Leap Year Calculator

The Leap Year Calculator is a tool designed to determine whether a given year is a leap year or not. This calculator is useful for understanding the concept of leap years and their importance in our calendar system.

What is a Leap Year?

A leap year is a year that contains an additional day, February 29th, making it 366 days long instead of the usual 365 days. This extra day is added to keep our calendar year synchronized with the astronomical year.

Formula and Its Components

The determination of a leap year follows these rules:

1. If the year is divisible by 4, proceed to step 2. Otherwise, it's not a leap year.
2. If the year is divisible by 100, proceed to step 3. Otherwise, it's a leap year.
3. If the year is divisible by 400, it's a leap year. Otherwise, it's not a leap year.

Mathematically, we can express this as:

\[ \text{Leap Year} = \begin{cases} \text{True,} & \text{if year mod 4 = 0 and (year mod 100 ≠ 0 or year mod 400 = 0)} \\ \text{False,} & \text{otherwise} \end{cases} \]

Where:

• \(\text{year}\) is the year being evaluated
• \(\text{mod}\) represents the modulo operation (remainder after division)

Calculation Steps

1. Check if the year is divisible by 4:
   \[\text{year} \mod 4 = 0\]
2. If step 1 is true, check if the year is divisible by 100:
   \[\text{year} \mod 100 \neq 0\]
3. If step 2 is false, check if the year is divisible by 400:
   \[\text{year} \mod 400 = 0\]

Example

Let's determine if the year 2024 is a leap year:

1. \(2024 \mod 4 = 0\) (True, proceed to step 2)
2. \(2024 \mod 100 \neq 0\) (True, it's a leap year)

Therefore, 2024 is a leap year.

Visual Representation

This decision tree illustrates the step-by-step process for determining whether a year is a leap year. Follow the path based on the divisibility rules to reach the conclusion.