Infos about religious holidays
The Date of Easter
The Easter Formula

Day	Month	Year

Today it is Sunday, 20. May 2012

The choosen day is Sunday, 20. May 2012

April 2012
Week	Mo	Tu	We	Th	Fr	Sa	Su
13							1
14	2	3	4	5	6	7	8
15	9	10	11	12	13	14	15
16	16	17	18	19	20	21	22
17	23	24	25	26	27	28	29
18	30

May 2012
Week	Mo	Tu	We	Th	Fr	Sa	Su
18		1	2	3	4	5	6
19	7	8	9	10	11	12	13
20	14	15	16	17	18	19	20
21	21	22	23	24	25	26	27
22	28	29	30	31

June 2012
Week	Mo	Tu	We	Th	Fr	Sa	Su
22					1	2	3
23	4	5	6	7	8	9	10
24	11	12	13	14	15	16	17
25	18	19	20	21	22	23	24
26	25	26	27	28	29	30

Infos about religious holidays

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For the calculation of german / christian holidays the knowledge of the Easter date is very important. That's why it seems to be natural to have the special PHP function easter_date(). It is a very nice feature that handles the calculation

. You will find a little more about Easter at The Date of Easter.
Here you are a small table with the dependencies of the religious holidays on Easter. All other holidays are on fixed days like Chirstmas, Silvester,...

Name	Amount of days around Easter
Rosenmontag	-48 Tage
Karfreitag	-2 Tage
Ostersamstag	-1 Tag
Ostermontag	+1 Tag
Christi Himmelfahrt	+39 Tage
Pfingstsamstag	+48 Tage
Pfingstsonntag	+49 Tage
Pfingstmontag	+50 Tage
Fronleichnam	+60 Tage

The date of Easter

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I found this information while sneaking at the Internet:
Since the judes returned from babylonic exil the day of Easter (Pesach, Pascha) is calculated as Sunday after the first full moon after the beginning of spring (21. of March). The christian people took over this rule for their Easter festival.
The german mathematician Carl Friedrich Gauß (1777-1855) was able to calculate the date of Easter for every year after the Gregorian calendar reform (1582) from 1583-8201. But it is still unclear whether 3200 or 3600 the leap year has to be skipped for compensating some 'over time'.

At Wikipedia there is a quite a large section about Easter, some other calendar types and different calculations Wikipedia - Osterdatum. For those who are not interested in the whole paragraph - although it is very interesting - I provide you this link for Calendar FAQ from Claus Tondering. He doesn't only write about some background information about Easter but summarizes many calender systems and calculation with very nice and complex explanations.

The Easter formula

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As I analysed all of the formulas for Excel, php and so on, I was wondering about and intersted in the origin of the Easter formula and I found it. Because of its complexity I thought about writing a small table that shows the calculation step by step.

Easter formula in general
Formula	Value
C = Year / 100	20
G = Year mod 19	17
H = (C - C/4 - (8C+13)/25 + 19G + 15) mod 30	17
I = H - (H/28)(1 - (29/(H + 1))((21 - G)/11))	17
J = (Jahr + Jahr/4 + I + 2 - C + C/4) mod 7	6
L = I - J	11
Easter month = 3 + (L + 40)/44	4
Easter day = L + 28 - 31*(Easter month/4)	8

Easter formula for the years 1900-2099
Formula	Value
C = Year / 100	skipped
G = Year mod 19	skipped
H = (24 + 19*(Jahr mod 19)) mod 30	17
I = H - H / 28	17
J = (Jahr + Jahr/4 + I - 13) mod 7	6
L = I - J	11
Easter month = 3 + (L + 40)/44	4
Easter day = L + 28 - 31*(Easter month/4)	8

PHP Function easter_date() delivers: 07.04.2012

Additional a few explanations for this formula mass:

G is the Golden Number-1: From 1-19 and is related to the moon phases and days of the Year that repeats every 19 years
H is 23-Epact (modulo 30): something related to the 'age' of the new moon
I is the number of days from 21 March to the Paschal full moon
J is the weekday for the Paschal full moon (0=Sunday, 1=Monday, etc.)
L is the number of days from 21 March to the Sunday on or before the Paschal full moon (a number between -6 and 28)

For every closer explanations just visit Claus Tondering

Unfortunately the PHP function easter_date() has some restrictions:

it is only useable for the years 1970-2037,
it is only a function for PHP (there might be some other functions for other languages), and
a funny thing with my XAMPP the years between 1971-1974 are delivering a wrong date

Just for fun I added the date including the days name from Eastersunday 2012 (by using strftime('%A, %d. %B 1971',easter_date($Year)): Saturday, 07. April 2012 - Everything was OK after the online test! What a pity - I was so happy to find an error

If you look a little closer to the tabular you might wonder about no remainders. The FAQ from Claus Tondering tells something about (Again, the divisions are integer divisions, in which remainders are discarded.). So I used the PHP-funkcion floor() instead of round(). Nevertheless I tested both of them and as expected floor() delivered the same results as easter_date().
Here is my complete Esaster-function in PHP:



function osterdatum($osterjahr){
 $G = bcmod($osterjahr,19);
 $C = floor($osterjahr / 100);
 $H = bcmod($C - floor($C / 4) - floor((8 * $C + 13) / 25) + 19 * $G + 15, 30);
 $I = $H - floor($H / 28) * (1 - floor(29/($H + 1)) * floor((21 - $G) / 11));
 $J = bcmod($osterjahr + floor($osterjahr / 4) + $I + 2 - $C + floor($C / 4), 7);
 $L = $I - $J;
 $EasterMonth = 3 + floor(($L + 40) / 44);
 $EasterDay = $L + 28 - 31*floor($EasterMonth / 4);

 $H2 = bcmod(24 + 19*(bcmod($osterjahr, 19)), 30);
 $I2 = $H2 - floor($H2 / 28);
 $J2 = bcmod($osterjahr + floor($osterjahr / 4) + $I2 - 13, 7);
 $L2 = $I2 - $J2;
 $EasterMonth2 = 3 + floor(($L2 + 40) / 44);
 $EasterDay2 = ($L2 + 28 - 31 * floor($EasterMonth2 / 4));

 $osterdatum_arr = array("G" => $G, "C" => $C, "H" => $H, "I" => $I, "J" => $J, "L"
=> $L,"Ostermonat" => $EasterMonth, "Ostertag" => $EasterDay,"H2" => $H2, "I2" =>
$I2, "J2" => $J2, "L2" => $L2, "Ostermonat2" => $EasterMonth2, "Ostertag2" =>
$EasterDay2);

 return $osterdatum_arr;
}

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