Easter Date (Computus)
Core step of the Gregorian algorithm locating the Paschal full moon.
Formula
Variables
Example
Easter can fall anywhere from March 22 to April 25
How it works
This step computes the position of the Paschal full moon within the 30-day lunar cycle for a given Gregorian year. The quantity a = y mod 19 identifies the year’s place in the 19-year Metonic cycle, after which 19a + b is reduced mod 30 to turn that cycle position into a day offset d. In the full Easter computus, this lunar offset is combined with solar corrections for weekday and leap-year effects to determine the final Easter Sunday.
When to use it
Use this when implementing or studying the Gregorian Easter calculation, especially the lunar portion that finds the Paschal full moon. It is also useful in calendrical algorithms, historical date computation, and any problem that needs the Easter date from a year value.
Worked example, step by step
Take year y = 2025 Step 1: Compute a = y mod 19 = 2025 mod 19 = 11 Step 2: Compute 19a = 19 × 11 = 209 Step 3: Use the Gregorian constant b for the year in the full computus step; here we focus on the modular part, so compute d = (19a + b) mod 30 Step 4: Substituting the values gives d = (209 + b) mod 30 Step 5: If b = 24 in the full algorithm, then d = 233 mod 30 = 23 Final result: d = 23, meaning the Paschal moon is 23 days after the algorithm’s March-based reference point
Common mistakes to avoid
- Using the year number directly instead of first reducing it with y mod 19
- Forgetting that d is a remainder modulo 30, so the result must be between 0 and 29
- Assuming this step alone gives Easter Sunday, when it only finds the Paschal full moon offset
Did You Know?
Computing Easter drove centuries of calendar mathematics — Gauss published his own Easter algorithm in 1800.
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