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Why Do We Have Leap Years?

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I am a former maths teacher and owner of DoingMaths. I love writing about maths, its applications, and fun mathematical facts.

This article will break down why we have leap years.

This article will break down why we have leap years.

What Is a Leap Year?

As every school child learns, the year usually has 365 days and the month of February has 28 days. Once every four years this changes, however, and we add an extra day to the end of February, creating a 29-day month and a 366-day year. We call this extra day a leap day, and its year is known as a leap year. The last one happened in 2020, and it will happen again in 2024, 2028, 2032, etc.

But why is this the case? What is it that makes this extra day so important? Continue reading to find out.

Using the Heavens to Create a Calendar

For many millennia, humans have organised their days and years around the movements of the Earth and stars. One day is the time taken for the Earth to rotate once on its axis, one year is the time taken for the Earth to complete one orbit of the Sun, one lunar month is the time taken for the Moon to complete one orbit of the Earth, etc.

Unfortunately, these celestial movements are not related to each other and so don't quite fit together into one neat calendar. For example, it takes 365.2422 days for the Earth to orbit the sun; not helpful if you want to base a calendar around these two measurements. History is full of civilisations trying to make these measurements fit together as effectively as possible.

The lunar month is based upon the time taken for the Moon to orbit the Earth exactly once.

The lunar month is based upon the time taken for the Moon to orbit the Earth exactly once.

A Brief History of Calendars

Early civilisations used the moon to set their calendars, but as one lunar month equals approximately 29.5 days, a 12-month calendar gave a year of only 354 days. This calendar soon fell out of sync with the sun, causing the seasons to happen at the wrong calendar time and other related problems.

Some ancient calendars used 12 equal months of 30 days to create a 360-day calendar instead. To get over the problem caused by the missing five days, the ancient Egyptians added five days to the end of the year, known as epagomenal days. These days were particularly ominous for the ancient Egyptians. Workers were often given the time off and charms were often worn by the superstitious citizens to ward off bad luck.

Although these extra days made the calendar more accurate than before, using a 365-day calendar as opposed to the actual length of 365.2422 still created a difference which soon added up over time and the calendar continued to diverge from the seasons.

The Julian Calendar

The Romans also used a lunar calendar of 365 days and so had the same problem. It was Julius Caesar who, according to the writings of Pliny the Elder, consulted with the Greek astronomer Sosigenes of Alexandria to create a new calendar which we call the Julian calendar.

This calendar added a leap day every four years, in effect creating a year of length 365.25 days, much closer to the actual value of 365.2422 days.

To reset the calendar back in line with the seasons, the year 46 BC was decreed to be the 'Year of Confusion' and was 445 days long. The Julian calendar then began on January 1st 45 BC and became the dominant calendar throughout much of Europe for the next 1600 years.

Julius Caesar, for whom the Julian calendar is named.

Julius Caesar, for whom the Julian calendar is named.

The Gregorian Calendar

The Julian calendar with its more accurate approximation of the solar year was better than most things that had come before, but it still wasn't perfect. By the 16th century, the difference between its 365.25 days approximation and the actual value of 365.2422 days had begun to add up and the calendar and seasons were once again beginning to split.

The Julian calendar had overcorrected the approximation for the solar year and was 0.0078 days too long. There are 1440 minutes in a day and so this equates to:

0.0078 × 1440 = 11.232 minutes too much every year.

This doesn't seem like much, but over time this equates to roughly an entire day every 128 years. By the 16th century, this meant the calendar was 10 days out.

This error put Christian celebrations like Easter out of time and so Pope Gregory XIII commissioned the Gregorian calendar in 1582 which skipped a leap year on every leap year divisible by 100, but not by 400. For example, 1600 and 2000 were leap years, but the years 1700, 1800 and 1900 were not.

The omission of these few leap years effectively gives us a calendar year of 365.2425 days which is roughly half a minute longer than the actual solar year.

To reset the calendar, 10 days were skipped. People went to sleep on the evening of the 4th October 1582 and woke up on the morning of the 15th October 1582.

Pope Gregory XIII commissioned the Gregorian Calendar in 1582.

Pope Gregory XIII commissioned the Gregorian Calendar in 1582.

Protestant England

As the calendar change had been implemented by the Catholic pope, Protestant England initially didn't change with the rest of Catholic Europe, leading to an offset in their calendars.

By the mid-18th century however, it became apparent that things needed to change. By this point, the Julian calendar was a further day out and so 11 days were shaved from September 1752 in order to reset the calendar and start afresh with the Gregorian calendar.

This caused some outrage among the general public, some of whom thought they were losing 11 days of their life.

How Accurate Is the Gregorian Calendar?

As mentioned above, the Gregorian calendar uses an approximation of 365.2425 days as opposed to the real value of 365.2422. This is an error of approximately 0.0003 days or 27 seconds every year. At this rate, it will be one day off roughly every 3200 years.


This content is accurate and true to the best of the author’s knowledge and is not meant to substitute for formal and individualized advice from a qualified professional.

© 2021 David