Calculate Easter: this is how the date is created every year
Easter falls on a different day each year. The time for Easter can be calculated. Mathematician Carl Friedrich Gauß found out how to do this. We provide you with the necessary mathematical foundations and explain the formula.
Calculate Easter - the mathematical basics
Gauss used the so-called modulo calculation for the formula for calculating the Easter date. You must understand this modulo calculation if you want to calculate the date. But that's not that difficult.
- The modulor calculation is the remainder that remains when two numbers are divided. Only whole numbers are used in the calculation, there are no comma numbers here. The abbreviation for the modulo calculation is "mod".
- An example makes the principle easier to understand: divide 15 by 2, the rest is 1, because 2 times 7 is 14, the rest is 1. As a modulo calculation, it would be written as follows: 15 mod 2 = 1 (pronounced 15 modulo 2 is equal to 1).
How to calculate the date for Easter
The date for Easter is relatively easy to determine for the coming years. The individual elements of the formula are as follows:
- a = year mod 4
- b = year mod 7
- c = year mod 19
- d = (19c + 24) mod 30
- e = (2a + 4b + 6d + 5) mod 7
- f = (c + 11d + 22e) / 451
- You can determine Easter Sunday from this as follows: 22 + d + e-7f
- If this result is greater than 31, Easter is in April. Then the following formula must be used for the calculation of Easter Sunday = 22 + d + e -7f-31 = d + e-7f-9.
- The result shows you the month in which Easter falls in the given year. If it is larger than 31, Easter is in April. To find the date for Easter Sunday, you need to use this formula: 22 + d + e -7f-31 = d + e-7f-9.
- Gauss himself found a special feature in his formula: If the invoice shows April 26 as the Easter date, you must set March 19 instead.
Example of the Easter formula: calculate the date for the year 2020
Easter is always celebrated in March or April. With the specifications explained in the previous section, you can calculate which day in the Easter 2020 calendar falls.
- a = 2020 mod 4 = 0
- b = 2020 mod 7 = 4
- c = 2020 mod 19 = 6
- d = (19x6 + 24) mod 30 = 138 mod 30 = 18
- e = (2x0 + 4x4 + 6x18 +5) mod 7 = 129 mod 7 = 3
- f = (6 + 11x18 + 22x3) / 451 = 270/451 = 0
- The date of Easter Sunday can be determined as follows: 22 + 18 + 3 - 7x0 = 43
- The result is greater than 31, so the holiday is in April, as explained in the second section. So this formula applies: 22 + 18 + 3 - 7x0 -31 = 12.
- Easter Sunday thus falls on April 12, 2020. By the way, we also explain why we celebrate Easter, albeit in a different article. You will also find out where the name Easter comes from.
Easter is the highest festival in Christianity, but Easter Sunday is only one of many public holidays in Germany. An overview of all federal states can be found in the next article.