Write a program to check if the year entered by the user is a leap year or not.

Programming Exercises · Q4

Q. Write a program to check if the year entered by the user is a leap year or not.

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Concept understanding — Leap Year Determination

Leap Year Determination

You already know a year is 365 days. But the Earth actually takes about 365.2422 days to orbit the Sun — a little more than 365 days. That extra 0.2422 day (roughly 6 hours) adds up. After 4 years, it becomes almost a full day. So we add an extra day every 4 years to keep the calendar aligned with the seasons. That extra day is February 29, and that year is a leap year.

But if we added a leap day every 4 years without exception, we'd overshoot. Because 0.2422 × 4 = 0.9688 day, not exactly 1 day. So every 4 years we add a bit too much — about 0.0312 day too much. Over centuries, that error accumulates. To fix it, we skip some leap years.

The precise rule

A year is a leap year if:

It is divisible by 4, and
If it is divisible by 100, it must also be divisible by 400.

In other words:

\text{Leap year} \iff ( \text{year} \bmod 4 = 0 ) \land ( \text{year} \bmod 100 \neq 0 \lor \text{year} \bmod 400 = 0 )

Let's break that down.

Step 1: Every year divisible by 4 is a leap year — unless it's a century year.

Step 2: Century years (like 1900, 2000, 2100) are leap years only if they are divisible by 400.

So 2000 was a leap year (divisible by 400). 1900 was not (divisible by 100 but not by 400). 2100 will not be a leap year.

Watch out

A common mistake is to think every year divisible by 4 is a leap year. That's almost true, but the century-year exception is crucial. 1900 was divisible by 4, yet it was not a leap year.

Why this works

The Gregorian calendar (the one we use) was designed to keep the average year length very close to 365.2422 days. The rule gives an average year length of:

$\frac{1}{4} - \frac{1}{100} + \frac{1}{400} = 0.2425 \text{ extra days per year}$ …

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A year is a leap year if it is divisible by 4 but not by 100 — unless it is also divisible by 400:

year = int(input("Enter a year: "))
if (year % 4 == 0 and year % 100 != 0) or (year % 400 == 0):
    print(year, "is a leap year")
else:
    print(year, "is not a leap year")

Enter a year: 2024
2024 is a leap year
``` …

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Apply the calendar rule with one boolean expression — (year % 4 == 0 and year % 100 != 0) or (year % 400 == 0) — and print the verdict via if–else.

The idea: the Gregorian leap-year rule. A year is a leap year when it is divisible by 4, except century years (divisible by 100), which are leap only when divisible by 400. This three-part rule collapses into a single boolean condition using the modulo operator % (remainder), and the two-way outcome maps to if–else:

year % 4 == 0 and year % 100 != 0 → ordinary leap year (2024, 2016)
year % 400 == 0 → century leap year (2000, 1600)
Everything else → not a leap year (1900, 2023)

Program

year = int(input("Enter a year: "))

if (year % 4 == 0 and year % 100 != 0) or (year % 400 == 0):
    print(year, "is a leap year")
else:
    print(year, "is not a leap year")

Sample runs

Enter a year: 2024
2024 is a leap year

Enter a year: 1900
1900 is not a leap year

Verifying the tricky cases

| Year | % 4 == 0 | % 100 != 0 | % 400 == 0 | Verdict |

| --- | --- | --- | --- | --- | …

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Q.Write a program to check if the year entered by the user is a leap year or not.

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