The science behind leap years and how they work

February 23, 2016 by Daniel Brown, Nottingham Trent University, The Conversation
A strange day. Credit: Shutterstock

Most of the time, a year is made up of 365 days. But this year, just like 2012, and the year four years before that, has 366. And that vital extra day, a leap day, is (partly) what keeps our calendars in working order.

As users of a solar calendar, we rely on the sun to tell us how long a year is and when each of the four seasons begins. It was devised to match our farming habits and as a reliable – and visible – guide to the passing of time. The sun's position on the horizon as it rises and sets moves over the course of a year, further south in the winter, and further north in the summer. This significant change is used to mark midwinter or midsummer at famous locations such as Stonehenge and New Grange.

But as a very specific measure, one year, better described as a tropical year, is defined as the time between one spring equinox and the next being 365 days, five hours, 48 minutes and 45 seconds. This period is often rounded up to 365 and a quarter days – although even the Greek astronomer Hipparchus realised over 2,000 years ago that this was a generous approximation – and so to keep our years aligned and reassuringly predictable, a leap day is added to the calendar every four years to allow for the accumulation of those otherwise overlooked four extra quarters.

Summer at Stonehenge. Credit: Andrew Dunn, CC BY-SA

Moving seasons

If we kept every year at a fixed 365 days, the months would gradually shift with the sun until in 750 years' time, June, in the northern hemisphere, would fall in the middle of winter. Planning for the future would gradually become more and more complicated, and religious traditions with a seasonal element, such as Christmas and Easter, would become hopelessly out of kilter. So there has been a considerable motivation for cultures to keep their calendars precise and predictable – and establishing a workable system was a considerable demonstration of power by the rulers of historic empires.

The current length of each month and therefore the length of a year dates back to the Roman dictator Julius Caesar. This "Julian" calendar included leap days but they instead occured every three years. When Augustus – Julius Caesar's heir –became emperor he corrected this mistake and celebrated his power and understanding of celestial movements through monuments such as the giant sundial of Augustus. This huge meridian sundial once stood on the Campus Martius in Rome, its calendrical functionality a constant reminder of Augustus' greatness.

But the Julian calendar was not perfect either, since the year was in fact just a little bit shorter than 365.25 days. Pope Gregory corrected this mistake in his Gregorian calendar of 1582. As well as adding a leap day every four years, he also opted to lose three days every 400 years. This was a Catholic decision, which Protestant and Orthodox calendars resisted for some time. Greece was the last country to accept the Gregorian reform in 1923.

More time needed

The modern result of all this squabbling is our current system of adding an extra day every four years. To adjust for the uneven precision of the fraction, every 100 years we also skip this rule and drop the extra day. Then, every 400 years we skip the skipping rule and have an extra day again. Yes, it's complicated.

The year 2000, for example, was a leap year, since it was divisible by four. But since it was also divisible by 400, the dropping of the extra day every 100 years was not carried out. This long-term solution creates an average year length of 365.2425 days, still slightly off the required target of 365.2421897 days, making even this complicated modern arrangement incorrect by one day over a period of just under 4,000 years.

This error is part of the reason why we sometimes include leap seconds at the end of June or December. However, this is not done in a regular fashion and is determined by the deviation of the calendar by the International Earth Rotation and Reference Systems Service. Since this adjustment is so small it is influenced by the general slowing down of the Earth's rotation and the complex system of all the solar system bodies upon Earth.

So not only are leap the result of millennia of mathematical work, they are also the consequence of rulers imposing their will on people's day to day lives, and the gradual understanding of our place in the universe. Controlling calendars means controlling the rhythms of a culture – which is something for all of us to think about on February 29.

Explore further: Leap years prevent 'calendar climate change'

Related Stories

Leap years prevent 'calendar climate change'

March 1, 2012

Without leap years, Earth would experience "calendar climate change" and the seasons would completely swap every 750 years, a Queensland University of Technology scientist says.

'Leaping' into the realm of science

March 1, 2012

Yesterday was Feb. 29, the extra day we add to the calendar in leap years. But why do we need this extra day, and what is the science behind it? And what about the lesser-known leap second – which delegates from more ...

How long is a day on Earth?

November 6, 2015

I'm going to ask you how long a day is on Earth, and you're going to get the haunting suspicion that this is a trap. Your instincts are right, it's a trap! The answer may surprise you.

Why we need to keep adding leap seconds

July 1, 2015

Today at precisely 10am Australian Eastern Standard time, something chronologically peculiar will take place: there'll be an extra second between 09:59:59 and 10:00:00.

Recommended for you

Solar-powered rover approaching 5,000th Martian dawn

February 16, 2018

The sun will rise on NASA's solar-powered Mars rover Opportunity for the 5,000th time on Saturday, sending rays of energy to a golf-cart-size robotic field geologist that continues to provide revelations about the Red Planet.

Hubble sees Neptune's mysterious shrinking storm

February 15, 2018

Three billion miles away on the farthest known major planet in our solar system, an ominous, dark storm - once big enough to stretch across the Atlantic Ocean from Boston to Portugal - is shrinking out of existence as seen ...

Kepler scientists discover almost 100 new exoplanets

February 15, 2018

Based on data from NASA's K2 mission, an international team of scientists has confirmed nearly 100 new exoplanets. This brings the total number of new exoplanets found with the K2 mission up to almost 300.


Please sign in to add a comment. Registration is free, and takes less than a minute. Read more

Click here to reset your password.
Sign in to get notified via email when new comments are made.