When Does Easter Fall?

Every year, as we eagerly prepare to go egg hunting, bake hot cross buns, or simply enjoy a nice spring day, we ask ourselves the same question: “On what day does Easter fall?”

Easter is well-known for its unusual characteristic of not having a fixed date. While its origin dates back to the Bible, it was only in AD325 that the day of its celebration was first specified by the Council of Nicea as the first Sunday after the first full moon following the vernal equinox.

This single line gave birth to a problem that has stumped scientists for almost two thousand years. Indeed, the ‘computus’ (the term given to the mathematics used to determine the Easter date) reached its modern solution only in the nineteenth century, when a student pointed out a mistake in his professor’s algorithm — his professor being the eminent mathematician Carl Friedrich Gauss.

Moreover, Easter's mutable nature is the reason behind our Gregorian calendar. In 1582, Pope Gregory XIII realised that the equinox had drifted further and further away from the traditional date of 21 March and decided to fix the problem. Consequently, Catholic and Orthodox Christians typically celebrate Easter on different dates.

But why is determining Easter so complicated? The answer stems from the difference between calendar systems and astronomical time. While a common calendar year is 365 days long, it actually takes Earth 365.2425 days to orbit around the Sun — the reason why leap years exist. Lunar months differ as well; contrary to the standard length of 30/31 days, the Moon takes approximately 27.3 days to orbit Earth during what is called a ‘sidereal month’.

Considering lunar phases and ‘synodical months’, the time the Moon takes to return to the same phase must be mentioned. In this case, we are interested in the full moon, namely when the face of the Moon is fully illuminated, when Earth is between it and the Sun. This happens when the Moon lies in a straight line passing through us and our star. Since Earth simultaneously moves around the Sun, our satellite has to travel slightly farther after completing its orbit to end up on such a line, taking around 29.5 days.

Subsequently, this means that twelve solar months do not correspond to twelve lunar months, and after one solar year, the Moon’s extended travel leads to it being in a different phase compared to the same day of the previous year. The two cycles re-synchronise approximately every nineteen years in what is known as the ‘Metonic cycle’. In other words, by knowing the year in the cycle, we can know how off-phase the Moon is.

In finally locating the following Sunday, the days of the week shift one place forward every year and two every leap year. Therefore, by knowing any weekday in one year, we can predict any weekday in any year. As such, the Easter date can finally be determined.

All of this has required not only deep insight into physics and astronomy, but also patience from the greatest minds of the past and present in a collective effort that has spanned history. So now, whenever you ask yourself that initial question, think back to all the hard work that has gone into its solution. And before you start worrying about finding out when Easter will be this year, do not worry, I have got you covered: it is 20 April. You can thank me later.

Illustration by Sandra Palazuelos Garcia