How can I calculate what date Good Friday falls on, given a year?

Question

Does anyone have a good algorithm to calculate what date Good Friday falls on given the year as an input? Preferably in C#.

Solution 1

Here's a great article that should help you build your algorithm

http://www.codeproject.com/KB/datetime/christianholidays.aspx

Based on this example, you should be able to write:

DateTime goodFriday = EasterSunday(DateTime.Now.Year).AddDays(-2);

Full Example:

public static DateTime EasterSunday(int year)
{
    int day = 0;
    int month = 0;

    int g = year % 19;
    int c = year / 100;
    int h = (c - (int)(c / 4) - (int)((8 * c + 13) / 25) + 19 * g + 15) % 30;
    int i = h - (int)(h / 28) * (1 - (int)(h / 28) * (int)(29 / (h + 1)) * (int)((21 - g) / 11));

    day   = i - ((year + (int)(year / 4) + i + 2 - c + (int)(c / 4)) % 7) + 28;
    month = 3;

    if (day > 31)
    {
        month++;
        day -= 31;
    }

    return new DateTime(year, month, day);
}

Solution 2

Don't Repeat Yourself

Think

Realize that calculating Easter is what you are really dependent upon.

Research

Here is the offical Naval Observatory page for calculating Easter.

http://aa.usno.navy.mil/faq/docs/easter.php

Execute

Use the formula for calculating Easter then shift to the previous Friday (or subtract 2 days, details up to you).

Solution 3

Try this:

// test code:
Console.WriteLine(CalcGoodFri(2008));
Console.WriteLine(CalcGoodFri(2009));
Console.WriteLine(CalcGoodFri(2010));

private static DateTime CalcGoodFri(int yr)
{
 //int yr = 2010;  // The year for which to determine the date of Good Friday.
 int a = yr % 19;      
 int b = yr / 100;     
 int c = yr % 100;   
 int d = b / 4;
 int e = b % 4;      
 int i = c / 4;
 int k = c % 4;
 int g = (8 * b + 13) / 25;
 int h = ((19 * a) + b - d - g + 15) % 30;
 int l = ((2 * e) + (2 * i) - k + 32 - h) % 7;
 int m = (a + (11*h) + (19*l)) / 433;
 int days_to_good_friday = h + l - (7*m) - 2;  
 int mo = (days_to_good_friday + 90) / 25;
 int da = (days_to_good_friday + (33 * mo) + 19) % 32;
 return new DateTime ( yr, mo, da) ;    // Returns the date of Good Friday
}

Logic ported from here: http://www.kenhamady.com/form25.shtml

Solution 4

Wikipedia knows: http://en.wikipedia.org/wiki/Good_Friday#Calculating_the_date

Good Friday is the Friday before Easter, which is calculated differently in Eastern Christianity and Western Christianity (see Computus for details). Easter falls on the first Sunday following the Paschal Full Moon, the full moon on or after 21 March, taken to be the date of the vernal equinox. The Western calculation uses the Gregorian calendar, while the Eastern calculation uses the Julian calendar, whose 21 March now corresponds to the Gregorian calendar's 3 April. The calculations for identifying the date of the full moon also differ. See Easter Dating Method (Astronomical Society of South Australia).

In Eastern Christianity, Easter can fall between March 22 and April 25 on Julian Calendar (thus between April 4 and May 8 in terms of the Gregorian calendar, during the period 1900 and 2099), so Good Friday can fall between March 20 and April 23, inclusive (or between April 2 and May 6 in terms of the Gregorian calendar). (See Easter.)

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Comments

[Gordon Broom]

also see en.wikipedia.org/wiki/Computus (which may or may not be linked from that wikipedia entry). One method that has been used historically is table lookup -- don't discount this method (unless of course your question is for homework :-)

[hunter]

I don't know what you're referring to... j/k, I fixed it

[hunter]

I can't believe how complex that is for something so seemingly simple... I wonder if I can refactor that... (wonders)

[hunter]

@Sarah And what would you suggest for year mod 19? int yearMod19?

[hunter]

@Sarah If you clicked the link in my post you'll see I used the example from that link

[hunter]

@Sarah I guess the point is that it is really meaningless anyway. I think with algorithms meaningful names can be ignored when there's no meaningful name to give. for(int incrementingInteger = 0; incrementingInteger < blah.Count(); incrementingInteger++) <= If I see you write that I will be very sad

[Sarah Vessels]

@Hunter: for a loop like that, the int could easily be an index into something, so gooseIndex would be more appropriate. Not that I do this, I usually do i or j or whatever, but I had a prof that insisted on no meaningless variable names, even in loops...

[rmac]

The last line 'return new DateTime(month, day, year);' seems to have the arguments in the wrong order. The DateTime constructor takes first year, then month, then day.

[Contango]

@rmac Corrected the last line that returns the DateTime.

[Black Light]

Its heartening to see that quality code like this never goes out of style. I especially like the use of meaningful variable names. Although, that said, I do wonder about the use of "days_to_good_friday" as a variable name, when "o" would have been more in keeping with the coding standards. Also, nice to see that "f" hasn't been used... which would allow the last three variables to be w, t and f.

[Paul Sasik]

@BlackLight: LOL! +1... Honestly, I tried a refactor on this but quickly gave up. The math is quirky enough that I would have been working for days to make basically an entire class with many a constant and private method to make this readable... The frequency of magic numbers per line of code may actually be a world record! (about 2:1)

[Engr.MTH]

g is the position within the 19 year lunar cycle; known as the golden number. c is the century. h is the number of days between the equinox and the next full moon. Pretty sure that i is the number of days between the full moon after the equinox and the first sunday after that full moon.

[Stefan Steiger]

And then realizing that there's both an Orthodox and a Catholic easter-sunday (at a different date): Priceless

[pbaris]

Any algorithm that i found in the web about Orthodox Easter has the same solution with yours. If the year is 2100, then with those algorithms i get 2100-05-01. But if i check it with some online "calculators" i get 2100-05-02. This "calculators" are wolframalpha.com/input/?i=orthodox+easter+at+2100 eortologio.net/pasxa/etos/2100 What am i missing?