Date of Easter facts for kids

A calendar showing Easter dates from 532 to 632, made of marble, found in the Museum of Ravenna Cathedral, Italy.

Easter is a special holiday that moves around on the calendar each year. Its date is figured out using a calculation called computus (say: kom-POO-tus). Easter is always celebrated on the first Sunday after the Paschal full moon. This special full moon is the first one that happens on or after March 21. March 21 is a date chosen to be close to the March equinox, which is when day and night are about equal length.

Figuring out this date ahead of time is tricky. It needs to connect the lunar months (based on the Moon) with the solar year (based on the Sun). It also has to consider the month, date, and day of the week in either the Julian calendar or the Gregorian calendar. The calculation is complex because Christians wanted to link Easter to the Jewish holiday of Passover. Christians believe Jesus was crucified around the time of Passover.

Long ago, the pope would announce the date of Easter each year. But by the early 200s, communication in the Roman Empire became difficult. So, the church wanted a way for priests to figure out the date themselves. They also wanted to stop relying on the Hebrew calendar for Easter's date. Instead, they wanted to find Easter's date directly from the March equinox.

In a book from 725 called The Reckoning of Time, a scholar named Bede used computus to mean any kind of calculation. But later, by the end of the 700s, computus specifically meant calculating time, especially for Easter.

The way Easter is calculated gives different results depending on which calendar is used. The Catholic Church and Protestant churches use the Gregorian calendar. Most Eastern Orthodox Churches still use the Julian calendar. This is why they celebrate Easter on different days. The Gregorian calendar was created to fix a problem. The date March 21 was no longer lining up with the actual equinox.

Why Does Easter Move?

Easter celebrates the resurrection of Jesus. Christians believe this happened on the third day after Passover. In the Hebrew calendar, Passover is on the 14th day of Nisan. Nisan is the first month of spring in the northern hemisphere. The 14th day of Nisan is always a full moon. By the 100s AD, many Christians decided to celebrate Easter only on a Sunday.

The Hebrew calendar is a lunisolar calendar. This means it uses both the Moon and the Sun. It adds a "leap month" every two or three years to stay in sync with the solar year. This happens before the lunar new year on the 1st of Nisan.

Sometimes, the 14th of Nisan could happen before the equinox. Some early Christians thought this was wrong. So, they decided to separate Easter's date from the Hebrew calendar. They chose to find the first full moon after the March equinox.

By the time of the First Council of Nicaea in 325 AD, the Church of Alexandria set March 21 as the official date for the equinox. This was used for church purposes, no matter what the actual stars showed. In 395, a leader named Theophilus published a table of future Easter dates. This table used the Alexandrian rules. From then on, the computus became the way to find the first Sunday after the first ecclesiastical full moon (church full moon) that falls on or after March 21.

A Brief History of Easter Calculations

The first known Roman tables for Easter were made in 222 by Hippolytus of Rome. They used an eight-year cycle. Later, 84-year tables were used in Rome by Augustalis around the late 200s. A 19-year cycle, called the Metonic cycle, was suggested around 277 by Bishop Anatolius of Laodicea. But this idea didn't become popular until the Alexandrian method became the main one in the late 300s.

The Alexandrian computus was changed to fit the Julian calendar around 440. This led to a table of Easter dates (linked to Pope Cyril of Alexandria) for the years 437 to 531. This table inspired Dionysius Exiguus, who worked in Rome from about 500 to 540. He created his famous Easter table for the years 532 to 616. Dionysius also introduced the Christian Era (counting years from Jesus's birth) when he published this new Easter table in 525.

A different 84-year cycle was used in Rome in the early 300s. Victorius of Aquitaine tried to use the Alexandrian method with Roman rules in 457. He made a 532-year table, but it had some big mistakes. These Victorian tables were used in Gaul (now France) and Spain. They were replaced by Dionysian tables in the late 700s.

The tables from Dionysius and Victorius didn't match the ones used in the British Isles. The British tables used an 84-year cycle, but they had an error that made the full moons appear too early. This difference caused problems. For example, Queen Eanflæd (who used the Dionysian system) was fasting on her Palm Sunday while her husband, King Oswiu of Northumbria, was feasting on his Easter Sunday!

