How Leap Years Work: Why 2100 is NOT a Leap Year (The 400-Year Exception Rule)
Unpack the fascinating astronomy behind calendar mathematics: how a 365.2422-day solar orbit requires skipping leap years on century marks unless divisible by 400.
Introduction: The Solar Drift Problem
Most people believe leap years occur strictly every four years. However, if you check calendar history, the year 1900 was not a leap year, and the upcoming year 2100 will also NOT be a leap year!
Understanding this century-skipping rule reveals the brilliant mathematics of the Gregorian calendar.
The Gregorian 3-Step Logic Gate
A year in the modern Gregorian calendar is a leap year if and only if it satisfies this logical algorithm:
$$\text{IsLeap} = (\text{Year} \% 4 == 0 \land \text{Year} \% 100 \neq 0) \lor (\text{Year} \% 400 == 0)$$
- Rule 1: The year must be divisible by 4.
- Rule 2 (Exception): If the year is divisible by 100, it is NOT a leap year...
- Rule 3 (Exception to the Exception): ...UNLESS the year is also divisible by 400!
Check any historical or future year with visual mathematical proofs on our **Leap Year Checker**.
Frequently Asked Questions
Published by AnantAstra's engineering and research desk. All calculations, privacy guarantees, and algorithms referenced in this article are open-source and run client-side in the browser.
Recommended Further Reading
Comprehensive FY 2025-26 salary tax analysis: understand the ₹75,000 standard deduction, the ₹7.75 Lakh tax-free threshold under 87A rebate, and the exact deduction breakeven point.
Read GuideUnderstand exact GST mathematical formulas: reverse-calculate original base prices from inclusive totals, add tax to net amounts, and accurately split CGST, SGST, and IGST.
Read GuideDemystify monthly loan repayments: uncover the reducing-balance EMI formula, how banks front-load interest in amortization schedules, and how small prepayments shave years off your tenure.
Read Guide