Ashok Patel’s Method To Determine The Day Of The Week For Any Date Since The Start Of The Gregorian Calendar (1582)

Ashok Patel’s Method To Determine The Day Of The Week For Any Date Since The Start Of The Gregorian Calendar (1582)

Total = Date + Month Code + YY + floor(YY/4) + 2*(3- CC mode 4)

Month Codes: Jan=0, Feb 3, March=3, April=6, may=1, June=4, July=6, Aug= 2, Sep=5, Oct=0, Nov=3, Dec=5 If leap year Jan=6 and Feb=2

Day of the Week: (Total mod 7) gives you the day of the week.
Total mod 7 means remainder of (Total/7)which will give Day of the week as under:

  • 0 = Sunday
  • 1 = Monday
  • 2 = Tuesday
  • 3 = Wednesday
  • 4 = Thursday
  • 5 = Friday
  • 6 = Saturday

Ashok Patel’s method for determining the day of the week for any date since the start of Gregorian Calendar (1582) onwards involves a series of calculations. Here’s how it works:

Step-by-Step Calculation:

  1. Date: This is simply the day of the month (1 to 31).
  2. Month Code: Each month has a specific code:
    • January: 0 (6 if it’s a leap year)
    • February: 3 (2 if it’s a leap year)
    • March: 3
    • April: 6
    • May: 1
    • June: 4
    • July: 6
    • August: 2
    • September: 5
    • October: 0
    • November: 3
    • December: 5
  3. YY: The last two digits of the year. (Example 1947 so YY=47)
  4. Century is CC: The first two digits of the year. (Example 1947 so CC=19)
  5. (CC mod 4) means CC divided by 4 and the remainder is considered. If CC=19 then (19 mod 4) = 3
  6. Leap Year Adjustment:
    • If the year is a leap year and the month is January or February, adjust the month code as mentioned.

Calculation:

  • Total = Date + Month Code + YY + Floor (YY/4) + 2*(3 – CC mod 4)
  • Day of the Week: (T mod 7) gives you the day of the week:
    • 0 = Sunday
    • 1 = Monday
    • 2 = Tuesday
    • 3 = Wednesday
    • 4 = Thursday
    • 5 = Friday
    • 6 = Saturday
      • Let us check this formula to find the Day of the week for the following dates:
      • 15-04-1653
      • 02-09-1782
      • 20-11-1834
      • 04-07-1976
      • 25-12-2008
      • 29-02-1968

 

      • Calculations:
      • 15-04-1653 (April 15, 1653):
        • Date = 15
        • Month Code (April) = 6
        • YY = 53
        • floor(YY/4) = 13
        • CC = 16 (16 mod 4 = 0, so 3 – 0 = 3, 2*3 = 6)
        • Total = 15 + 6 + 53 + 13 + 6 = 93
        • Day = 93 mod 7 = 2 (Tuesday)

         

      • 02-09-1782 (September 2, 1782):
        • Date = 2
        • Month Code (September) = 5
        • YY = 82
        • floor(YY/4) = 20
        • CC = 17 (17 mod 4 = 1, so 3 – 1 = 2, 2*2 = 4)
        • Total = 2 + 5 + 82 + 20 + 4 = 113
        • Day = 113 mod 7 = 1 (Monday)

         

      • 21-11-1834 (November 21, 1834):
        • Date = 21
        • Month Code (November) = 3
        • YY = 34
        • floor(YY/4) = 8
        • CC = 18 (18 mod 4 = 2, so 3 – 2 = 1, 2*1 = 2)
        • Total = 21 + 3 + 34 + 8 + 2 = 68
        • Day = 68 mod 7 = 5 (Friday)

         

      • 04-07-1976 (July 4, 1976):
        • Date = 4
        • Month Code (July) = 6
        • YY = 76
        • floor(YY/4) = 19
        • CC = 19 (19 mod 4 = 3, so 3 – 3 = 0, 2*0 = 0)
        • Total = 4 + 6 + 76 + 19 + 0 = 105
        • Day = 105 mod 7 = 0 (Sunday)

         

      • 25-12-2008 (December 25, 2008):
        • Date = 25
        • Month Code (December) = 5
        • YY = 08
        • floor(YY/4) = 2
        • CC = 20 (20 mod 4 = 0, so 3 – 0 = 3, 2*3 = 6)
        • Total = 25 + 5 + 8 + 2 + 6 = 46
        • Day = 46 mod 7 = 4 (Thursday)

         

      • 24-02-1968 (February 24, 1968) – Leap Year:
        • Date = 24
        • Month Code (February in Leap Year) = 2
        • YY = 68
        • floor(YY/4) = 17
        • CC = 19 (19 mod 4 = 3, so 3 – 3 = 0, 2*0 = 0)
        • Total = 24 + 2 + 68 + 17 + 0 = 111
        • Day = 111 mod 7 = 6 (Saturday)

         

    • Summary:
      • 15-04-1653: Tuesday
      • 02-09-1782: Monday
      • 21-11-1834: Friday
      • 04-07-1976: Sunday
      • 25-12-2008: Thursday
      • 24-02-1968: Saturday