(d+y+y/4+mlookup) mod 7

mlookup starting with January, is….
0,3,3,6,1,4,6,2,5,0,3,5
you can use -1 instead of 6 or -2 instead of 5 if you prefer

‘d’ is still days, and ‘y’ is still years from 1900. Every 28 years the mod7 and /4 restart the years so you can use smaller numbers (i.e. for 1930, you can use y=30-28=2) Using this fact, when using this trick for friends around my age I make ‘y’ years from 1984 (1984=1900+28*3)
For the y/4 you ignore any remainder. (i.e. 7/4=1).
The one exception to the dates is that IF y is evenly divisible by 4, AND the month is January, or February, then you need to subtract 1 from your answer.
As before, 0=Sunday, 1=Monday,….

Test Oct 30, 2010, (note: I find it easier to mod the numbers before adding)
y=2010-1984=26, Oct=0
(30+26+6.5+0)mod7=(2+5+6)mod7=6 (Saturday, which is correct)

Test Feb 24, 1920
y=20, Feb=3
(24+20+5+3)mod7=3 But since 20/4 has no remainder, and we are dealing with a month before Leap day, we subtract 1 and get 2 or Tuesday.

This method works for dates from Jan 1,1901 to Dec 31 2099 as described. If you are interested in dates outside that range just look up the rule for leap years every 100 & 400 years and shift accordingly.
Hope this helps.

At first let me convey, Blissful belated NEW YEAR Wishes.
I heartfuly thank you and also appreciate for this wonderful formula. It is really amazing.

But can you please help me with 14th feb 1981.
Bcoz as per the formula it should be sunday, i believe, but in the calendar it is saturday.
I am still confused how can we apply this to the leap year. can you please explain it with an example.

That would be of great help.

Athreya.
Cinematographer.

My formula for months is simpler to remember and you subtract:

for the 3rd, 5th and 7th month of the year it is the number of the month (negative), so -3 for March, -5 for May and -7 for July.

For the even numbered months from June onwards it is the number of the month + 10.

April is the same as July, September is the same as December and November the same as March.

In a leap year January is the same as July (and April) and February is the same as August. Otherwise January equates with October and February with March (and November)

Easier year formula is to divide the number of the year by 4 and add that to the year itself (subtracted from 1900). You can round it down to the nearest 28 to make it easier (so 1977 is 21 years on from 1956 and the current year 2010 is 26 years on from 1984. 2012 will be the next “base” year.

Using all this Saturday is 0, Sunday is 1 etc.

17 April 1977 is:
17 for the date
-7 for the month
21 + 5 for the year.

adds to 36 = 1 mod 7, thus Sunday.

(18 + 2 + (10 * 76)/8 + 10 ) mod 7″

shouldn’t it be
77 instead of 76? or am I missing something

I suspect your Day numbers are off, the calculator page you link to has 0=Saturday, 1=Sunday, etc. In that case it works.