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Sunday, 14 February 2016

How To Derive Easter Calendar - A Step by Step Approach

This procedure is a dramatic and accurate simplification of the official procedure used to calculate Easter Sunday dates, as described in Christian Prayer Books. Paschal Full Moon dates are copied directly from these Books. It was produced in 1995 by Ronald W. Mallen, Adelaide, South Australia. It requires just one division on a calculator, and three simple additions. To know more about the History of the Easter Dating Method Click Here.

This procedure appears more compactly in the 1988 Australian Almanac (titled "The Dating of Easter") held in the Canberra Library, Australia.

There are three steps to calculating the Easter Sunday date: 

Step 1) Obtain the Paschal Full Moon (PFM) date from Table 1
  • Use a calculator to divide the year by 19
  • Obtain the 3 digits after the decimal point
  • Find the Paschal Full Moon (PFM) date in Table 1 below
Then continue below with Step 2

Step 2) Add the 3 numbers obtained from Tables 2, 3 and 4

Add the 3 numbers you obtain from the "result" lines of Tables 2, 3 and 4 below.

For example, the year 2008 gives us a PFM date of M22 in Table 1 (for years 326 to 2599 A.D.)
  • M21 gives 3 from Table 2
  • the 20 in 2008 gives 0 from Table 3
  • the 08 in 2008 gives 3 from Table 4

Step 3) Find the Easter Sunday date from Table 5
Use the total result from step 2 to find the day of week of the PFM date in Table 5, then add the number of days shown to the PFM date to find the Easter Sunday date.

***Worked examples were situated after the tables below.

Table 1: PFM Date for Years 326 to 2599 (M=March, A=April)
Fraction
after dividing
year by 19
326
- 1582
1583
- 1699
1700
- 1899
1900
- 2199
2200
- 2299
2300
- 2399
2400
- 2499
2500
- 2599
.0 (none)
A5
A12
A13
A14
A15
A16
.052
M25
A1
A2
A3
A4
A5
.105
A13
M21
M22
M23
M24
M25
.157
A2
A9
A10
A11
A12
A13
.210
M22
M29
M30
M31
A1
A2
.263
A10
A17
A18
A18
M21
M22
.315
M30
A6
A7
A8
A9
A10
.368
A18
M26
M27
M28
M29
M30
.421
A7
A14
A15
A16
A17
A18
.473
M27
A3
A4
A5
A6
A7
.526
A15
M23
M24
M25
M26
M27
.578
A4
A11
A12
A13
A14
A15
.631
M24
M31
A1
A2
A3
A4
.684
A12
A18
M21
M22
M23
M24
.736
A1
A8
A9
A10
A11
A12
.789
M21
M28
M29
M30
M31
A1
.842
A9
A16
A17
A17
A18
M21
.894
M29
A5
A6
A7
A8
A9
.947
A17
M25
M26
M27
M28
M29




Table 2: PFM Date for year
(M=March, A=April)

-
-
M21
M22
M23
M24
M25

M26
M27
M28
M29
M30
M31
A1

A2
A3
A4
A5
A6
A7
A8

A9
A10
A11
A12
A13
A14
A15

A16
A17
A18
-
-
-
-
Result:
0
1
2
3
4
5
6

Table 3: First 2 digits of year
(eg 19 for 1995, or 03 for 326)

-
-
-
-
03
04
05

06
07
08
09
10
11
12

13
14
15*
-
-
15*
16

-
17
-
18
-
19
20

-
21
-
22
-
23
24

-
25
-
26
-
27
28

-
29
-
30
-
31
32

-
33
-
34
-
35
36

-
37
-
38
-
39
40
Result:
6
5
4
3
2
1
0
* for years 1500 to 1582, use the result of 4
*
 for years 1583 to 1599, use the result of 1

Table 4: Last 2 digits of year

00
01
02
03
-
04
05

06
07
-
08
09
10
11

-
12
13
14
15
-
16

17
18
19
-
20
21
22

23
-
24
25
26
27
-

28
29
30
31
-
32
33

34
35
-
36
37
38
39

-
40
41
42
43
-
44

45
46
47
-
48
49
50

51
-
52
53
54
55
-

56
57
58
59
-
60
61

62
63
-
64
65
66
67

-
68
69
70
71
-
72

73
74
75
-
76
77
78

79
-
80
81
82
83
-

84
85
86
87
-
88
89

90
91
-
92
93
94
95

-
96
97
98
99
-
-
Result:
0
1
2
3
4
5
6


Table 5: Following Sunday
Step 2 result:
0
1
2
3
4
5
6

7
8
9
10
11
12
13

14
15
16
17
18
-
-

Day of week
of PFM date:
Sun
Mon
Tue
Wed
Thu
Fri
Sat

Days to add for
next Sunday:
7
6
5
4
3
2
1


Example: To calculate the Easter Sunday Date for Year 2020
Solution: We have to go through three steps as stated earlier.

Step 1: Divide the year 2020 by 19
               = 106.315
So use the .315 part of the result obtained to find the Pashal Full Moon (PFM) date on Table 1.
The result from table 1 is A8, which implies April 8, 2020 A.D
Note: A8 was the result from table 1 not only because it falls under the 0.315 category but be cause it also falls between the year 1900 and 2199 category.

Step 2: it involves adding the three numbers obtained from the "result" lines of table 2,3 and 4
  • The first number that will be used to obtain result from table 2 will be the result from table 1 which is A8. So A8 gives 6 (on the result line) from table 2
  • The second number that will be used to obtain result from table 3 will be the first two digits of the year which is 20 in 2020 (e.g. 21 in 2134; 07 in 745). So 20 gives 0 (from the result line) in table 3.
  • The third number that will be used to obtain result from table 4 will be the last two digits of the year which s 20 in 2020 (e.g. 94 in 1894). So 20 gives 4 from table 4.
The total of these results is 6 + 0 + 4 = 10

Step 3: The total of the results obtained from step 2 will be used to find the day of the week of the PFM date in Table 5. Thereafter add the number of days shown to the PFM date to find the Easter Sunday date.
From the table 5, 10(result obtained from step 2) shows that the PFM date occurs on Wednesday, so we need to add 4 days to find the next Sunday which will be, 8 + 4 = 12
So therefore, 12th April will be the Easter Sunday date for the Year 2020 A.D.

Hope you did find this more educative. You can kindly pick a year at random but not later than 2599 because our PFM calendar stops at 2599. We will add more in subsequent lectures. Feel free to add your streamlined calculations to the comment box. You might be helping somebody out there.

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