Formula
Marais Formula
Copyright © Etienne A Marais 1991 
1. WHAT DOES A CALENDER
TELL US? 
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. 
2.
STRUCTURE OF THE QUESTION: 
The most accurate answer can
be given if you have four of the abovementioned elements of
a calendar.
Examples:
[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. 
3. CALCULATING THE ANSWER: 
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 

4.
USING THE MARAIS FORMULA 
Click on any value in the formula
below to view its method:
(Date Value)
+ (Month Value)
+ (Year Value)
+ (Century
Value)
7
Calculation:
You add up all the calculated values and divide
by seven. The remainder is the answer (fractions
are not used).
Note: 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 12digit 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 12digit number, but consider
that most telephone numbers are 10digit 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 mindpeg method. If you struggle to
memorise the calendar key, the mindpeg method is
described
here.

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.
Examples:
(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.
Examples:
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).
Examples:
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.] 
11.
JULIAN CALENDAR CONVERSION 
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).
Examples:
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.) 