Zeller’s Rule: What Day on This Date ?

Zellers Rule

Zeller’s rule is used to calculate the day on which each date falls for any year. This technique gives you a calendar for a specific year. Zeller’s rules have no practical application for students, but some of you may still want to learn the technique, so I included it in the application. Since the rules are standardized, I will keep the variables as they are.

Zellers Rule
Zellers Rule

Zeller’s Rule: What Day on This Date?

You can find the day on which any date falls using the formula:
F = k + [(13 x m-1)/5] + D + [D/4] + [C/4] – 2 x C

where

  • k — Date
  • m — Month number
  • D — Last two digits of the year
  • C — The first two digits of the century

Check today is Monday after 61 days it will be

RULES TO FIND DAY DAY:

  • In Zeller’s Rule, the year begins with March and ends in February. Hence, the month number for March is I. April is 2, May is 3, and so on up to January, which is 1 I , and February is 12.
  • January and February are counted as the 11″ and 12″ months of the previous year. Hence, if we calculate the day of any date on January 2026, the notation will be (month = 11 and year = 25) instead of (month = 1 nd Year = 26).
  • While calculating, we drop off every number after the decimal point.
  • Once we have found the answer we divide it by 7 and take the remainder. Remainder 0 corresponds to Sundi remainder 1 corresponds to Monday; remainder WO° corresponds to Tuesday; and so on…
  • If the remainder is negative, then add seven.

Example 1:  Find the day on 26th June 1983
(Here, k is 26, m is 4, D is 83, and C is 19.)
F= k + [(13 x m -1)/5] + D + [D/4] + [C/4] -2 x C
F= 26 + [(13 x 4 – 1)/5] + 83 + [83/4] + [19/4] -2 x 19
F= 26 + [51/5] + 83 + [2035] + [4.75] – 38
F= 26 + 10 + 83 + 20 + 4 – 38 (we drop the digits aft* the decimal)
F= 105
When 105 is divided by 7, the remainder is 0 and hence day is a Sunday.
Thus, 26th June 1983 is a Sunday.

Example 2: Find the day on 4th February 2032

Solution: As mentioned in the rules, February is taken as mon number 12 and the year will be the previous year. Hence, the value of D will be 31 instead of 32. (The values of k, m, D, and C are 4, 12, 31, and 20 respectively.) F F= k + [(13 x m -1)/5] + D + [D/4] + [C/4] – 2 x C
F= 4 + [(13 x 12 — 1)/5] + 31 + [31/4] + [20/4] – 2 x 20
F= 4 + [155/5] + 31 + 7 + 5 – 40
F= 4 + 31 + 31 + 7 + 5 — 40
F= 38

 

I hope this will help you to find the day of a previous date in your respective competitive exams.

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