You may know that every four years February gets an extra day and we have what’s called a “leap year”. But how are leap years calculated and who worked it out? The answers lie in astronomy and early agriculture with a little help from Julius Caesar and Pope Gregory XIII, explains Dr James McCormac, an expert in astrophysics from the University of Warwick’s Physics Department.

Before the invention of agriculture people only really needed to know roughly what season it was and what season was coming up next. However, after the invention of agriculture, it became important for farmers to keep track of each day in the year. This would allow them to plant crops and harvest them at the correct times with respect to the different seasons.

An easy way of measuring time back then was by tracking the position of the sun in the sky. A solar day was defined as the time it takes for the sun to return to the highest point in the sky on two consecutive days. The solar (or tropical) year was defined as the time it takes for the sun to return to the same position in the sky after a complete cycle of the four seasons. Early astronomers found that a solar year was not exactly divisible by a whole number of solar days. In fact, the solar year was 365 and one quarter solar days long.

Therefore, if we assume that a year is 365 solar days long, the timing in our calendar and the position of the sun (and therefore the seasons) drift apart by a quarter of a day each year. This is not ideal as agricultural and religious events would not be in sync with the earth’s position around the sun year after year. The Romans knew about this drift and at that time the Pontifex Maximus (the chief high priest) would correct the calendar by occasionally adding an extra day to minimise the drift. However, the Romans believed that the correction during war time was bad luck. As they were always at war, the calendar and the solar year quickly got out of sync.

An overcorrection

In the year 46 BC, Julius Cesar proposed the new Julian Calendar which would add an additional day to the shortest month of the year (February) every four years in an attempt to allow for a predictable correction to the issue of the quarter day drift.

However, this was actually a slight overcorrection to the problem. As the solar year was not exactly 365.25 days but was in fact slightly less at 365.2422 solar days, the Julian Calendar and the solar year were now drifting apart again, albeit much more slowly, at a rate of 11.2 minutes per year.

By the late 1500’s this small overcorrection in the Julian calendar had accumulated to a drift of 13 days with respect to the solar year. Cue Pope Gregory XIII, the Pontifex Maximus of the Catholic church at the time. In 1582 he gave us the Gregorian calendar, which modified the Julian Calendar to account for the 11.2-minute drift. Many countries including the UK still use the Gregorian calendar today.

How are leap years calculated?

To improve upon the over correction made by the Julian calendar, the Gregorian calendar skips three leap days every 400 years. This gives an average year of 365.2425 solar days which is much closer to the solar year of 365.2422 solar days.

The following process is used to determine if a given year is a leap year in the Gregorian calendar.

 

1. If a year is equally divisible by four it is a leap year
2. Years that are equally divisible by 100 are not leap years.
3. Except for years that are equally divisible by 400, which remain as leap years.

 

So, for example, the years 1700, 1800 and 1900 were not leap years, but the years 1600, 1996 and 2000 were. Interestingly, even the Gregorian calendar is still not perfect and produces an error of one day every 3030 years. However, this is clearly a vast improvement over the one-day error every 128 years from the Julian calendar.

Why is it called a leap year?

The term leap year comes from the fact that in the Gregorian calendar a given date, for example your birthday, advances by one day of the week from one year to the next except for the year following the 29 February where it advances by 2 days. For example, if your birthday was March 3 it would have fallen on a Saturday in 2012, a Sunday in 2013, a Monday in 2014, a Tuesday in 2015 and then leapt over Wednesday landing on Thursday in 2016.

 

Published:

26 February 2020

About:

Dr James McCormac is a researcher in Warwick's Astrophysics Group.

He is an expert in the field of Transiting Exoplanets and is a Senior Research Fellow working on the PLAnetary Transits and Oscillations (PLATO) space mission. PLATO is a European Space Agency medium class mission to be launched in 2026 with the goal of discovering and characterising Earth-like planets around Sun-like stars.

He is also a member of the team on the NGTS, GOTO and SuperWASP projects in which Warwick University plays a leading role.

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The text in this article is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).

 

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