diamond geezer

 Sunday, March 31, 2024

You've probably noticed that Easter Day moves around a lot. Yes, it can fall on any date between 22nd March and 25th April, but it never seems to end up on the same weekend it did last year. And indeed it never can.

This year Easter is quite early, being Sunday 31st March. The matching Sunday next year would be 30th March but Easter Day won't be that, it's jumping ahead three weekends to land on Sunday 20th April.

Let's take a look at how the date jumps around during the 2020s. See how the date never appears in the same column two years running.

Date of Easter Day
 25-31 Mar1-7 Apr8-14 Apr15-21 Aprgap
2020  12 April  
2021 4 April  357 days
2022   17 April378 days
2023  9 April 357 days
202431 March   357 days
2025   20 April385 days
2026 5 April  350 days
202728 March   357 days
2028   16 April385 days
2029 1 April  350 days
2030   21 April385 days

The gap between Easters is never 364 days, only ever 350 days, 357 days, 378 days or 385 days.

In other words Easters are only ever 50, 51, 54 or 55 weeks apart, never 52 or 53.

Let's look at that last column more closely.
Here's a graph which shows the gaps between Easters for the first quarter of the 21st century.

See how the number of days jumps around, always missing 364 days and 371 days. There seems to be no obvious repeating pattern, but 2022 stands out as a bit of an oddity.

In particular some of the gaps seem to occur more frequently than others. So I checked the date of Easter for the whole of the 20th and 21st centuries, that's 200 gaps, and these are the results I found.

If you prefer that as a table...

Gaps between Easters
350 days50 weeks23%
357 days51 weeks41%
378 days54 weeks7%
385 days55 weeks30%

A 51 week gap is most common, i.e. Easter is a week earlier than last year. That's what's happened in 2024.
A 55 week gap occurs about a third of the time, i.e Easter is three weeks later than last year.
A 50 week gap occurs about a quarter of the time, i.e Easter is two weeks earlier than last year.
A 54 week gap only occurs about once every 15 years.

An interesting consequence of this is that next Easter is more likely to be earlier than later.
earlier: 50 weeks + 51 weeks = 64%
later: 54 weeks + 55 weeks = 36%
A lot more likely.

Meanwhile 52 and 53 week gaps never happen.
But why is that?

As usual with Easter it's all because of the Moon.

Specifically it's because full moons occur 29½ days apart (more accurately 29.531 days) and 29½s don't divide exactly into one year. 12 full moons take 354 days and 13 full moons take 384 days, near enough, neither of which are anywhere close to 364 days.

Ecclesiastically speaking, Easter is always the first Sunday after the first full moon after the spring equinox. So by the time a year's gone round, the full moon which triggers Easter is always about 10 days earlier or 20 days later, never ever around the same time.

If there are 12 full moons, i.e. 354 days, the gap between Easters will always be 350 or 357 days.
If there are 13 full moons, i.e. 384 days, the gap between Easters will always be 378 or 385 days.
The reason 378 day gaps are rare is because 384 days is a lot closer to 385 than 378.

Looking carefully at the sequence of gaps reveals a few more patterns.

» A 50 week gap is always followed, the next year, by a later Easter.
» A 55 week gap is always followed, the next year, by an earlier Easter.
» Sometimes you get two 51 week gaps in a row, but never three.
» A 54 week gap is always preceded, and followed, by a 51 week gap.

Finally, as you might expect with a 22nd March-25th April window, the date of Easter affects what the next gap is.

If Easter is between 22nd and 28th March, next Easter is always 55 weeks later.
If Easter is between 29th March and 2nd April, next Easter could be 54 or 55 weeks later.
That's us this year, with a 55 week gap until Easter 2025.

If Easter is 3rd, 4th or 5th April, next Easter could be 51, 54 or 55 weeks later.
If Easter is 6th or 7th April, next Easter could be 50, 51 or 54 weeks later.
And if Easter is between 8th and 25th April, next Easter could be 50 or 51 weeks later.

Two conclusions I hope it's been worth waiting for...
If Easter is before 3rd April, next Easter will always be later.
If Easter is after 7th April, next Easter will always be earlier.
And a final corollary which I think is worth knowing.
There can never be two consecutive March Easters.
So we can at least hope next Easter will be a bit warmer.

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