4 centuries. So, we can use this book to find out any day of any date without doing any calculation,for ever. So I Given the title of this book "CALENDAR FOR EVER". There are so many calculations beyond this book. But, those who are using this book they need not to do any calculation. Everything explained in the pre-face of the BOOK. I need the help of publishers and marketing agencies all over the world. So far nobody has prepared such a book still now.

March 17, 2016 at 6:21 AM

I am having trouble with 7 may 1963 and 7 may 2063 can someone please check my thinking. 7 = 0, may = 0 , 2063 by the 7 rules = 0 so it should be sunday but it is monday, and 1963 is add 1 monday but it is tuesday please can someone correct my mistake

March 17, 2016 at 8:47 AM

63 - 56 = 7
Effectively, from the 'starting at 2000' idea, we're saying 2007
But that's three years after 2004, and the adjustment for 2004 is _5_.
5 + 3 = 8
clearing multiples of seven gives us 1 - a Monday, in 2063.
Add 1 for 1900-1999 and it's 2 - a Tuesday, in 1963.

March 18, 2016 at 4:15 AM

Thanks quin, that way of working should help with other problems i had

March 18, 2016 at 6:36 AM

You're most welcome. Good luck with it - it's been an incredibly useful thing to learn and beats the internet or lookup tables hands down.

March 22, 2016 at 8:02 AM

I have a maths qualification so I'm not one of these people who can't solve problems, but nobody is actually explaining the formula properly on this thread or article at all.

You've all commented knowing things bwfore reading the article...

Can someone reply to me a proper straight dowb the line way of working it out and explaining what the random numbers are?!

In one comment somebody randomly done 31 - 28 without explaining where 28 came from...

March 22, 2016 at 9:44 AM

I'm sure I haven't claimed prior knowledge - not of day calculation, at least.

I also can't explain the origin of the system, although, I will tell you, if you learn it, it works - it just takes reading through the tabs and learning the conversion figures required - this isn't a method pitched for understanding, it's a method presented to allow quick working.

By the time folks are down to the comments, they know the method and are asking for help from other people who've been there before and know where the 28 comes from.
Multiples of seven, such as twenty eight, show up a lot, thanks to the seven day week. If the line you mean is "6 + 31 - 28 = 9 - 7 = 2", The writer is referring to a calculation for January. The value for use in calculations for January is 6 (see the month table on the Basics tab above http://gmmentalgym.blogspot.co.uk/2011/03/day-of-week-for-any-date-revised.html#ndatebasics) and 31 - 28 refers to only needing the remainder of any day of the month when the number is divided by seven. It's easier to say

date - 'nearest lower multiple of seven'

than to do any actual dividing.
So 31 - 28 = 3. The third day into the last week. We don't need to bother with the previous weeks, so we discard them.

If you want a discussion of methods, Wikipedia has an interesting article on day calculation at https://en.wikipedia.org/wiki/Determination_of_the_day_of_the_week

However, it's easiest, I promise, to work through the article and just learn the numbers, if all you want is a fast way of finding a day from a date.

For myself, I evaluate the year, then the century, the month and finally the day of the month. Years are by far the most troublesome part of the calculation so I prefer to get it out of the way first.

I break the year down to a number related to the First Seven Leap Years table, knowing that leap years repeat every 28 years. (http://gmmentalgym.blogspot.co.uk/2011/03/day-of-week-for-any-date-revised.html#ndateleaps)

Then I add in the number referenced in the Other Centuries tab (http://gmmentalgym.blogspot.co.uk/2011/03/day-of-week-for-any-date-revised.html#ndate1900s) Note that there's a lot of chat about this in the comments above; It's not such plain sailing for dates before 1752 in Britain and America due to a calendar change which Europe had implemented in, I think, 1582, but don't quote me. This fact isn't of any trouble if you're only working within current lifetimes, anyway.

I take the month number from the Basics tab
http://gmmentalgym.blogspot.co.uk/2011/03/day-of-week-for-any-date-revised.html#ndatebasics
taking into account any adjustment for January or February in a leap year. (minus one from the value of either)

Then I add in the day of the month.
Throughout, I've also been subtracting multiples of seven, which makes the calculations far easier.

for example.
Today's date 22 Mar 2016

year: 16 ==> 6 (see http://gmmentalgym.blogspot.co.uk/2011/03/day-of-week-for-any-date-revised.html#ndateleaps)

century: 20 ==> 0 (see http://gmmentalgym.blogspot.co.uk/2011/03/day-of-week-for-any-date-revised.html#ndate1900s)

Month: 3 ==> 2 (see http://gmmentalgym.blogspot.co.uk/2011/03/day-of-week-for-any-date-revised.html#ndatebasics)

Day: 22 ==> 1 (22-21, 21 being nearest lowest multiple of seven )

6 + 0 + 2 + 1 = 9
And 9-7 = 2, a Tuesday (see http://gmmentalgym.blogspot.co.uk/2011/03/day-of-week-for-any-date-revised.html#ndatebasics) Why minus seven? We only need the remainders. If you think, there are four or so weeks in a month, but we just need a reference into A week - it doesn't matter whether it's the first, second third or fourth.

No. That's not particularly comprehensible at first look.
Work through the article; if you don't get any particular points, I'll gladly help explain.

QB

March 25, 2016 at 10:20 PM
This comment has been removed by the author.
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June 28, 2016 at 6:59 PM

July 27, 1965 was a Tuesday. Yet, I always get a Saturday.

July = 5
Day 27 -> 6
1965 -> 1 away from 1964 (leap year) + 1 (for 20th century)

5+6+2 = 13 - 7 = 6 - Saturday

What'd I do wrong?

June 29, 2016 at 7:18 PM
Anonymous
June 29, 2016 at 10:54 PM

Hi Unknown,
65 is [65-56=9] ---> 4 [9 because 8 ---> 3 and then add 1 to get you to the one year past that leap year] then add in century adjustment, etc.

June 29, 2016 at 10:56 PM

Hi Unknown,
65 is [65-56=9] ---> 4 [4 because 8 ---> 3 and then add 1 to get you to the one year past that leap year] then add in century adjustment, etc.

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Hi Unknown,
65 is [65-56=9] ---> 4 [9 because 8 ---> 3 and then add 1 to get you to the one year past that leap year] then add in century adjustment, etc.
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10 June 1843 gives me Sunday though. Internet says Saturday.

May 23, 2017 at 12:54 AM

Ansh

10 June 1843

43-28 = 15
15 maps to the nearest leap year(12), the value of which is 1.
15-12 = 3
add the 1 to the 3 = 4

Adjust for century (1800 gives a value of 3)
4+3=7, so 'throw it away' - all multiples of 7 are discarded.
June gives 3
add in the day of the month (10): 10+3=13

subtract multiples of 7 again, gives us a remainder of 6

and 6 maps to Saturday.
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