Leap Year Math

What Is a Leap Year?

A leap year (or intercalary year) is a year containing one or more extra days (or, in case of lunisolar calendars, an extra month) in order to keep the calendar year synchronized with the astronomical or seasonal year. For example, February would have 29 days in a leap year instead of the usual 28. Seasons and astronomical events do not repeat at an exact number of full days, so a calendar which had the same number of days in each year would over time drift with respect to the event it was supposed to track. By occasionally inserting (or intercalating) an additional day or month into the year, the drift can be corrected. A year which is not a leap year is called a common year. Source: Wikipedia

Thirty days hath September,
April, June, and November;
All the rest have thirty-one,
Excepting February alone,
And that has twenty-eight days clear,
And twenty-nine in each leap year.
—Mother Goose

What Years Are Leap Years? How to Calculate Leap Years

It takes the earth approximately 365.2422 days to go around the sun. The normal calendar year is only 365 days.

The extra fraction of a day adds up over the time.

After four years we would have 1460.9688 days. Four calendar years adds up to 1460 days (365 x 4).

The .9688 is very close to a full day, so we round up.

Every 4 years we add an extra day in February. Consequently leap years are always divisible by 4.

However, since we have been rounding up, we end up adding back too many days. So in 1582 Pope Gregory made up a new set of rules. The previous Julien calendar was replaced by the Gregorian Calendar which has the following rules:

Every fourth year is a leap year.
e.g., 2008, 2012, 2016 are leap years
Every hundredth year is not a leap year.
e.g., 1900, 2100, 2200, 2300 are not leap years
Every four hundred years has a leap year.
e.g., 2000, 2400, 2800 are leap years

Skip Count by Fours

Since every fourth year is a leap year (with a few exceptions) you have to sing along with Cat Man Math and practice skip counting by fours today! Lyrics

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Leap Year Birthdays

How many people do you know with a leap year day birthday? What’s the probability of being born on February 29th? If you were born on February 29th 1996, how old are you now? How many leap years are there between 1940 and 2040? How many leap years have you lived through? How many more leap years has your grandfather lived through?

Leap Year Resources

Origami Frog

A Joke!

What do you get when you multiply a kangaroo with a calendar?
A leap year!

Susan Jarema is the founder of Googol Learning, the Crazy 4 Math Contest, TVvgFREE.com, New Earth Marketing and Kidzinfo. The Googol Learning Website has many free resources to inspire mathematics and family learning in your home through music, games, stories and layered learning.

This article may be reprinted with the above author credit and website link.