Because of this, the southern Irish started using the Dionysian tables after the Synod of Magh-Lene in 630. The northern English followed after the Synod of Whitby in 664.

Bede fully explained the Dionysian way of calculating Easter in 725. It might have been adopted by Charlemagne for the Frankish Church as early as 782. The Dionysian/Bedan computus was used in Western Europe until the Gregorian calendar was reformed. It is still used by most Eastern Churches today, including most Eastern Orthodox Churches and Non-Chalcedonian Churches. The only Eastern Orthodox church that doesn't follow this system is the Finnish Orthodox Church, which uses the Gregorian calendar.

By the 900s, almost all churches had adopted the Alexandrian Easter. This system still set the spring equinox on March 21. However, Bede had already noticed in 725 that this date was drifting away from the actual equinox. By the 1500s, it had drifted even more. Also, the calculated Moon used for Easter was fixed to the Julian year by the 19-year cycle. This caused an error of one day every 310 years. So, by the 1500s, the church's lunar calendar was four days off from the real Moon.

The Gregorian Easter has been used by the Roman Catholic Church since 1583. Most Protestant churches adopted it between 1753 and 1845.

Some German Protestant states used an astronomical Easter from 1700 to 1776. This was based on the Rudolphine Tables by Johannes Kepler. These tables used real observations of the Sun and Moon. Sweden also used this from 1739 to 1844. This astronomical Easter was the Sunday after the actual full moon that occurred after the spring equinox. However, it was delayed one week if that Sunday was the Jewish date Nisan 15 (the first day of Passover week).

This Nisan 15 rule affected two Swedish years, 1778 and 1798. Instead of being one week before the Gregorian Easter, they were delayed to be on the same Sunday. Germany's astronomical Easter was one week before the Gregorian Easter in 1724 and 1744. Sweden's astronomical Easter was one week before in 1744, but one week after in 1805, 1811, 1818, 1825, and 1829.

Two modern astronomical Easter dates were suggested but never used by any church. Both used the same rule as the German and Swedish versions. But they used modern astronomical calculations and did not include the Nisan 15 rule.

How the Calculation Works

The Easter cycle groups days into lunar months. These months are usually 29 or 30 days long. There's one exception: the month ending in March usually has 30 days. But if February 29 of a leap year falls within it, it has 31 days. These groups are based on the lunar cycle. Over time, the average lunar month is very close to a synodic month, which is about 29.53 days long.

A lunar year has 12 synodic months, totaling either 354 or 355 days. This is about 11 days shorter than a calendar year (365 or 366 days). These extra 11 days are called epacts.

Epacts are important because they help us connect the lunar calendar to the solar calendar. We need to add them to the solar year's day to find the correct day in the lunar year. When the epact reaches 30 or more, an extra month (called an intercalary month) of 30 days is added to the lunar calendar. Then, 30 is subtracted from the epact.

The 19-year Metonic cycle assumes that 19 solar years are about the same length as 235 synodic months. So, after 19 years, the Moon's phases should fall on the same days in the solar year, and the epacts should repeat. However, over 19 years, the epact actually increases by 29 (not 0). This is a problem if we only add 30-day months to fix it.

So, after 19 years, the epact must be corrected by one day for the cycle to repeat. This is called the saltus lunae (meaning "leap of the moon"). The Julian calendar handles this by making the lunar month that starts on July 1 in the last year of the cycle 29 days long. This creates three 29-day months in a row.

The saltus and the seven extra 30-day months were mostly hidden. They were placed where the Julian and lunar months started around the same time. The extra months began on January 1 (year 3), September 2 (year 5), March 6 (year 8), January 3 (year 11), December 31 (year 13), September 1 (year 16), and March 5 (year 19).

The number of the year in the 19-year cycle is called the "golden number". You can find it with this formula:

GN = 1 + (Y mod 19)

Here, Y is the year number in the Christian era. You divide the year by 19, and the remainder plus 1 is the golden number.

