## Earliest Easter for 100 years

March 21st, 2008 at 6:34 pm by David Farrar

According to National Review, Easter will not be this early again until 2160. It can in theory be one day earlier than it is this year, but will not be until 2285, and last was in 1818.

Incidentially Easter is observed on the Sunday after the first full moon on or after the day of the vernal equinox which is normally 21 March.

National Review says the formula to work out the date for Easter is:

((19*t+u-w-(u-(u+8)\25)+1)\3)+15)mod30)+(32+2*x+2*y-(19*t+u-w- (u-(u+8)\25)+1)\3)+15)mod30)-z)mod7)-7*(t+11*(19*t+u-w(u- (u+8)\25)+1)\3)+15)mod30)+22*(32+2*x+2*y-(19*t+u-w-(u- (u+8)\25)+1)\3)+15)mod30)-g)mod7)+114)\31

Looks Greek to me. I prefer the Meeus/Jones/Butcher Gregorian algorithm:

1. a = Y mod 19
2. b = Y/100
3. c = Y mod 100
4. d = b/4
5. e = b mod 4
6. f = (b + 8) / 25
7. g = (b – f + 1) / 3
8. h = (19 × a + b – d – g + 15) mod 30
9. i = c / 4
10. k = c mod 4
11. l = (32 + 2 × e + 2 × i – h – k) mod 7
12. m = (a + 11 × h + 22 × L) / 451
13. month = (h + L – 7 × m + 114) / 31
14. day = ((h + L – 7 × m + 114) mod 31) + 1

Simple really. So let us try it for 2008 (you use integers only by truncating)

1. a = 2008 mod 19 = 13
2. b = 2008/100 = 20
3. c = 2008 mod 100 = 8
4. d = 20/4 = 5
5. e = 20 mod 4 = 0
6. f = (20 + 8 )/ 25 = 28/25 = 1
7. g = (20 – 1 + 1) / 3 = 20/3 = 6
8. h = (19 × 13 + 20 – 5 – 6 + 15) mod 30 = 271 mod 30 = 1
9. i = 8 /4 = 2
10. k = 8 mod 4 = 0
11. l = (32 + 2 × 0 + 2 × 2 – 1 – 0) mod 7 = 35 mod 7 = 0
12. m = (13 + 11 × 1 + 22 × 0) / 451 = 46/451 = 0
13. month = (1 + 0 – 7 × 0 + 114) /31 = 115/31 = 3
14. day = ((1 + 0 – 7 × 0 + 114) mod 31) + 1 = 22 +1 = 23

So in 2008 Easter Sunday is the 23rd day of the third month.

I’ve even been bored enough that I have set up a spreadsheet in Excel with the formula so I can now instantly calculate Easter for any year!

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### 29 Responses to “Earliest Easter for 100 years”

1. kiwitoffee (382) Says:

Nice work. Retailers can now plan their staff holidays.

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2. artandmylife (15) Says:

You ARE bored – is that because the shops were closed? Interestingly my partners gym was open today

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3. Simon Lyall (88) Says:

If you are really bored could you update the Blogroll secton of the blog? It doesn’t have a link to (or list of) your blogroll anymore.

[DPF: Had some tech issues with it but will be back soon]

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4. mara (545) Says:

Dear God! I am going to print this stuff to read in bed next time I cannot sleep. Farrar, you should sell your post to the Insomnia Foundation of NZ. Better still, patent it and go global. You are on a winner.ZZZZzzzzz.

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5. francis (711) Says:

lol, no wonder Easter always catches me by surprise.

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6. Lee C (4,499) Says:

Have you ever considered getting diagnosed for Aspergers?

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7. Anthony (622) Says:

The better question is why do we follow such a complicated formula for setting the date for Easter when Christmas is always 25 December?

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8. Peak Oil Conspiracy (2,392) Says:

I’ve been looking here to try making sense of “a = Y mod 19″. Could someone please explain to a mathematical ignoramus like me why “a = 2008 mod 19 = 13″?

[DPF: When it is expressed like that, it is really asking for what the remainder is. If you divide 2008 by 19 to the nearest integer, the remainder is 13]

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9. barry (1,317) Says:

DPF – you are one sad bugger.
People who cant stand their own company suffer from low pesonal opinion of themselves and find themselves very boring company.
You need more time off for contemplation of your awful situation. In fact you should take time off until you can live with yourself again !!!!

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10. Chris Diack (723) Says:

Anthony:

In short, the formula reconciles two different calendars. There is no theological reason for it.

