What’s the most probable date for Easter? What’s the least?

This is a nice chance to highlight one of my older pieces. I had been wondering about the most and the least likely dates for Easter. And I calculated several hundred years’ worth of Easters, to find when they’re most and least likely to happen.

The 22nd of March is the least probable date for Easter. That date was last Easter in 1818, and will next be Easter in 2285. The 12th of April, though? That’s one of the most likely dates for Easter. To say what is “the” most probable date for Easter requires some thought. First, what it means to talk about the chance of an algorithmically defined quantity. Second, what it means to look at Easter. The holiday is intended to happen early in the European spring. But the start of European spring is moving through the calendar. Someday we will abandon the Gregorian calendar, or radically change the calculation of Easter. This makes it harder to say how often each possible date turns up. But we can make some rough answers.

The 15th of April is the most probable date for Easter, if we look at a 532-year span. (There are astronomical reasons to look at 532 years.) If we look at a more limited stretch, 1925 to 2100, on the assumption that that’s the maximum spread of dates that anyone alive today can be expected to see, then we have ten dates equally common, the 12th of April among them.


Author: Joseph Nebus

I was born 198 years to the day after Johnny Appleseed. The differences between us do not end there. He/him.

2 thoughts on “What’s the most probable date for Easter? What’s the least?”

  1. Isn’t the algorithm to calculate the date of Passover (which is itself based on a lunar calendar with incredibly byzantine leap-year rules to keep it more or less in sync with the solar year) and then find the next Sunday after the next Friday after that?


    1. To a first approximation, yes. To be precise, it’s complicated. You program; you understand.

      The first historical complication is that the early Christians did not actually know exactly how the Jewish calendar was computed. They had to reverse-engineer the thing (the alternative was asking Jewish people) and while the rough scheme for the calendar can be calculated, it’s got what look to the outsider like fiddly little rules, about keeping holidays away from the Sabbath and all, that the outsider might not recognize. And it’s occasionally possible for Passover to happen before the spring equinox, which was a hard no for the Christian role. Then there’s the added stipulation that Easter and Passover not happen the same date. That particular scheme fails sometimes, most recently in 1954 and 1981, and next in 2123, but that’s what they were going for.

      Anyway calculating Easter is a great horrible mess, even granted that it uses a simplified model of the Moon rather than the actual Moon, even when everybody is trying to do their best.


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