Cycles of 19 years are not all the same length. This is because they can have either four or five leap years. But a period of four cycles (76 years) has a length of 27,759 days (if it doesn't cross a century). There are 940 lunar months in this period. So, the average length is about 29.530851 days. Since this is longer than the true length of a synodic month (about 29.53059 days), the calculated Paschal full moon gets later and later compared to the actual full moon. This is why corrections are needed in the Gregorian system.

The Paschal or Easter-month is the first month in the year where its 14th day (its official church full moon) is on or after March 21. Easter is the Sunday after this 14th day. This means Easter is the Sunday within the third week of the Paschal lunar month.

The Paschal lunar month always starts between March 8 and April 5. Its 14th day always falls between March 21 and April 18. So, Easter Sunday will always fall between March 22 and April 25. This is true for both the Western (Gregorian) and Eastern (Julian) systems. In the solar calendar, Easter is called a moveable feast because its date changes within a 35-day range. But in the lunar calendar, Easter is always the third Sunday in the Paschal lunar month. So, it's not really "moveable" in the same way as other holidays.

Gregorian Calendar Changes

The main reason for creating the Gregorian calendar in 1582 was to fix the Easter calculation. So, a new way to calculate Easter was introduced with the new calendar. This method was explained by Clavius in 1582.

Easter Sunday is the Sunday after the Paschal full moon. The Paschal full moon is the church full moon on or after March 21. The Gregorian method finds these dates by figuring out the epact for each year. The epact is the age of the moon in days on January 1, minus one day. It can be from 0 to 29 days.

The 14th day of the lunar month is considered the day of the full moon. This is the day when the actual full moon is most likely to happen. The "new moon" is most likely to be seen as a thin crescent after sunset on the first day of the lunar month.

Historically, the Paschal full moon date was found from its golden number in the Metonic cycle. This cycle repeats the lunar phase on January 1 every 19 years. This method was changed in the Gregorian reform because the dates in the tables became inaccurate after about two centuries. But using the epact method, a simpler table can be made that works for one to three centuries.

Here are the epacts for the current Metonic cycle, which started in 2014:

As you can see, the date of the Paschal full moon in a year is usually 11 days earlier than the year before, or 19 days later. The Gregorian calendar also corrects the solar year by skipping three leap days every 400 years (in century years like 1700, 1800, 1900, but not 2000). This is called the solar correction.

However, 19 Julian years are a bit longer than 235 lunar cycles. This difference adds up to one day in about 310 years. So, in the Gregorian calendar, the epact is corrected by adding 1 eight times every 2,500 Gregorian years. This is called the lunar correction. The first one was in 1800, the next is in 2100.

The solar and lunar corrections work in opposite ways. In some century years (like 1800 and 2100), they cancel each other out. This means the Gregorian lunar calendar uses an epact table that works for 100 to 300 years. The table above is good from 1900 to 2199.

The dates of Easter repeat after 5,700,000 years! Over this huge period, the average length of a church month is very close to the real mean lunar cycle. This means the system is very accurate over long periods.

Dates of Easter from 1900 to 2199.

The frequency of Easter dates changes over time. The current system (1900-2199) shows that March 22 can never happen, but March 31 happens 13 times in this 300-year span.

This graph shows how often Easter falls on each date over the complete 5.7 million year cycle.

If we look at the very long term (over the full 5.7 million year cycle), the distribution of Easter dates is different. April 19 is the most common date for Easter in the Gregorian calendar, happening in about 3.87% of years. March 22 is the least common, happening in only 0.48% of years.

The way the calendar is set up, the lunar and solar calendar dates are linked without needing to worry about leap days. The Gregorian calendar still uses a leap day every four years. The 19-year Metonic cycle has either 6,940 or 6,939 days. The lunar cycle only counts 6,935 days. By not counting the leap day with an epact number, the current lunar cycle gets an extra day. This means the 235 lunar cycles cover as many days as the 19 years. So, the job of keeping the calendar in sync with the Moon is given to the solar calendar.

