Happy New Year! As you get used to writing the year 2016, here is a tip that can help you adjust to the new calendar year. You will be able to figure out the day of the week just from hearing a date this year, so you’ll be able to mentally figure out things like when your birthday lands or when holidays are.

The rule is pretty easy to understand. And it’s easy to adapt the rule for dates in other years too, so you’ll find this rule handy every year.

I posted a video that explains the rule.

Calculate The Day Of The Week For Any Date In 2016 (And Up To 2099)

Keep reading for a text explanation.

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"All will be well if you use your mind for your decisions, and mind only your decisions." Since 2007, I have devoted my life to sharing the joy of game theory and mathematics. MindYourDecisions now has over 1,000 free articles with no ads thanks to community support! Help out and get early access to posts with a pledge on Patreon. .

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Calculate the day of the week for a date in 2016

The method is known as the doomsday rule and it was devised by the mathematician John Conway.

The idea is certain calendar days in a year always fall on the same day of the week, called the doomsday.

In 2016, a leap year, all of these dates will fall on a Monday (the doomsday). The dates are written in the month/day convention.

Leap year dates

1/4

2/29

3/14

4/4, 6/6, 8/8, 10/10, 12/12

5/9, 9/5, 7/11, 11/7

This might look difficult, but it’s only 12 dates to memorize. Also, there are patterns that will make most of the dates easy to remember.

First, in the even months numbers 4 and higher, remember the day is the same as the month. This gives the dates 4/4, 6/6, 8/8, 10/10, and 12/12.

Next, for many odd months, think of the phrase: “I work from 9 to 5 at the store 7/11.” The sentence gives the dates 9/5 and 7/11, and then swap the numbers to get 5/9 and 7/11.

The March date of 3/14 is Pi Day (since π ≈ 3.14…).

The February date is the last day of the month. In a leap year like 2016, this is 2/29. In a common year the corresponding date is 2/28.

The January date can also vary slightly. In a leap year like 2016, that occurs every 4 years, the date is 1/4. In a common year, or the other 3 years, the date is 1/3.

Using the doomsday method for 2016

The date 1/4 is a Monday and 2016 is a leap year, so all of these dates are also on a Monday.

Leap year dates

1/4

2/29

3/14

4/4, 6/6, 8/8, 10/10, 12/12

5/9, 9/5, 7/11, 11/7

These dates give anchor points for each month. You can then calculate every other day in the month in relation to them.

For example, what day is Christmas 12/25 for 2016? Start by using the anchor 12/12 which is a Monday. One week later (7 days) will be a Monday too, so 12 + 7 = 19 is also a Monday, and so is 19 + 7 = 26. This means 12/26 is a Monday. So Christmas is one day earlier, which means Christmas falls on a Sunday.

You can speed up the mental calculation in a couple of ways. You can subtract the day values to find the number of days between the anchor point and the date. So to find the days between 12/25 and 12/12, you would do 25 – 12 = 13. Then reduce by multiples of 7, since every 7 days is the same day of the week. So do 13 – 14 = -1. So you want 1 day before a Monday, which is a Sunday.

You can be even faster if you think of the days of the week in terms of number codes. Here are the day codes and a mnemonic rule to help remember them.

0 – Sunday (“Nones-day”)

1 – Monday (“Ones-day”)

2 – Tuesday (“Two-a-day”)

3 – Wednesday (“Threes-a-day”)

4 – Thursday (“Fours-day”)

5 – Friday (“Five-day”)

6 – Saturday (“Six-a-day”)

For example, what day is October 27 (10/27) in 2016? The closest reference point is 10/10, which is a Monday. So calculate 27 – 10 = 17. Then reduce by 7s to get 17 – 14 = 3. Then 3 days after Monday (“Ones-day”) is found as 1 + 3 = 4 (“Fours-day” / Thursday). Thus 10/27 is on a Thursday.

Adjusting for other years

Mostly you will need to calculate dates in the current year, so this rule will help figure out dates in 2016. But it can be modified for future years too.

In common years (not leap years), the dates are the same, except you need to change the January and February dates.

Common year (not leap year)

1/3

2/28

3/14

4/4, 6/6, 8/8, 10/10, 12/12

5/9, 9/5, 7/11, 11/7

Here is one way to remember this, as explained above. The February date is the last day of the month. In leap years like 2016, this is 2/29. In common years this is 2/28. The January date is related to leap years. In leap years like 2016, every 4 years, the date is 1/4. In common years, the other 3 years, the date is 1/3.

You can also figure out the day of the January date. In the years 2000 to 2099, if the year is written 20YY, you can figure out the day of the week of New Years from the following formula:

New Years day code = -1 + YY + roundup(YY/4) mod 7

That is, start with -1, add the year, add the year divided by 4 (result rounded up), and then reduce the result by multiples of 7.

So the year 2055, do -1 + 55 + roundup(55/4) = 54 + 14 = 68 ≡ 5 (mod 7), so the New Year in 2055 falls on a “fives-day” or a Friday. Then 1/3 happens two days later, which is a Sunday. Now all the dates in 2055 can be found using the memorable dates for a typical year.

The doomsday rule is a fun method to figure out the day of the week in your head. You’ll be surprised by how often this comes in handy, and others will be impressed at how you know all your dates.

More stuff

For more, check out Grey Matters with a slightly different method for Calculating the day of the week for any date.

Or learn more about the doomsday rule for calculating dates.

I previously made a video that explains this method for any year.

Calculate The Day Of The Week For Any Date Until 2099