Leap Year — Definition, Formula & Examples
A leap year is a year that has 366 days instead of the usual 365, with the extra day added as February 29. Leap years happen roughly every 4 years to keep our calendar lined up with Earth's orbit around the Sun.
A leap year is a calendar year in the Gregorian system that contains an intercalary day (February 29), occurring in years that are divisible by 4, except for years divisible by 100, which must also be divisible by 400 to qualify as leap years.
How It Works
Earth takes about 365.2422 days to orbit the Sun, but a regular calendar year has only 365 days. That leftover quarter-day adds up, so every 4 years we add an extra day to February to correct the drift. To check whether a year is a leap year, first see if it is divisible by 4. If it is, it's usually a leap year — unless it is also divisible by 100. Years divisible by 100 are not leap years, except when they are also divisible by 400. For example, 1900 is divisible by 100 but not by 400, so it was not a leap year, while 2000 is divisible by 400, so it was a leap year.
Worked Example
Problem: Is the year 2028 a leap year?
Step 1: Check if 2028 is divisible by 4.
Step 2: Yes, it divides evenly. Next, check if 2028 is divisible by 100.
Step 3: It is not divisible by 100, so the century rule does not apply. Since 2028 is divisible by 4 and not by 100, it is a leap year with 366 days.
Answer: 2028 is a leap year. February will have 29 days that year.
Another Example
Problem: Is the year 1900 a leap year?
Step 1: Check if 1900 is divisible by 4.
Step 2: Yes, it is divisible by 4. Now check if 1900 is divisible by 100.
Step 3: It is divisible by 100, so check whether it is also divisible by 400.
Step 4: 1900 is not divisible by 400, so the century exception applies. 1900 is not a leap year.
Answer: 1900 was not a leap year. February had only 28 days that year.
Visualization
Why It Matters
Understanding leap years helps in elementary math when you count days between dates or figure out what day of the week a date falls on. Programmers and software engineers must handle leap years correctly so that calendars, scheduling apps, and banking systems don't produce errors. The leap year rules also show how real-world measurement — Earth's orbit — connects directly to divisibility, a core arithmetic skill.
Common Mistakes
Mistake: Thinking every year divisible by 4 is automatically a leap year.
Correction: Years divisible by 100 are not leap years unless they are also divisible by 400. So 1900 was not a leap year, but 2000 was.
Mistake: Believing a leap year adds an extra day to the end of the year (December 31).
Correction: The extra day is added to February, making it 29 days long instead of 28.