About

Time is not a constant variable in software engineering; it is a complex construct full of edge cases. This utility provides a definitive, ISO 8601-compliant verification of the Gregorian leap year algorithm. It is designed for QA engineers, backend developers, and data scientists who require absolute precision in date-time handling.

The Gregorian calendar's mean year length is 365.2425 days. To maintain synchronization with the solar year, we adhere to a specific inclusion/exclusion logic: years divisible by 4 are leap years, unless they are divisible by 100, but exception is granted if they are divisible by 400. Failure to implement this exact logic results in the "Century Bug," a common error in legacy banking systems and long-term interest accrual models.

Formulas

The status of a year y is determined by the boolean function f(y):

f(y) ≡ (y mod 4 = 0) ∧ [

(y mod 100 ≠ 0)∨(y mod 400 = 0)

This ensures the calendar year stays within 26 seconds of the solar year. Without this correction, the calendar would drift by approximately 3 days every 400 years.

Reference Data

Language / Context	Implementation Logic	Complexity	Return Type
Standard Math	y % 4 == 0 ∧ (y % 100 != 0 ∨ y % 400 == 0)	O(1)	Boolean
Excel / Sheets	OR(MOD(A1,400)=0, AND(MOD(A1,4)=0, MOD(A1,100)<>0))	O(1)	Boolean
SQL (PostgreSQL)	SELECT (date_trunc('year', now()) + interval '1 year') - date_trunc('year', now()) = 366	System	Boolean
JavaScript (Date)	new Date(year, 1, 29).getMonth() === 1	API	Boolean
Julian Calendar	y % 4 == 0 (Obsolete 1582)	O(1)	Boolean
Solar Year	~365.24219 days	N/A	Float

Frequently Asked Questions

A simple "every 4 years" rule adds 0.25 days per year, making the calendar year 365.25 days long. However, the actual solar year is approximately 365.2422 days. This small difference (0.0078 days) accumulates to 3 days every 400 years. To compensate, we skip the leap year at the turn of most centuries (1700, 1800, 1900) but add it back every 400th year (1600, 2000) to maintain precision.

This tool uses the Proleptic Gregorian Calendar, extending current rules backward indefinitely. In historical reality, the Gregorian calendar started in 1582. For BCE years, year 0 does not exist in standard history (it goes 1 BCE to 1 CE), but in ISO 8601/Astronomical year numbering, 1 BCE is year 0, 2 BCE is -1, etc. This tool expects positive integers (CE/AD) for standard checks.

The probability is approximately 1 in 1,461. This is derived from the 4-year cycle (365 + 365 + 365 + 366 = 1461 days). However, due to the 100/400 year exceptions, the true long-term average is slightly rarer: 97 leap days every 400 years, or 97 / 146,097 days (approx 1 in 1,506).

No. Although 2100 is divisible by 4, it is also divisible by 100. Since it is NOT divisible by 400, it falls into the exclusion rule. February 2100 will have only 28 days.

Incorrect leap year logic is a frequent cause of "Downtime on Leap Day." Systems that hardcode 365 days, or assume "current year + 1" equals the same date next year, often crash on Feb 29 or Mar 1. Validating date logic ensures robust behavior in banking, subscription services, and security certificates.