Data Source and Methodology

Calculations are based on the rules of the Gregorian calendar, which is the international standard for civil use. This system was introduced in 1582 to correct the drift of the Julian calendar.

All calculations are based rigorously on the formulas and data provided by this source.

The Formula Explained

A year is a leap year if it meets one of two conditions. The logic, which we can express as an algorithm, is as follows: A year $Y$ is a leap year if:

( $Y \pmod{4} = 0$ AND $Y \pmod{100} \neq 0$ )
OR
( $Y \pmod{400} = 0$ )

In plain English, this means:

  1. A year is a leap year if it is divisible by 4.
  2. However, if that year is also divisible by 100, it is not a leap year...
  3. Unless that year is *also* divisible by 400, in which case it is a leap year.

Glossary of Variables

  • Year (Input): The year to be checked. This calculator accepts any year from 1582 onwards, which is the year the Gregorian calendar was instituted.
  • Is Leap Year (Output): A simple 'Yes' or 'No' answer to the query.
  • Reasoning (Output): A brief, clear explanation of *why* the given year is or is not a leap year, based on the formula's rules.

How It Works: A Step-by-Step Example

Let's test the year 1900:

  1. Is $1900 \pmod{4} = 0$? Yes. The first check passes.
  2. Is $1900 \pmod{100} = 0$? Yes. This triggers the exception. We must now check the third rule.
  3. Is $1900 \pmod{400} = 0$? No. It fails the final exception.
  4. Result: Because it is divisible by 100 but not by 400, **1900 was not a leap year.**

Now let's test 2000:

  1. Is $2000 \pmod{4} = 0$? Yes. The first check passes.
  2. Is $2000 \pmod{100} = 0$? Yes. This triggers the exception.
  3. Is $2000 \pmod{400} = 0$? Yes. It passes the final exception.
  4. Result: Because it is divisible by 400, **2000 was a leap year.**

Frequently Asked Questions (FAQ)

Why do we have leap years?

We have leap years to keep our modern Gregorian calendar aligned with the Earth's revolutions around the sun. An astronomical year (the time it takes for the Earth to orbit the sun) is approximately 365.2425 days, not exactly 365. Adding an extra day (February 29) nearly every four years compensates for this difference and prevents the seasons from "drifting" over time.

Who invented the leap year?

The concept of a leap year was first introduced by Julius Caesar in the Roman Empire (the Julian calendar) around 45 B.C. However, his rule (a leap year every 4 years) was slightly inaccurate. The modern Gregorian calendar, introduced by Pope Gregory XIII in 1582, refined the rule (adding the exceptions for years divisible by 100 but not 400) to be much more accurate.

What is the difference between a leap year and a leap second?

A leap year adds a full day (February 29) to the calendar to synchronize it with the Earth's orbit around the sun (the astronomical year). A leap second is a one-second adjustment added to Coordinated Universal Time (UTC) to account for the slowing of the Earth's rotation. They are unrelated concepts that solve different timekeeping problems.

Was 1700 a leap year?

No, 1700 was not a leap year. Like 1900, it was divisible by 4 and 100, but not by 400. Therefore, it fell under the exception rule and was a common year.

When is the next leap day?

After 2024, the next leap day will be February 29, 2028. Following that, the leap years will be 2032, 2036, and so on, continuing the four-year cycle until the next century exception in 2100 (which will not be a leap year).

Tool developed by Ugo Candido. Contents verified by the CalcDomain Editorial Board.
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