Zeller Rule



As  in many competitive exams such as CAT , CSAT , SSC and other exams.Sometimes questions based on the calendar are  asked in the placement recruitment tests .

Here is the one of the easiest method to find the day of any date given.

In the beginning you might feel uncomfortable with the formula and steps.But once you practice it .It can be done mentally and answer the questions without much involvement of other steps. It is one line formula.

Zeller’s Rule

The following formula is named Zeller’s Rule after a Reverend Zeller. [x] means the greatest integer that is smaller than or equal to x.

You can find this number by just dropping everything after the decimal point. For example, [7.75] is 7.

Here’s the formula:

f = k + [(13*m-1)/5] + D + [D/4] + [C/4] – 2*C


In the above formula , the terms involved are as follows.

  1. k is the day of the month. Let’s use January 29, 2064 as an example.
  2. m is the month number. Months have to be counted specially for Zeller’s Rule: March is 1, April is 2, and so on to February, which is 12. (This makes the formula simpler, because on leap years February 29 is counted as the last day of the year.) Because of this rule, January and February are always counted as the 11th and 12th months of the previous year.
  3. D is the last two digits of the year. Because in our example we are using January of previous year .
  4. C stands for century: it’s the first two digits of the year

Lets take today’s date as example here.

3rd Aug 2016

Here , k=3




Now let’s substitute our example numbers into the formula.

f = k + [(13*m-1)/5] + D + [D/4] + [C/4] – 2*C
= 3 + [(13*6-1)/5] + 16 + [16/4] + [20/4] – 2*20
= 3 + [15.4] + 16 + [4] + [5] – 40
= 3 + 15 + 16 + 4 + 5 – 40
= 3.

Once we have found f, we divide it by 7 and take the remainder. Note that if the result for f is negative, care must be taken in calculating the proper remainder. Suppose the value of f obtained is -3 , then convert it to positive value by adding the value 7 or its multiples.

A remainder of

0 corresponds to Sunday,

1 means Monday

2 means Tuesday..

3 means Wednesday

4 means Thursday

5 means Friday

6 means Saturday 

For our example, 3/ 7 = 3, remainder 3, so 3rd August 2016 is Wednesday


Try it for your birthdays and aslo birthdays of  your special ones 🙂


Image Source : Google



About Praveenkumar P Kalikeri

ABOUT US Hey,Thanks for dropping by .First I would like to Appreciate for your love towards the Mathematics Subject. My name is Praveenkumar Kalikeri. I'm an Engineering Student from Karnataka , India. My Passion for Mathematics , encouraged me to start this blog . I Started loving the Mathematics subject from my schooling days.I was greatly motivated by teachers, parents who always helped me .        Numbers have Beauty !! They fascinated me .. As we all know best method to try out something new is to study old theories , concepts , its drawbacks, etc. I ,myself Started learning Vedic Mathematics at age of 15. Here , I will share vedic maths tricks learned and modified by me in simple manner which will be useful in various competitive exams. "If You Believe , You Can Do".
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