This means the calculated age of the moon might be off by a day. Also, lunar cycles that include a leap day might be 31 days long, which wouldn't happen with the real Moon. This is the trade-off for having a regular calendar that fits the solar year.

Julian Calendar Calculations

This graph shows the distribution of Easter dates in most Eastern churches (1900–2099) compared to Western Easter dates.

The way Easter was calculated for the Western Church before the Gregorian reform, and still used by most eastern Christians today, uses the 19-year Metonic cycle with the Julian calendar. This system doesn't have the corrections found in the Gregorian calendar. So, the church's full moon drifts away from the actual full moon by more than three days every 1,000 years. It's already a few days later.

Because of this, Eastern churches celebrate Easter one week later than Western churches about half the time. Sometimes, Eastern Easter is even four or five weeks later. This happens because the Julian calendar is 13 days behind the Gregorian calendar between 1900 and 2099. So, the Gregorian Paschal full moon sometimes happens before the Julian March 21.

The number of a year in the 19-year cycle is called its golden number. This name was first used in a poem by Alexander de Villa Dei in 1200.

The Catholic Church claimed in 1582 that the Gregorian calendar brought back "the celebration of Easter according to the rules fixed by... the great ecumenical council of Nicaea." But the First Council of Nicaea (325 AD) didn't actually give specific rules for the date. It only said that Christians in the East should celebrate Easter at the same time as the Romans and the Church of Alexandria.

The medieval computus was based on the Alexandrian computus. This was developed by the Church of Alexandria in the early 300s. The eastern Roman Empire accepted it after 380. Rome accepted it between the 500s and 800s. The British Isles accepted it in the 700s. Before these dates, other methods led to Easter Sunday dates that could be different by up to five weeks.

Here is the table of Paschal full moon dates for all Julian years since 931:

As mentioned, these Paschal full moons are 4, 5, or 34 days later than in the Western system. They are also about three days later than the actual astronomical full moon. For example, the April 2015 lunar eclipse was on April 4 in the Gregorian calendar (or March 22 in the Julian calendar). But the Paschal full moon for that year (golden number 2) was March 25 in the Julian calendar.

Let's do an example calculation using this table: For the year 1573, the golden number is 16. (You get this by adding 1 to 1573, then dividing by 19, and the remainder is 16). From the table, the Paschal full moon for golden number 16 is March 21. If March 21 was a Saturday, then Easter Sunday would be the next day, March 22.

For any given date of the church full moon, there are seven possible Easter dates. The cycle of Sunday letters (which tells you what day of the week each date is) doesn't repeat in seven years. Because of leap days every four years, the full cycle where weekdays repeat in the same way is 28 years. This is called the solar cycle. So, the Easter dates repeated in the same order after 532 years (4 × 7 × 19). This paschal cycle is also called the Victorian cycle.

When Easter Dates Seem "Off"

Sometimes, the calculated Easter date doesn't match what you'd expect if you used exact astronomy. These differences are called "paradoxical" Easter dates. They happen because the church's calculations are approximations, not exact astronomical measurements.

For example, in 1474, a scholar named Regiomontanus found 30 times when the Julian Easter calculation didn't match Easter calculated using the actual new moon. In 18 cases, the date was off by a week. In seven cases, it was off by 35 days, and in five cases, by 28 days.

A physicist named Ludwig Lange studied these "paradoxical" Easter dates for the Gregorian system.

• If the actual full moon falls on a Sunday, but the calculation says Easter is that same Sunday, then Easter is celebrated one week earlier than the "astronomically" correct date. Lange called this a "negative weekly paradox."
• If the actual full moon falls on a Saturday, and Easter is celebrated one week later than the next Sunday, then Easter is celebrated one week too late. He called this a "positive weekly paradox."

The differences can be even bigger if the calculated spring equinox is different from the actual one.

• If the actual equinoctial full moon happens before the calculated one, Easter will be celebrated four or even five weeks too late. This is a "positive equinoctial paradox."
• If the calculated equinoctial full moon happens a month before the actual one, Easter is celebrated four or five weeks too early. This is a "negative equinoctial paradox."

