The day for any date by mental calculation
Scope
This page describes a method by which you can find the day for any date entirely in your head.
It deals with any date, past, present or future, since the adoption of the modern Gregorian calendar, which happened in different parts of the world at different times from 1582 onward.
For dates in the current year or the following one it takes only 1 or 2 seconds to obtain the result. For other dates it takes a little longer.
I will illustrate the method with 30 October 2008.
The first step is to calculate the add on number for the month in question, in this case October 2008.
Calculating the "add on number"
We start by adding three numbers
- The century number
- The year number
- The month number
For example, to find the add on number for October 2008 we proceed as follows.
The century number for the 21st century is 0 (as explained lower down on this page).
The year number for 2008 is 3 (as explained lower down on this page).
The month number for October is 6 (as explained lower down on this page).
Adding those three numbers gives 9.
Then we subtract as many sevens as we can. In this example we can subtract just one 7, leaving 2.
This result identifies the add on number for October 2008 as being 2.
Using the add on number to find the day of the week
We add the add on number to the date, in this case 30, to give 32. Then we subtract as many sevens as we can from the 32, giving 4.
This result identifies the day of the week, where 0 means Sunday, 1 means Monday, 2 means Tuesday, etc. Therefore 30th October 2008 was a Thursday.
Century, year and month numbers
To calculate the add on number, we need the century number, the year number and the month number.
The Century Number
1500 to 1599: 1
1600 to 1699: 0
1700 to 1799: 5
1800 to 1899: 3
1900 to 1999: 1
2000 to 2099: 0
2100 to 2199: 5
2200 to 2299: 3
and so on
The pattern repeats endlessly.
The year number
I will illustrate the method by calculating the year number for 1985.
We take the last two digits of the year, 85.
We divide by 4, discarding any remainder, obtaining 21.
We add the 21 to the 85, obtaining 106.
We subtract as many sevens as we can from the 106, obtaining 1.
Therefore the year number for 1985 is 1.
I find that in everyday life the date for which I want the day is almost always in the current year or the next one. It's no great feat of memory to remember the year number for the current year and the following year, enabling me to obtain very quickly the day for any date in those two years.
Even faster is to remember the add on number for the current month and the following month.
The month number
The month numbers are given by the following table. But I don't remember them as numbers. I use mnemonics.
| Month | Month number |
| January | 6 in non leap years 5 in leap years |
| February | 2 in non leap years 1 in leap years |
| March | 2 |
| April | 5 |
| May | 0 |
| June | 3 |
| July | 5 |
| August | 1 |
| September | 4 |
| October | 6 |
| November | 2 |
| December | 4 |
Here are the mnemonics by which I remember those numbers (only the non leap year ones — one must simply remember that for leap years, the month numbers for January and February have to be reduced by one).
I visualise for each month the first so many letters of its name. The number of letters gives the month number.
| Month | Month number | What I visualise | Memory aid |
| January | 6 | Januar | The german word for January |
| February | 2 | Fe | The chemical symbol for iron |
| March | 2 | Ma | My ma (mother) was born in March |
| April | 5 | April | The whole word |
| May | 0 | Just an empty space (or see below) | |
| June | 3 | Jun | One less than one would expect |
| July | 5 | July+ | One more than one would expect |
| August | 1 | A | A1 = first-class |
| September | 4 | Sept | The usual abbreviation |
| October | 6 | Octobe | Rhymes with Obe Wan Knobe |
| November | 2 | No | Oh No! I can't remember that month number. Er... oh yes I can, the clue is what I just said, "No". |
| December | 4 | Dece | Like "dessicated coconut", as abbreviated by someone with poor spelling (ok, this one is lame, but it's so lame that it's unforgettable). |
For May, I can alternatively visualise a motorway where Fred Flintstone is driving his wooden and stone car. Since he lived so long ago, it cannot be the M1 (the first motorway built in the UK), so it must be the M0. So the month number for May is 0.
Ok, those are horribly lame, but they work for me. I'm sure that you will be able to invent some mnemonics that work for you.
Which years are leap years?
Leap years are years that are divisible by 4, except that there is a special rule for years that end in 00. Years that end in 00 are leap years only if they are divisible by 400. Therefore 1900 was not a leap year but 1600 and 2000 were.
In non leap years, February has 28 days. In leap years, it has 29.
The purpose of the leap year system is to keep the Gregorian calendar in step with the seasons.