The Vatican has been organising conferences of Latin Rite (and Protestant off shoot) Churches to discuss the matter and attempt some agreement – the last one was in 1997 I think.

The real question for DPF is this: how does the Pope’s determination of Easter find force of law here.

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11. Monty (868) Says:

latest date for eater is 25 April and that will happen on 2038

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12. dad4justice (7,339) Says:

I sincerely hope that this lunar phase the double yolk egg team,that is, the Minister and Commissioner of Police do not blame rabbits for the road toll and full Moon violent attacks.

One can only hope.

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13. PaulL (5,197) Says:

DPF: politics shouldn’t be that boring. Not too many posts, and I see some other sites (Hive for example) are finding things to comment on? Are you losing your enthusiasm?

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14. mara (545) Says:

Barry, I’m with you. Night night.

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15. Doug (397) Says:

DPF: you must have gone to a good school unlike most New Zealanders.

http://www.stuff.co.nz/4445826a7694.html

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16. side show bob (3,660) Says:

Ah!!, now I know what you do for a living David, you work for the IRD and you write those poxy tax forms.

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17. SMF (21) Says:

Why is the church allowed to set the dates of public holidays in this secular age? How about fixing Easter (we can keep the name) as either side of the first weekend in April? That would provide far more certainty for businesses and, for those of us in the Northern hemisphere, it would also ensure better weather for the long weekend.

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18. peterwn (2,165) Says:

I vaguely remember seeing much simpler formulae for this, one came with the HP 67 calculator (PC’s with spreadsheets spelt the end of such calculators), and one in ‘Live Lines’ for information of power board IT managers. My HP 67 has long since gone and I cannot remember even the year of ‘live lines’ to start looking at (presumably the national Library has them). They both depended on very creative use of truncations for their brevity as far as I remember.

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19. skyblue (101) Says:

2011 – Easter Monday = Anzac Day. Do you reckon we will get the Tuesday off, Tui Billboard.
Also, that year Waitangi day is a Sunsay.
Summary, both 2010 & 2011 we lose 2 public holidays as they are on week ends or Easter Monday.
Double damm.

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20. Camryn (385) Says:

I’m not aware of the mathematical purpose of the 8)

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21. barry (1,317) Says:

for all those who complain about a connection between a holiday and a religion…

….you are not compelled to have a holiday
(and not being able to shop isnt classified as a holiday – go to europe and youll not be able to shop on any sunday and most saturdays).
In fact those who complain about religion and holidays shouldnt have any easter holidays or xmas or new year holidays
For those who dont like the head of state set up – then no queens birthday.
For those who dont like the idea of armed forces – no anzac day
and of course there wouldnt be any labour day off as you al want to work, work, work.

That only leaves waitangi day left – and thats a farce.

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22. ray (60) Says:

Like David also had a boring Easter friday and did some research
The date of the first Easter Sunday may have been
3 of April AD33
That came out of a dodgy site but it seems to stack up, there are a couple of possible varibles
So if there was a fixed date rather than a movable feast that could be it

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23. metcalph (1,039) Says:

2011 – Easter Monday = Anzac Day. Do you reckon we will get the Tuesday off, Tui Billboard.

It’s happened before. A five day weekend resulted.

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24. PaulL (5,197) Says:

Barry, no. Most people are OK with a connection between holidays and religion, the argument is about whether holidays should be compulsary v’s just being a default. Everyone in NZ gets a set number of stat holidays in a year, is there any particular reason that if it suits your employer and it suits you, that you shouldn’t be able to move your stat holiday to a different time. Maybe you want Chinese New Year off and are happy to work New Years Day. Maybe you want Hanukkah off and are happy to work Christmas Day. Maybe you just want to move it a couple of weeks so you can go camping at a time when every other bastard isn’t at the camping ground. As it stands, the law prevents this on certain days, or at least makes it harder than it needs to be.

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25. peterquixote (231) Says:

yous not a proper christian farrar and you lucky the inquisition is gone,

[DPF: If there was an inquisition, I'd be in charge of it!]

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26. peterquixote (231) Says:

gulp,

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27. NoCash (177) Says:

Peak Oil Conspiracy

2008 / 19 = 105.6842
2008 – (19 x 105) = 13

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28. Peak Oil Conspiracy (2,392) Says:

NoCash:

Thanks – much appreciated (I couldn’t see how one got from 105 to 13).

I dare say you’ll make a lot of spare cash selling your mathematical services

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29. PaulL (5,197) Says:

Now there’s a name we haven’t seen for a while!! Election year is it?

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