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Marais Formula Copyright Etienne A Marais 1991


There are six elements involved in our formula:

Using an example date of Monday, 13 January 1964 we have the following elements:

1.1  Day of the week - Monday
1.2  Date - 13
1.3  Month - January
1.4  Century - 19
1.5  Year - 64
1.6  1964 was a leap year.

Even if this seems obvious, it's essential to be aware of all the different factors that influence the formula.


The most accurate answer can be given if you have four of the above-mentioned elements of a calendar.

[What was the day of the week?] If you have 14 July 1949, you can calculate that it was a Thursday.
[What month was it?] If you have Thursday the 14th, 1949, you can calculate that the month was either July or April.

The answer most likely to be required is the first example. This is also the simplest calculation.

This is simply a general description of the formula. Every value will be explained in detail further on.

Each given element has to be converted to a numerical value, and then be added together for the final answer.

Using an example date of 14 July 1949, the different values would be determined the following way:
  Method Example Value
Date Same Value 14 14
Month Set Value
(calendar key)
July 0
Year Calculation 49 5
Century Set Value 19 0
Final Answer: 14 + 0 + 5 + 0 = 19
19 / 7 = 2 (remainder 5)
Day of the week Set Value Thursday 5

Click on any value in the formula below to view its method:

(Date Value) + (Month Value) + (Year Value) + (Century Value)

Calculation: You add up all the calculated values and divide by seven. The remainder is the answer (fractions are not used).

If it is a
leap year and the date is either in January or February, subtract 1 from your final answer.

Example question: "On what day was the fourteenth of July 1949?". 

The answer must be a day of the week

14 July 1949: 14(day) + 0(month) + 5(year) + 0(century) = 19

19 divided by 7 is 2 with 5 remaining. The final value for the day of the week is 5, thus the answer is Thursday.

(Practice by using different dates and checking your answers here.)

5. VALUE: Day of the Week
The values are set and range from 0 to 6, starting on Saturday:
Saturday 0
Sunday 1
Monday 2
Tuesday 3
Wednesday 4
Thursday 5
Friday 6
6. VALUE: Date
The date value is the date itself.
7. VALUE: Month
The calendar key is utilized and is a set value attributed to each month. This is the central element that will enable you to do the whole calculation in your head. It is a 12-digit number that you will need to memorise: 144 025 036 146.

Each digit represents a certain month:
January 1 July 0
February 4 August 3
March 4 September 6
April 0 October 1
May 2 November 4
June 5 December 6

It might initially seem difficult to memorise a 12-digit number, but consider that most telephone numbers are 10-digit numbers. If you can remember a phone number, you can memorise the calendar key.

There is an alternative way to remember this key by using a mind-peg method. If you struggle  to memorise the calendar key, the mind-peg method is described

8. VALUE: Year
This is the only part of the formula that involves a bit of arithmetic and it is calculated the following way:

Any given year must be divided by 4. The answer must be multiplied by 5 and then that answer must be divided by 7.
Note: You only work with whole numbers. No fractions are used.
The remainders of your first answer and your last answer must be added to give you the final value.

Example: If the given year is 49:

(1) 49 divided by 4 is 12 with 1 remaining.
(2) 12 multiplied by 5 is 60.
(3) 60 divided by 7 is 8 with 4 remaining.
(4) Add remainder of (1) to remainder of (3). That gives you 1 + 4 and a final answer of 5.

[Tip: If the year is ..00, ..01, ..02, ..03 - these years obviously cannot be divided by 4 as the answer would be 0 (fractions are not used). In only these four cases would the year also constitute the year value, e.g. 1901 would have value 1 and 1900 value 0]
9. VALUE: Century
The century values are set the following way:

It has a set value of either 6, 4, 2, or 0. If a century is divisible by 400, then the value is 6. The following century would have the value of 4, the next one would have the value of 2 and the following one 0.

(1) 1600's - value 6 (divisible by 400)
(2) 1700's - value 4
(3) 1800's - value 2
(4) 1900's - value 0
(5) 2000's - value 6 (divisible by 400)
(6) 2100's - value 4
10. VALUE: Leap Years
The final element that will influence your answer is whether the date in question falls in a leap year. If it is a leap year and the date is either in January or February, subtract 1 from your final answer.

How do you determine whether it is a leap year?

If a year is divisible by four, it is a leap year. In such a year, the month of February will have one extra day; the 29th. 

1972 - 72 is divisible by 4, thus it is a leap year.
1789 - 89 is not divisible by 4, so it is not a leap year.

It follows that every fourth year is a leap year, but there is an exception to this rule: At the turn of each century a leap year is skipped, except if the century is divisible by 400 (Gregorian Calendar reforms).

1700 is not divisible by 400, so that year was not a leap year. 2000 is, so it was a leap year. 

It follows that only in every four hundred years will the turn of the century be a leap year. 

Examples: 400, 800, 1200, 1600, 2000, 2400, etc. 

[1896 was a leap year, 1900 was skipped, so eight years passed before the arrival of the next leap year, which was 1904.] 
Up to 10 October 1582 a calendar was used that was introduced by Julius Caesar in 45 BC. This calendar covers all dates from January 1, 4713 BCE (before current era). The major difference between this calendar and the current Gregorian calendar is that it had every fourth year as a leap year, including every turn of a century. This led to the calendar being incorrect with an error margin of 10 days by 1582. The Gregorian calendar corrected this by dropping the leap year at every turn of the century, except where the century is divisible by 400.

To convert to Julian Calendar dates, follow these steps:

(1) Using  the Marais formula, add the date, month and year values.
(2) Add one day for each century prior to the 1500's (example: for 1100's you add 4, for 700's you add 8).
      Subtract one day for each century after the 1500's (example: for 1900's you subtract 4, for 2100's you subtract 6).
(3) Add three to your final answer.
(4) Divide by 7, remainder is the answer (no fractions).


A) Date:  13 October 1307
(1) Using the Marais Formula you calculate a value of 22.
(2) Add 2 for the century value (1500 - 1300).
(3) Add 3.
(4) Divide the total by 7 with the remainder as the final answer (fractions are not used).
      22 + 2 + 3 = 27
      27 / 7 = 3 (remainder 6)
      Final answer is 6 (Friday)

B) Date:  25 December 872
(1) Using the Marais Formula you calculate a value of 37.
(2) Add 7 for the century value (1500 - 800).
(3) Add 3.
(4) Divide the total by 7 with the remainder as the final answer (fractions are not used).
      37 + 7 + 3 = 47
      47 / 7 = 6 (remainder 5)
      Final answer is 5 (Thursday)

C) Date:  4 July 2345
(1) Using the Marais Formula you calculate a value of 11.
(2) Subtract 8 for the century value (2300 - 1500).
(3) Add 3.
(4) Divide the total by 7 with the remainder as the final answer (fractions are not used).
      11 - 8 + 3 = 6
      6 / 7 = 0 (remainder 6)
      Final answer is 6 (Friday)

(Practice by using different dates and checking your answers here.)

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Copyright ZAbra December 2008