Equinoctial paradoxes are true everywhere on Earth. This is because the order of the equinox and full moon doesn't change with location. But weekly paradoxes are usually local. They only apply to certain parts of the Earth because the change from Saturday to Sunday depends on your longitude (where you are east or west).

In the 2000s and 2100s, negative weekly paradoxical Easter dates happen in years like 2049, 2076, and 2119. Positive weekly paradoxical dates happen in 2045, 2069, and 2089. Positive equinoctial paradoxical dates happen in 2019, 2038, and 2057. In 2076 and 2133, both a positive equinoctial and a negative weekly paradox happen at the same time. Negative equinoctial paradoxes are very rare. They only happen twice until the year 4000: in 2353 (five weeks too early) and 2372 (four weeks too early).

How Computers Calculate Easter

When writing computer programs to find Easter dates, it's common to use simple math operations like adding, subtracting, multiplying, dividing, and finding remainders. This works well with basic calculators or computers. It's easy to convert a "day of March" number (like 22 to 56) into a specific date like March 22 or April 25.

Using these kinds of rules also makes the main part of the Gregorian calculation simpler.

Gauss's Easter Algorithm

In 1800, a famous mathematician named Carl Friedrich Gauss shared a way to calculate the Julian or Gregorian Easter. He later fixed a part of his formula in 1816.

Gauss's algorithm works in two main parts. The first part figures out d, which is the number of days from March 22 to the day after the full moon. The formula for d uses a (the year's position in the 19-year lunar cycle) and M (a constant for each century). The 19-year cycle assumes the Moon's movement repeats every 19 calendar years. This is very close to reality, as 235 lunar months are about 6939.68 days, and 19 years are about 6939.61 days.

The term 19a helps correct for the fact that a calendar year (365 days) doesn't perfectly match a whole number of lunar months (12 months = 354 days). There's an 11-day difference. So, the next year's full moon needs to be moved back 11 days. In math where numbers "wrap around" at 30 (called modulo 30), subtracting 11 is the same as adding 19. That's why 19a is added for each year.

The M in the formula helps set the correct starting point for each century. It accounts for leap years that are skipped every 100 years (unless it's a 400-year leap year). The p variable corrects for small differences in the lunar orbit that can't be described with whole numbers.

The range of days for the full moon to determine Easter is March 21 to April 18 (29 days). Once d is found, it tells you how many days to add to March 22 (the day after the earliest possible full moon) to get the date of the day after the full moon.

The second part of the algorithm finds e. This is the extra number of days needed to get to a Sunday. Since a week has 7 days, e will be between 0 and 6. The formula for e (2b + 4c + 6d + N mod 7) might look strange, but it makes sense with modulo 7 math. It adjusts for how weekdays shift each year. A normal year has 365 days, which is 52 full weeks plus one day. So, each year, the weekday "slides one day forward." The formula makes sure to compensate for this.

In total, e tells you how many days to add from the day after the full moon to reach the next Sunday. The constant N sets the starting point for calculations in each century.

The combined d + e can give dates from March 22 to April 26. For historical reasons, some dates (like April 26) are never Easter Sunday. If the calculation gives April 26, it's moved back to April 19. This means April 19 is a more common Easter date. These final adjustments are just for historical consistency, not for math reasons.

Using Gauss's Easter algorithm for years before 1583 doesn't make historical sense, as the Gregorian calendar wasn't used then. Using it far into the future is also uncertain, as churches might change how they define Easter. Easter calculations are based on agreements and traditions, not just on how the Moon and Sun move.

Meeus's Julian Algorithm

Jean Meeus, in his book Astronomical Algorithms (1991), provides a way to calculate the Julian Easter on the Julian Calendar. This is not the Gregorian Calendar used by most of the world today. To get the date of Eastern Orthodox Easter on the Gregorian calendar, you need to add 13 days (for years between 1900 and 2099) to the Julian dates.

Images for kids

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  A table from Sweden to find the date of Easter 1140–1671 according to the Julian calendar. Notice the runes used as symbols.

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  A chart showing the date of Easter for 600 years, from the Gregorian calendar reform to the year 2200, created by Camille Flammarion in 1907.